# Department of Mathematics past events

The Department of Mathematics maintains a regular series of research seminars. Here you will find details of our past seminars from 2012/13 to 2020/21.

## Seminar Series 2022-23

### Autumn 2022

**October 4, 2022**

Speaker: Steve Alpern (Warwick)

Title: Crazy Ants and Shortest Paths with Unreliable Information: The SatNav Problem

Abstract: This paper gives a stochastic take on the familiar shortest path problem in a network. At every branch node of a network Q, a Satnav (GPS) points to the arc leading to the destination, or home node, H - but only with a high known probability p. The pointer is fixed in time, so does not change when a node is revisited. Always trusting the Satnav's suggestion may lead to an infinite cycle. If one wishes to reach H in least expected time, with what probability q=q(Q,p) should one trust the pointer (if not, one chooses randomly among the other arcs)? We call this the Faulty Satnav (GPS) Problem.

We also consider versions where the trust probability q can depend on the degree of the current node and a `treasure hunt' where two searchers try to reach H first. The agent searching for H need not be a car, that is just a familiar example -- it could equally be a UAV receiving unreliable GPS information. This problem has its origin not in driver frustration but in the work of Fonio et al (2017) on ant navigation, where the pointers correspond to pheromone markers pointing to the nest.

**October 11, 2022**

Speaker: Anindita Maiti (Northeastern)

Title: A Study of Neural Network Field Theories

Abstract: The backbones of modern-day Deep Learning, Neural Networks (NN), define field theories on Euclidean background through their architectures, where field interaction strengths depend on the choice of NN architecture width and stochastic parameters. Infinite width limit of NN architectures, combined with independently distributed stochastic parameters, lead to generalized free field theories by the Central Limit Theorem (CLT).

Small and large deviations from the CLT, due to finite architecture width and/or correlated stochastic parameters, respectively give rise to weakly coupled field theories and non-perturbative non-Lagrangian field theories in Neural Networks. I will present a systematic exploration of Neural Network field theories via a dual framework of NN parameters: non-Gaussianity, locality by cluster decomposition, and symmetries are studied without necessitating the knowledge of an action. Such a dual description to statistical or quantum field theories in Neural Networks can have potential implications for physics.

**October 18, 2022**

Speaker: Chay Paterson (Manchester)

Title: Fast simulations of clonal expansion on networks: Cancer, copy number alterations, and age

Abstract: Multi-stage mathematical models have contributed a great deal to our understanding of cancer, from Armitage and Doll's original work in the 1950s, to Knudson's studies of retinoblastoma in the 1970s. My ongoing research extends these models from linear paths to networks, with different pathways representing different mutational mechanisms (SNVs, LOH, etc.). This approach links population incidence, genomic data, and molecular mechanisms.

The mathematical problem that must be solved for these models to be useful is to compute the incidence curve. There is currently no standard way to do this on graphs/networks: there are several approximate methods each with their own advantages and drawbacks. In this talk, I show how some of these approaches can be used to constrain mutation dynamics in colorectal cancer and vestibular schwannoma, and describe my current progress in developing new algorithms.

**October 25, 2022**

Speaker: Noemi Picco (Swansea)

Title: Modelling the Brain: Development, Evolution and Disease

Abstract: Most biological systems span multiple spatial and temporal scales. It is often the case that the experimental data is available at a coarse-grained level, while the process of interest operates at much finer scales. Mathematical modelling can help the understanding of how dynamical interactions at different scales filter through at the level of the observable data. I will talk about the developing brain as a model system, to show how data-driven modelling can describe the processes of interest and make testable predictions. I will focus on neurogenesis in the mammalian cerebral cortex, with a view of mapping normal development to answer questions related to abnormal development and evolution across mammals.

Critically, to fully characterize the processes involved in neurogenesis we are faced with the challenge of understanding the temporal changes in the cell division strategies of neural progenitor cells to produce the required number of cortical neurons. I will introduce a set of mathematical models, designed with experimental colleagues, that aim at bridging between experimental models and capture the many spatial scales involved. I will present some preliminary findings and highlight the current limitations in the interpretation of model predictions, identifying a specific need for experimental quantifications.

**November 1, 2022**

Speaker: Luca Capizzi (SISSA, Trieste)

Title: Spreading of a local excitation in a Quantum Hierarchical Model

Abstract: Long-range-interacting systems, characterized by slow decaying power-law potentials, are known to exhibit a plethora of peculiar behaviors which cannot be understood within the traditional framework of many-body systems. In this talk, I discuss the dynamics of a quantum chain in the presence of long-range interactions.

For instance, I consider the quantum hierarchical Ising model, characterized by a tree-like structure of the interactions, and analyze the spreading of an initially localized excitation. A peculiar localization mechanism is found, and its features, traced back to the symmetry of the interactions, are characterized analytically. The talk is based on joint work with G. Giachetti, A. Santini, and M. Collura.

**November 15, 2022**

Speaker: David X. Horváth (SISSA, Trieste)

Title: Entanglement evolution and steady-state entanglement in the presence of unstable quasiparticles

Abstract: The effect of unstable quasiparticles in the out-of-equilibrium dynamics of certain integrable systems has been the subject of several recent studies. In this talk I focus on the stationary value of the entanglement entropy density, its growth rate, and related functions, after a quantum quench. I consider several quenches, each of which is characterised by a corresponding squeezed coherent state. In the quench action approach, the coherent state amplitudes K(θ) become input data that fully characterise the large-time stationary state, thus also the corresponding Yang-Yang entropy.

It is found that, as function of the mass of the unstable particle, the entropy growth rate has a global minimum signalling the depletion of entropy that accompanies a slowdown of stable quasiparticles at the threshold for the formation of an unstable excitation. One observes also a separation of scales governed by the interplay between the mass of the unstable particle and the quench parameter, separating a non-interacting regime described by free fermions from an interacting regime where the unstable particle is present.

This separation of scales leads to a double-plateau structure of many functions, where the relative height of the plateaux is related to the ratio of central charges of the UV fixed points associated with the two regimes, in full agreement with conformal field theory predictions. The properties of several other functions of the entropy and its growth rate are also studied in detail, both for fixed quench parameter and varying unstable particle mass and vice versa.

**November 22, 2022**

Speaker: Gennady El (Northumbria)

Title: Spectral theory of soliton gases in integrable dispersive hydrodynamics

Abstract: Soliton gases represent infinite random ensembles of interacting solitons displaying nontrivial large-scale behaviours ultimately determined by the properties of the elementary two-soliton collisions. The emergent hydrodynamics of non-equilibrium soliton gases in integrable dispersive systems such as the Korteweg-de Vries and nonlinear Schrödinger equations is described by the universal nonlinear integro-differential kinetic equation for the density of states in the spectral (Lax) phase space.

The same equation describes the large-scale dynamics of non-equilibrium quantum and classical integrable many-body systems---the generalised hydrodynamics (GHD). In my talk, I will outline the main ideas of the spectral theory of soliton gases and its connection with the fundamental concept of "integrable turbulence’’ introduced by Zakharov in 2009.

**November 29, 2022**

Speaker: Yan Fyodorov (King's)

Title: "Escaping the crowds": extreme values and outliers in rank-1 non-normal deformations of GUE/CUE

Abstract: Rank-1 non-normal deformations of standard random matrices (Hermitian like GUE or unitary like CUE) provide the simplest model for describing the scattering matrix poles (aka "resonances") in a quantum chaotic system decaying via a single open channel. The joint probability density of those poles provide examples of a 2D Coloumb gas in the complex plane (in the half-plane for deformed GUE or the unit disk for CUE) subject to certain global constraints.

Of particular interest are imaginary parts for deformed GUE or distance to the unit circle for CUE, identified with the resonance "widths". In the case of deformed GUE we provide a detailed description of an abrupt restructuring of the resonance density in the complex plane as the function of the deformation parameter, identify the critical scaling of typical extreme imaginary parts, and finally describe how an atypically ''broad'' resonance (an outlier) emerges from the crowd.

In the case of deformed CUE we are further able to study the Extreme Value Statistics of the ''widest resonance'' most remote from the unit circle. We find that in the critical regime it is described by a distribution nontrivially interpolating between Gumbel and Frechet. The presentation will be based on the joint works with Boris Khoruzhenko and Mihail Poplavskyi.

**December 6, 2022**

Speaker: Paul Ryan (King's)

Title: Quantum Spectral Curve and string theory on AdS3 x S3 x T4

Abstract: The spectrum of single-trace local operators in N=4 Super Yang Mills, dual to Type IIB string theory on AdS5 x S5, in the planar limit can be encoded by a handful of Riemann-Hilbert relations for a set of so-called Q-functions. This integrability-based framework is known as Quantum Spectral Curve (QSC) and has allowed for extensive precision spectroscopy of N=4 SYM perturbatively, numerically at finite coupling and analytically in some regimes.

QSC equations have recently been proposed for string theory on AdS3 x S3 x T4 with pure RR flux. In this talk I will review this construction and solve the resulting set of equations numerically at finite coupling and perturbatively at weak coupling. New tools are developed to deal with a salient feature of string theory on this background - massless modes. We obtain the first ever predictions for non-protected string excitations on this background and shed light on the mysterious CFT2 dual.

**December 13, 2022**

Speaker: Alison Feder (Washington)

### Winter 2023

**January 31, 2023**

Speaker: Yagmur Erten (Jyväskylä)

Title: Modelling cancer and ageing through the lens of evolution

Abstract: Cancer is a risk all multicellular organisms face: each cell division comes with a probability of mutations that can eventually cause cancer. Yet some species like elephants achieve long lifespans and large body sizes even though they need more cell divisions (Peto’s paradox), possibly thanks to their high cancer suppression.

How do organisms attain their mature sizes without succumbing to cancer? Can cancer risk constrain body size evolution? What happens when large-bodied lineages like dinosaurs shrink in size? In this presentation, I will tackle some of these questions and talk about life history evolution under cancer risk and what modelling approaches can tell us about the evolution of cancer and ageing.

**February 7, 2023**

Speaker: Giuseppe Del Vecchio Del Vecchio (UCL)

Title: Entanglement entropy dynamics from Hydrodynamic fluctuations

Abstract: Non-equilibrium dynamics of quantum many-body systems is notoriously difficult to tackle due to the highly complex correlation structure of the wave function. The entanglement entropy is probably the defining feature of quantum mechanical systems and nowadays, with the surge of promising quantum technologies, it is more than ever important understanding the dynamics of this quantity.

During the last years, great progress has been made in the context of integrable systems where it was understood that a generalized thermalization mechanism keeps the system out-of-equilibrium even at large time and a linear growth of entanglement followed by saturation has been generically observed. In addition to the entanglement, Renyi's entropies represent a relatively good measure of quantum correlations.

With respect to dynamical properties, the quasi-particle picture provides quantitative results and qualitative intuition about the quench protocols for the entanglement but not for the Renyi's. In this talk I will present results from Ballistic Fluctuation Theory with applications to the quench dynamics of Renyi's entropies in various situations showing explicitly that ballistic hydrodynamic modes are responsible for the linear growth and eventual saturation. Moreover, I will stress how the different nature of correlations present in the initial state allow or prevent having a relatively simple formula for entanglement dynamics at large space-time distances.

**March 14, 2023**

Speaker: Eva-Maria Gräfe (Imperial)

Title: Phase-space features of quantum systems with non-Hermitian Hamiltonians

Abstract: While traditional quantum mechanics focusses on systems conserving energy and probability, described by Hermitian Hamiltonians, in recent years there has been ever growing interest in the use of non-Hermitian Hamiltonians. These can effectively describe loss and gain in a quantum system. In particular, systems with a certain balance of loss and gain, so-called PT-symmetric systems, have attracted considerable attention. The realisation of PT-symmetric quantum dynamics in optical systems has opened up a whole new field of investigations.

The properties of non-Hermitian quantum systems are often less intuitive than those of conventional Hermitian systems. Here we make use of the Husimi representation. In phase space to analyse dynamical and spectral features. We consider the flow of the Husimi phase-space distribution in a semiclassical limit, leading to a first order partial differential equation, that helps illuminate the foundations of the full quantum evolution. Further, we demonstrate how ingredients of the dynamics can be used to construct approximate Husimi distributions of characteristic quantum states.

**March 23, 2023 (1 of 2)**

Speaker: Yannick Viossat (Dauphine)

Title: Game dynamics and irrational behavior

Abstract: Economic theory often assumes that agents act in their best interest, and in particular, do not use actions that are dominated, in the sense of being always worse than another fixed action. Intuitively, given enough time, even weakly rational agents should learn which actions should be avoided. But is this really true? A formal test is to examine whether dominated strategies tend to become extinct under evolutionary game dynamics, which model phenomena such as natural selection, or imitation of successful agents, in populations of agents interacting strategically. We will survey results on elimination or survival of dominated strategies by such dynamics, including some of my recent contributions.

**March 23, 2023 (2 of 2)**

Speaker: Andrew Belmonte (Penn State)

Title: Wealth-Driven Patterns in Evolutionary Games

Abstract: Evolutionary games are typically based on the assumption that players evaluate their current strategy, in comparison to the success of other strategies played, on the basis of winning more - the highest instantaneous payoff. However, many biological and social systems indicate that success / survival is determined not only by current winnings, but by an integration over the past, via stored winnings or wealth.

I will present results from a mathematical study of a repeated game on a lattice, in which strategy updates are governed by a Boltzmann distribution, and player dynamics is determined by the imitation of strategies corresponding to higher wealth (current bank balances). For a parameterized Rock-Paper-Scissors game, we find a condition under which stationary local communities form; under other conditions, migrating communities occur.

The imposition of a linear temperature ramp leads to the progressive melting of these patterns. Comparison is made with numerical results for similar patterns in 2D, and for other games. This is joint work with Connor Olson and Christopher Griffin.

**March 28, 2023**

Speaker: Takato Yoshimura (Oxford)

Title: Ballistic macroscopic fluctuation theory

Abstract: Macroscopic fluctuation theory (MFT) is a large deviation theory that describes important dynamical properties of the system such as current fluctuations in a universal way, using hydrodynamic data of the system only. Since its inception it has been applied to a variety of driven diffusive systems, but the underlying idea of MFT suggests its applicability to other transport types.

In this talk, I will explain how one can formulate an MFT-like theory for systems that support ballistic transport, and use the theory, which we dub “ballistic macroscopic fluctuation theory (BMFT)”, to compute objects of interest. The BMFT turns out to predict a novel dynamical phenomenon, which is the existence of universal long-range correlations at the Euler scale.

There are a number of important models that exhibit ballistic transport (e.g. continuum Hamiltonian systems such as anharmonic chains and integrable spin chains), but to illustrate the idea I will focus on the hard-rods system, which is a prototypical integrable many-body system. The talk is based on my recent work with B. Doyon, G. Perfertto, and T. Sasamoto, arXiv:2206.14167.

**April 4, 2023 (1 of 2)**

Speaker: Francesco Buccheri (Heinrich-Heine)

Title: Interface states in topological Weyl semimetals

**April 4, 2023 (2 of 2)**

Speaker: Ali Zahabi (LIMS / IMB)

Title: Some analytic aspects of phase transitions in quiver gauge theories and matrix models

Abstract: In this talk, we elaborate on the phase structure of the toric quivers and matrix models, via the analytic tools in number theory and operator formalism such as Mahler measure, and Fredholm determinant. In the first part, applying the Mahler measure machinery, we study the dynamical features and phase transitions in toric quivers stemming from the dimer model and 3d crystal melting model in the thermodynamic limit.

In the second part, we consider the 2d crystal models equipped with probability measures, known as random partitions and their closed cousins, the matrix models. We study their novel features that are emerging in the asymptotic limit such as the appearance of a typical state known as limit curve and the universal fluctuations around that.

We extract the phase structure of the model using the analytic results from random matrix theory, namely the Tracy-Widom distribution. If time permits, we comment on the possible unifications of the above two approaches in the context of Toeplitz determinants and Szegö limit theorems.

**April 11, 2023**

Speaker: The Anh Han (Teesside)

Title: Cost-efficient interventions for promoting cooperation and AI safety development

Abstract: In this talk, I will discuss evolutionary game theory as a powerful and unified mathematical and simulation tool for studying dynamics and evolution of collective behaviours. I will present some recent findings from our group where evolutionary game theory is adopted, including: i) The analysis of cost-efficient intervention mechanisms such as rewarding of good behaviours and punishment of bad ones, for promoting enhanced cooperation. We obtain analytical results for the optimal cost of intervention in the well-mixed population settings.

We also show how exploiting local information in spatial networks can improve cost-efficiency of interventions; ii) The modelling of cooperation and competition dynamics in an Artificial Intelligence development ecosystem. We examined the evolution of safety development behaviours and what incentive mechanisms can efficiently drive the evolutionary dynamics towards a beneficial outcome for society.

## Seminar Series 2021-22

### Autumn 2021

**October 5, 2021**

Speaker: Ian Leary, (Southampton)

Title: Cat(O) groups need not be biautomatic.

Abstract: Ashot Minayan and I construct groups that that establish the result implicit in the title, resolving a 25-year old question. I will show you our groups and why they answer this and another question asked by Dani Wise. No prior knowledge of CAT(0) groups or of biautomaticity will be assumed!

**October 12, 2021**

Speaker: Nicholas Manton (Cambridge)

Title: Skyrmions: Topology, Symmetry, Physics

**October 19, 2021**

Speaker: Kieran Sharkey (Liverpool)

Title: Localization of eigenvector centrality and an alternative perspective

Abstract: Eigenvector centrality is a common metric for determining the most significant individuals in a network. However, it is increasingly apparent that it has significant flaws which can make it unreliable. I will discuss recent work in the physics literature on the phenomenon of `localization’ of eigenvector centrality.

Localization in this context means that the centrality becomes unreasonably focussed on specific parts of the network which can lead to uninformative results and incorrect conclusions. It is well-known that localization occurs when there are highly connected individuals which take up a large proportion of the centrality.

Building on previous observations, I will also derive localization problems when the network can be easily fragmented. I suggest that these problems are symptomatic of fundamental problems with the justification of this metric. As a resolution, eigenvector centrality is perhaps better-interpreted as an approximation to more robust measures such as Katz centrality, rather than as a centrality itself.

**October 26, 2021**

Speaker: Ozgur Bayindir (City)

Title: Algebraic K-theory of formal differential graded algebras

Abstract: In this work, we compute algebraic K-theory of various formal differential graded algebras. The first part of my talk is going to consist of an introduction to ring spectra, algebraic $K$-theory and the Nikolaus Scholze approach to trace methods.

In the second part, I will introduce our results and the tools we develop to study the topological Hochschild homology of formal differential graded algebras. This is a joint work with Tasos Moulinos.

**November 2, 2021**

Speaker: Benjamin Allen (Emmanuel College)

Title: How to compute the fixation probability of just about anything (under weak selection)

Abstract: Evolution is driven by the arrival and fixation of mutations, where “fixation” refers to a single new mutation eventually spreading throughout an entire population. The probability that this occurs, for a particular mutation, depends on many factors, including selection pressures (which may depend on behavioral interactions), spatial structure, mating and replacement patterns, etc.

Calculating fixation probabilities can therefore be quite difficult, even in relatively simple mathematical models of evolution. I will present recent work showing a general method for calculating fixation probabilities, under the assumption that selection is weak. This method applies to arbitrary forms of spatial structure, behavioral interactions, and mating patterns (in the case of sexually reproducing diploids).

The method allows for fixation probabilities to be computed in polynomial time, as long as interactions that affect fitness are limited in scope. To illustrate, I will apply this method to fixation probabilities on graph-structured populations, for weak constant selection, under various update rules.

**November 16, 2021**

Speaker: Juan Garrahan (Nottingham)

Title: Making rare events typical: from dynamical large deviations to reinforcement learning

Abstract: I will discuss general ideas for studying atypical dynamics in stochastic systems. Rare events often play a significant role in phenomena occurring across science, but their systematic study is hampered by the fact that they occur with low probability.

I will describe the so-called ”thermodynamics of trajectories” framework, an ensemble method for quantifying the statistical properties of trajectories of the dynamics, based on the mathematics of large deviations (LDs).

I will discuss the use of tensor network methods for computing LD statistics accurately in lattice systems, their use in efficiently sampling rare trajectories, and consider the application of machine reinforcement learning for problems not tractable by LDs. Time permitting I will discuss the extension of this general approach to quantum dissipative systems.

**November 23, 2021**

Speaker: Nick Mavromatos (Trieste)

Title: Non-Hermitian Yukawa Interactions: Consistency, Dynamical Mass Generation issues and Physics Motivation

Abstract: I discuss a fermion-(pseudo)scalar field theory model in (3+1)-dimensions, with anti hermitian Yukawa interactions, and demonstrate its consistency as a unitary quantum field theory. The model may be understood within a wider PT-symmetry framework, in the sense of identifying conditions for real energy eigenvalues of the corresponding Hamiltonian operators.

Due to energetics, it is not possible to have dynamical mass generation for either the fermion or the (pseudo)scalar fields, unless suitable attractive four fermion interactions are included, with sufficiently strong couplings.

In the latter case, we estimate the dynamically generated masses using an appropriate Schwinger-Dyson treatment, for weak Yukawa couplings. Such models, with pseudoscalar-fermion Yukawa interactions, find partial motivation in neutrino physics, as providers of novel scenarios for Majorana neutrino mass generation, which could be of phenomenological interest.

**November 30, 2021**

Speaker: Michael Nicholson (Edinburgh)

Title: Transient instability in breast cancer examined via single cell DNA sequencing and stochastic modelling

Abstract: Many cancer genomes exhibit considerable alterations however the principles underlying the generation and maintenance of this pervasive phenomenon are still unclear. In this talk I will discuss pairing stochastic models with single cell DNA sequencing data to gain insights into cancer evolution.

I will outline how the genomic alterations are detected and propose a simple model to describe their accumulation. Finally, we will combine the model with sequencing data from breast cancer patients to examine whether a heightened period of genomic instability existed at the onset of cancer.

**December 7, 2021**

Speaker: Vittorio Peano (Max Planck)

Title: Exploration of Topological band structures using deep learning.

The fabrication of arbitrarily patterned structures, down to the nanoscale, allows a large degree of control of the propagation of light and other waves in the resulting metamaterial. Most of the information about the propagation of a wave inside a regular structure, e.g. which light colours can propagate and at what speed, is condensed in a single mathematical object, the so-called band structure.

The task of optimizing the fabrication pattern to achieve desired propagation properties is daunting because it involves exploration of the infinitely large space of all possible patterns, evaluating the band structure a large number of times. I will present our deep-learning-based method to map arbitrary fabrication patterns to the corresponding band structures.

This method involves a useful detour: Instead of directly predicting the band structure, a neural network learns to predict the parameters of an auxiliary “tight-binding” model that encodes not only the band structure but also the topological properties of the metamaterial. In a subsequent step, these properties can be accessed with an inexpensive computation based on the tight-binding model, accelerating by order of magnitudes the exploration of the configuration space.

**December 14, 2021**

Speaker: Paola Ruggiero (King's)

Title: Entanglement, area law & its violation in many-body systems

Abstract: At the center of the debate on quantum mechanics since its foundations, entanglement is arguably not one but rather the distinguishing signature of the quantum world. In this colloquium I will introduce this concept and motivate why it is still interesting and subject of ongoing research. I will argue that the problem of quantify entanglement is highly non-trivial, especially in the context of many-body systems.

At the same time, I will give some general existing results, in the form of conjecture or theorem, for the so-called “area law” of entanglement, and discuss more recent advances about its violation, with particular focus on disordered/inhomogeneous quantum many-body systems.

### Winter 2022

**February 8, 2022**

Speaker: Chaitanya Gokhale (Max Planck)

Title: Collective convictions catalyse cooperation.

Abstract: How did humans take over the world? Via large scale cooperation. We hypothesise that the evolution of language allows humans to not only communicate but to tell stories building cooperatives. Furthermore, humans invest in fantastic stories – mythologies. Recent evolutionary theories suggest that cultural selection may favour moralising stories that motivate prosocial behaviours. A key challenge is to explain the emergence of mythologies that lack explicit moral exemplars or directives.

Here, we resolve this puzzle with an evolutionary model in which arbitrary mythologies transform a collective of egoistic individuals into a cooperative. Relative to contemporary populations, our model also functions in smaller sized populations reflecting hunter-gatherers societies.

Taking the cognitive trade-off hypothesis into account, the model is robust to the cognitive costs in adopting fictions. This approach resolves a fundamental problem across the human sciences by explaining the evolution of otherwise puzzling amoral, nonsensical, and fictional narratives as exquisitely functional coordination devices.

**March 15, 2022**

Speaker: Bruno Bertini (Nottingham)

Title: BBGKY Hierarchy and Generalised Hydrodynamics

Abstract: The Bogoliubov–Born– Green–Kirkwood–Yvon (BBGKY) hierarchy and its reductions (such as the celebrated Quantum Boltzmann equation) form the foundation of our understanding of the non-equilibrium dynamics of weakly-interacting many-particle quantum systems. On the other hand the recently discovered Generalised Hydrodynamics (GHD) has led to very significant advances in our understanding of the dynamics of correlated many-particle systems with extensively many conservation laws.

For systems with extensively many conservation laws that are also weakly interacting both theories apply but their relation is not straightforward as they are formulated in terms of very different objects. I will show how to establish this relation for interacting fermions on a one-dimensional line. To do so I will perturbatively construct an extensive number conserved charges and establish a condition for them to have good locality properties. This condition selects the systems for which GHD can be applied.

**March 22, 2022**

Speaker: George Constable (York)

Title: Exploiting facultative sex in pathogens

Abstract: Abstract: Although sexual reproduction is nearly ubiquitous amongst eukaryotes, in many species it is facultative, allowing organisms to switch between sexual and asexual reproduction. In some species, these bouts of sexual reproduction can be exceedingly rare (the green algae Chlamydomonas reinhardtii is estimated to engage in sexual reproduction only once every 2000 generations). From a modelling perspective, this can present a challenge.

If one is interested in the evolution of some feature or trait of the organism associated with the sexual stage of the life cycle, one finds selective effects (present in the sexual stages) are swamped by noise (genetic drift during the asexual stages). Thus a stochastic modelling approach is necessary. Biologically however, this noise can be exploited to help us control facultatively sexual pathogens, as well as to gain a deeper empirical understanding of their life cycle.

In this talk I present ongoing work in this direction. In the first part of the talk I will use models to illustrate how facultative sex can be leveraged in tandem with gene drives to control plant-pathogenic fungi. In the second part of the talk I will show how stochastic models can be used to estimate the rate of sexual reproduction in the human parasite Leishmania.

**April 5, 2022**

Speaker: Philip Gerlee (Chalmers)

Title: Weak selection and time scale separation in ecological and evolutionary dynamics

Abstract: We show that under the assumption of weak frequency-dependent selection a wide class of population dynamical models can be analysed using perturbation theory. The inner solution corresponds to the ecological dynamics, where to zeroth order, the genotype frequencies remain constant. The outer solution provides the evolutionary dynamics and corresponds, to zeroth order, to a generalisation of the replicator equation.

We apply this method to a model of public goods dynamics and construct, using matched asymptotic expansions, a composite solution valid for all times. We also analyse a Lotka-Volterra model of predator competition and show that to zeroth order the fraction of wild-type predators follows a replicator equation with a constant selection coefficient given by the predator death rate. For both models we investigate how the error between approximate solutions and the solution to the full model depend on the order of the approximation, and show using numerical comparison, for $k=1$ and $2$, that the error scales according to $\varepsilon^{k+1}$, where $\varepsilon$ is the strength of selection and $k$ is the order of the approximation.

## Seminar Series 2020-21

### Autumn 2020

**October 6, 2020**

Speaker: Rob Noble (City)

Title: "Characterizing and forecasting tumour evolution"

**October 13, 2020**

Speaker: Wolfram Mobius (Exeter)

Title: Two layers of chance associated with spatially expanding populations: How demographic noise and environmental heterogeneity shape the evolutionary path of a population.

Abstract: In nature, populations expand into new habitat at different spatial and temporal scales, from bacterial cells forming a colony all the way to invasive species colonising new geographical regions.

The expansion process can thereby affect the evolutionary path of the growing population, a topic that has gathered much interest recently. The effects of environmental heterogeneity on the evolutionary dynamics of such range expansions remains poorly understood so far - not least due to the large variety of environmental heterogeneity found in nature. To understand the effects of this heterogeneity, we use a combination of simulations, analytical theory, and experiments with microbial model systems.

In a bottom-up approach we are seeking to first understand the effects of isolated inhomogeneities and then describe the evolution in complex heterogeneous environments. Specifically, we first consider the effects of isolated obstacles and hotspots as well as bumps in an otherwise flat habitat. The former two are regions which hinder and accelerate the invasion, respectively. We find that those structures have characteristic consequences for neutral genetic diversity (the distribution of individuals that are genetically different, but do not have a selective advantage or disadvantage). We observe an additional layer of ‘survival of the luckiest’ – complementary to, yet qualitatively different from, founder effects.

**October 20, 2020**

Alexander Kasprzyk (Nottingham)

Title: Exploring the landscape of Fano classification

Abstract: Our understanding of Fano classification via Mirror Symmetry has grown considerably over the past decade. Although still very much conjectural, we now have systematic ways to begin exploring what this classification might eventually look like. I will describe recent work, joint with Giuseppe Pitton, Liana Heuberger, and others, which builds upon the existing classifications of Fano polytopes in dimensions 3 and 4 and begins to systematically construct examples against which our conjectures and intuition can be tested. This is very-much work-in-progress.

**October 27, 2020**

Bernd Schroer (Edinburgh)

Title: Magnetic Skyrmions: Integrable Models and their Applications

Abstract: Chiral magnetic skyrmions are topological solitons in two-dimensional magnetic systems which are stabilised by the so-called Dzyaloshinskii-Moriya interaction (DMI). For each DMI term, there is a model for magnetic skyrmions which is integrable and where solitons can be written down explicitly in terms of holomorphic functions. In this talk I will explain the integrable models and how they can be used to obtain magnetic skyrmions in generic (non-integrable) models.

This approach reveals a remarkable diversity of magnetic skyrmions and suggests a new way of interpreting their structure. In particular, configurations with positive topological charge are best understood in terms of one-dimensional domain walls carrying chiral kinks. I will explain this point of view, and speculate about possible generalisations. The first part of the talk is based on arXiv:1905.06285, and the second part on joint work with Vlad Kuchkin, Bruno Barton-Singer, Filipp Rybakov, Stefan Bluegel and Nikolai Kiselev.

**November 10, 2020**

Marika Taylor (Southampton)

Title: Spacetime reconstruction and quantum error correction codes

Abstract: The holographic paradigm states that spacetime can be reconstructed from the data of a quantum field theory in one less dimension. In recent years there has been considerable interest in the relationship between spacetime reconstruction and quantum error correction. Much of the literature has been focussed on low dimensional spacetimes e.g. reconstruction of the hyperbolic plane. In this talk we will explore the relationship between certain classes of quantum error correction codes and reconstruction of general dimensional spacetimes via cellulations.

**November 17, 2020**

Roberto Tateo (Torino)

Title: The Relevance of Irrelevant perturbations

Abstract: The presence of an irrelevant operator in a quantum field theory is usually not good news, as far as understanding the high-energy physics of the model is concerned. In two space-time dimensions, the TTbar composite operator is an exception to this rule since this irrelevant field is well defined also at a quantum level.

For the TTbar deformations, we can reverse the renormalization group trajectory and gain exact information about ultraviolet physics. The outcome is stunning: while low energy physics resembles that of a conventional local quantum field theory, at high-energy the density of states on a cylinder shows Hagedorn growth similar to that of a string theory. In this talk, I will review various classical and quantum aspects of this particular deformation.

**November 24, 2020**

Jacopo Viti (UFRN)

Title: Entanglement dynamics in 1+1 dimensional quantum system: the example of the Ising spin chain

Abstract: Entanglement evolution represents nowadays an important theoretical diagnostic to detect whether a quantum system out-of-equilibrium can eventually relax toward a stationary state at late times.

In this talk, I will introduce the main ideas and motivations beyond the study of entanglement dynamics in many-body systems by analyzing a paradigmatic model of statistical physics: the Ising spin chain. In particular, I will review classic results such as the linear growth of the entanglement entropies and the quasi-particle picture. Eventually, I will discuss some new developments that were recently obtained in collaboration with O. Castro Alvaredo, Mate Lencses, and Istvan M. Szecseny.

**December 8, 2020**

Cesare Guilio Ardito (City)

Title: Classification of blocks and conjectures

Abstract: Donovan’s conjecture predicts that given p-group D there are only finitely many Morita equivalence classes of blocks of group algebras with defect group D. While the conjecture is still open for a general D it has been proven in many special cases. A harder question is the one to actually classify Morita equivalence classes in a given situation, i.e. to have a complete list of blocks that can occur determined up to Morita equivalence.

In this talk, I will introduce the topic, give the relevant definitions and then roughly describe the process of classifying blocks, with a focus on the methodology and the tools normally needed to obtain such a result. Then I will focus on some applications of having such a list, mentioning some(perhaps surprising) difficulties that can arise in verifying certain classical modular representation theory conjectures, even when a complete list of blocks is given.

### Winter 2021

**February 9, 2021**

Diana Fusco (Cambridge)

Title: The inevitable density-dependent dispersal in viral populations and its role in viral evolution

Abstract: Reaction-diffusion waves have long been used to describe the growth and spread of populations undergoing a spatial range expansion. Such waves are generally classed as either pulled, where the dynamics are driven by the very tip of the front and stochastic fluctuations are high, or pushed, where cooperation in growth or dispersal results in a bulk-driven wave in which fluctuations are suppressed. These concepts have been well studied experimentally in populations where the cooperation leads to a density-dependent growth rate. By contrast, relatively little is known about experimental populations that exhibit a density-dependent dispersal rate.

Using bacteriophage T7 as a test organism, we present novel experimental measurements that demonstrate that the diffusion of phage T7, in a lawn of host E. coli, is hindered by steric interactions with host bacteria cells. The coupling between host density, phage dispersal and cell lysis caused by viral infection results in an effective density-dependent diffusion rate akin to cooperative behavior. Using a system of reaction-diffusion equations, we show that this effect can result in a transition from a pulled to pushed expansion. Moreover, we find that a second, independent density-dependent effect on phage dispersal spontaneously emerges as a result of the viral incubation period, during which phage is trapped inside the host unable to disperse. Our results indicate both that bacteriophage can be used as a controllable laboratory population to investigate the impact of density-dependent dispersal on evolution, and that the genetic diversity and adaptability of expanding viral populations could be much greater than is currently assumed.

**February 16, 2021**

Paul Bushby (Newcastle)

Title: Dynamo action in convectively-driven flows

Abstract: Most stars and planets exhibit some degree of magnetism. In all probability, these magnetic fields are generated by hydromagnetic dynamo action, whereby the motions of electrically-conducting fluids in the astrophysical body are able to sustain magnetic fields against the action of ohmic dissipation. The surprising aspect of this is that many astrophysical dynamos seem to produce large-scale ordered magnetic fields rather than small-scale disordered fields that are structured on the scale of the underlying flow. Motivated by these considerations, I will describe simulations of a prototypical dynamo problem, namely dynamo action driven by convection in a rotating electrically-conducting fluid. I will discuss the circumstances under which such a system can drive small- and large-scale dynamos and will relate these results to the corresponding theoretical predictions.

**March 2, 2021**

Eric Verniers (CNRS-LPSM Paris)

Title: Probing symmetries of quantum many-body systems through spectral statistics

Abstract: The idea of describing properties of complicated physical systems using random matrices dates back to Wigner in the 1950s, originally in the context of heavy atomic nuclei. Since then, Random Matrix Theory has developed as an active branch of research at the interface between mathematics and physics, and is frequently used to diagnose whether a quantum many-body system behaves in a "regular" or "chaotic" way by comparing the statistics of its energy levels to theoretical predictions.

Certain physical systems however possess some extra, sometimes hidden, symmetries, which result in a modification of the statistics of spacings, somewhere between the “regular” and “chaotic” predictions. In this talk I will present how to extend the theory of spectral statistics to account for the presence of additional symmetries. This provides a tool to not only get a signature of chaos or regularity in systems with symmetries, but also to uncover these symmetries if they were previously unnoticed.

(based on arXiv:2008.11173, in collaboration with Olivier Giraud, Nicolas Macé and Fabien Alet)

**March 9, 2021**

Ross Cressman (Wilfrid-Laurier)

Title: Evolutionary games with interaction times and time between interactions

Abstract: Evolutionary game theory was developed under a number of simplifying assumptions. One that is not often explicitly stated is that each interaction among individuals takes the same amount of time no matter what strategies these individuals use. When interaction time is strategy-dependent, it is more natural to take individual fitness as the payoff received per unit time. For instance, two Hawks interacting in the standard two-player Hawk-Dove game are assumed to engage in a fight over a resource with fixed payoff, implying that they may be involved in fewer interactions than Doves who avoid such contests. Furthermore, there may be other payoffs received in the time between interactions.

The talk will first analyze how these individual fitnesses affect the game dynamics and evolutionary outcome (e.g. the evolutionarily stable strategy (ESS) and Nash equilibrium (NE)) in general two-player symmetric games (i.e. matrix games). The results will be applied to the Hawk-Dove (HD) game and to the repeated Prisoner’s Dilemma (PD) game when the number of rounds is under the players’ control. The analysis will then be extended to two-player asymmetric games (e.g. the Battle of the Sexes (BoS) with time to rear offspring) and multi-player games (e.g. the Public Goods Game (PGG)). It is shown that cooperation can coexist with defection in the PD and PGG games, a result consistent with empirical evidence from game experiments based on the corresponding opting out game.

This is joint work with Vlastimil Krivan, Czech Academy of Sciences, Biology Centre, Ceske Budejovice, Czech Republic.

**March 16, 2021**

Romuald Janik (Jagiellonian)

Title: From machine learning to entropy and physics, and back again...

Abstract: In this talk I would like to describe some fruitful interrelations between Machine Learning and Physics.

On the one hand, I will show how to use the tools of machine learning to estimate the entropy (and free energy) of a system directly from Monte Carlo configurations at a given temperature, which is commonly believed to be extremely difficult if not impossible by conventional means.

On the other hand, I will describe a proposed definition of complexity for deep neural networks, which is based on some intuitions from physics. I will show how one can use it together with a complementary notion of effective dimension to quantify the intuitive difficulty of a dataset or a learning task.

**March 23, 2021**

Chris Bowman (Kent)

Title: Diagrammatic Algebra

Abstract: In the past 20 years, representation theory has underdone a “diagrammatic revolution” whereby age-old conjectures have been reimagined and subsequently resolved using diagrammatic calculus. We give a friendly introduction to this field and show how these ideas can be used to understand the characters of simple representations of symmetric groups in terms of so-called “p-Kazhdan—Lusztig polynomials”. This is based on joint work with Anton Cox, Amit Hazi and Maud De Visscher (of City) and Emily Norton.

**March 30, 2021**

David Craven (Birmingham)

Title: The structure of group rings: algebra, combinatorics and topology

Abstract: In this talk I will discuss the structure of group rings of torsion-free groups (i.e., no elements g such that g^n=1 for n>1). This connects fundamental conjectures in both group theory and algebraic topology. We will look at some of these ideas, before talking about such groups. We introduce combinatorial ideas that can be applied to the group-theoretic conjectures, discuss recent progress, and the implications for topology.

## Seminar series 2019-20

### Autumn 2019

**1st October 2019**

Peter Millington (Nottingham)

Symmetry breaking in non-Hermitian, PT-symmetric quantum field theories

We consider the continuous symmetry properties of non-Hermitian, PT-symmetric quantum field theories. We begin by revisiting the derivation of Noether’s theorem and find that the conserved currents of non-Hermitian theories correspond to transformations that do not leave the Lagrangian invariant. After describing the implications of this conclusion for gauge invariance, we consider the spontaneous breakdown of global and local symmetries, and illustrate how the Goldstone theorem and the Englert-Brout-Higgs mechanism are borne out. We conclude by commenting on the potential avenues for model building in fundamental physics from the non-Hermitian deformation of the Standard Model of particle physics.

**8th October 2019**

Marko Medenjak (ENS)

The isolated Heisenberg magnet as a quantum time crystal

Isolated systems consisting of many interacting particles are generally assumed to relax to a stationary equilibrium state whose macroscopic properties are described by the laws of thermodynamics and statistical physics. Time crystals, as first proposed by Wilczek, could defy some of these fundamental laws and for instance display persistent non-decaying oscillations. They can be engineered by external driving or contact with an environment, but are believed to be impossible to realize in isolated many-body systems. I will show that the paradigmatic model of quantum magnetism, the Heisenberg XXZ spin chain, does not relax to stationarity and hence constitutes a genuine time crystal that does not rely on external driving or coupling to an environment. I will trace this phenomenon to the existence of periodic extensive quantities and find their frequency to be a no-where continuous (fractal) function of the anisotropy parameter of the chain.

**15th October 2019**

Fabian Ruhle (CERN)

Machine Learning and Complexity of String Vacua

I will start with an introduction to the fields of machine learning and computational complexity. Subsequently, I will discuss the complexity of problems encountered in searches for solutions to string theory’s physical and mathematical consistency conditions. Finally, I will illustrate how reinforcement learning, a branch of machine learning, can be used to tackle these types of problems. I will present an example in the context of Type II string theory, where the consistency conditions are a set of coupled, non-linear Diophantine equations. I will demonstrate that the machine learning algorithm discovers solution strategies that have previously been employed by humans, but also discovers new, previously unknown strategies.

**22nd October 2019**

Bernd Braunecker (St. Andrews)

Non-Markovian dynamics of a spin in a fermionic bath: quantum correlations, backaction and non-thermodynamic cooling

I will present a systematic analytical approach for calculating the dynamics of a spin system in contact with a bath of fermions [1]. The approach is set up such that the full time dynamics is captured by including all quantum coherent memory effects leading to non-Markovian dynamics. I will show on the example of the free induction decay how the full time range can be obtained analytically through a systematic study of the pole structure of the memory kernel of the density matrix, based on the Nakajima-Zwanzig master equation in the weak coupling limit. The result is an analytic expression showing how a quantum correlation dominated dynamics at short times evolves smoothly into the conventional exponential thermal decay at long times. I will conclude with the proposal of a quantum thermodynamic scheme to employ the temperature insensitivity of the non-Markovian decay to transport heat out of the electron system and thus, by repeated re-initialisation of a cluster of spins, to efficiently cool the electrons at very low temperatures.

[1] S. Matern, D. Loss, J. Klinovaja and B. Braunecker, Phys. Rev. B, Phys. Rev. B 100, 134308 (2019), arXiv:1905.11422.

**5th November 2019**

Klaus Ritzberger (Royal Holloway)

What can Index Theory Do for Game Theorists?

The concept of the fixed point index has been productively applied to a number of fields in economics. This presentation reviews the applications in game theory, with an emphasis on the equilibrium refinement debate. This is because the index has successfully served as a refinement concept for Nash equilibrium, as well as an identification of a necessary condition for asymptotic stability in evolutionary dynamics. Indeed, the index can also be used to relate the evolutionary approach to game theory with the rationalistic one. And quite a number of results developed for game theory extend to analogous results on general equilibrium theory. Finally, a few recent extensions of the logic of index theory in games are discussed.

**12th November 2019**

Misha Feigin (Glasgow)

Generalized Calogero-Moser-Sutherland systems

Calogero-Moser-Sutherland (CMS) system describes pairwise interaction of particles on a circle. It is a celebrated example of an integrable system partly due to its deep connections to geometry and algebra. For example, radial parts of Laplace-Beltrami operators on symmetric spaces give generalized quantum CMS systems related with root systems of Weyl groups with special values of coupling parameters. Algebraically, interesting cases are quantum systems with integer coupling parameters; in these cases generalised CMS operators admit special Baker-Akhiezer eigenfunctions. After reviewing some facts about generalized CMS systems I’ll introduce new integrable example of a two-dimensional CMS type system closely related to but different from G_2 case. This is based on joint work with M. Vrabec.

**19th November 2019**

Jean Alexandre (King's)

Spontaneous Symmetry Breaking or not?

Path integral quantisation of a scalar theory requires the one-particle irreducible effective potential to be a convex function of the background field. On the other hand, Spontaneous Symmetry Breaking (SSB) is based on a non-convex potential, so how are these two features consistent? This talk will review convexity properties, explain in what situation one can expect either SSB or convexity to happen, and show a semi-classical derivation of the convex effective potential. To conclude, an example where convexity could play a role will be discussed, in the context of cosmological Inflation.

**6th December 2019**

Ignacio Reyes (AEI)

Fermionic entanglement on the torus

Concepts from quantum information theory have become increasingly important in our understanding of entanglement in QFTs. One prominent example of this is the modular Hamiltonian, which is closely related to the Unruh effect. Using complex analysis, we determine this operator for the chiral fermion at finite temperature on the circle and show that it exhibits surprising new features. This simple system illustrates how a modular flow can transition from complete locality to complete non-locality, thus bridging the gap between previously known limits. We derive the first exact results for the entropy in the different spin sectors, and comment on the analytic continuation of the Rényi entropies to the complex plane.

### Winter 2020

**21st January 2020**

Elli Pomoni (DESY)

T_N, Toda and topological strings

In this talk we will consider the long-standing problem of obtaining the 3-point functions of 2D Toda CFT. We will propose a solution to this problem employing topological strings and the AGT relation between 4D gauge theories and 2D CFTs.

**28th January 2020**

Jacopo de Nardis (Ghent)

Emergent diffusion and super-diffusion in quantum and classical chains.

Finding a theoretical framework to explain how phenomenological transport laws on macroscopic scales emerge from microscopic deterministic dynamics poses one of the most significant challenges of condensed matter physics. In recent years, the advent of the generalized hydrodynamics in integrable quantum systems and more recent studies of quantum chaos and its relation to transport, reinvigorated the field of nonequilibrium physics in spin chains. Numerous results were found: lower bounds to diffusion constants, exact expressions for diffusion coefficients and remarkable anomalous features of transport in quantum and classical chains, deeply related to the Kardar-Parisi-Zhang dynamical universality class.I will present an overview of such results with a particular focus on anomalous transport and its relation to non-linear hydrodynamics.

**4th February 2020**

Rainer Klages (QMUL)

Stochastic modeling of diffusion in dynamical systems: three examples

Consider equations of motion yielding dispersion of an ensemble of particles. For a given dynamical system an interesting problem is not only what type of diffusion is generated but also whether the resulting diffusive dynamics matches to a known stochastic process. I will discuss three examples of dynamical systems displaying different types of diffusive transport: The first model is fully deterministic but nonchaotic

by showing a whole range of normal and anomalous diffusion under variation of a single control parameter [1]. The second model is a soft Lorentz gas where a point particles moves through repulsive Fermi potentials situated on a triangular periodic lattice [2]. It is fully deterministic by displaying an intricate switching between normal and superdiffusion under variation of control parameters. The third model randomly mixes in time chaotic dynamics generating normal diffusive spreading with non-chaotic motion where all particles localize [3]. Varying a control parameter the mixed system exhibits a transition characterised by subdiffusion. In all three cases I will show successes, failures and pitfalls if one tries to reproduce the resulting diffusive dynamics by using simple stochastic models.

Joint work with all authors on the references cited below.

[1] L. Salari, L. Rondoni, C. Giberti, R. Klages, Chaos 25, 073113 (2015)

[2] R.Klages, S.S.Gallegos, J.Solanp¨a¨a, M.Sarvilahti, Phys. Rev. Lett. 122, 064102 (2019)

[3] Y.Sato, R.Klages, Phys. Rev. Lett. 122, 174101 (2019)

**12th February 2020**

Shivaji Ratnasingham (U of North Carolina Greensboro)

An exact bifurcation diagram for a reaction diffusion equation arising in population dynamics

We analyze the positive solutions to

−∆v=λv(1−v); x∈Ω0,

∂v +γ√λv=0; x∈∂Ω0, ∂η

where Ω0 = (0,1) or is a bounded domain in Rn; n = 2,3 with smooth boundary and |Ω0| = 1, and λ,γ are positive parameters. Such steady state equations arise in population dynamics encapsulating assumptions regarding the patch/matrix in- terfaces such as patch preference and movement behavior. In this paper, we will discuss the exact bifurcation diagram and stability properties for such a steady state model.

**18th February 2020**

Jose Edelstein (Santiago de Compostela)

Beyond General Relativity: causality issues and geometric inflation

We will explore the consequences of imposing consistency conditions in the introduction of higher curvature corrections to the Einstein-Hilbert Lagrangian. We will discuss two separate issues. First, we will argue that causality and unitarity put some tough restrictions at tree level, pointing in the direction of a UV stringy completion. Second, we will show that it is possible to write down an action given by an infinite series in the Riemann tensor with nice properties in terms of its spectrum and cosmology, which suggests a tantalizing mechanism of geometric inflation.

**Later seminars were cancelled due to Covid-19.**

## Seminar series 2018-19

### Autumn 2018

- 2nd October 2018 - Lorenzo Bianchi (QMUL)
- 9th October 2018 - Luca Dell Anna (Padova)
- 16th October 2018 - Andrea De Luca (Oxford)
- 23rd October 2018 - Pascal Simon (Paris Sud)
- 6th November 2018 - Eric Vernier (Oxford)
- 13th November 2018 - Pedro Tamaroff (Trinity College, Dublin)
- 20th November 2018 - Paola Ruggiero (SISSA)
- 27th November 2018 - Guenter Wunner (Stuttgart)
- 4th December 2018 - Petr Siegl (Queen's University of Belfast)
- 22nd January 2018 - Chris Herzog (King's)
- 29th January 2018 - Rouven Frassek (IHES)

### Winter 2019

- 5th February 2019 - Alastair Rucklidge (Leeds)
- 12th February 2019 - Radu Tatar (Liverpool)
- 19th February 2019 - Olaf Lechtenfeld (Hannover)
- 5th March 2019 - Weini Huang (QMUL)
- 12th March 2019 - Ali Mostafazadeh (Koc)
- 19th March 2019 - Misha Portnoi (Exeter)
- 25th March 2019 - Sat Gupta (University of North Carolina, Greensboro)
- 2nd April 2019 - Seung-Joo Lee (CERN)

## Seminar series 2017-18

### Autumn 2017

- 3rd October 2017 - Ran Levi (Aberdeen) -
*Neuro-Topology: an Interaction between topology and Neuroscience* - 10th October 2017 - Sarben Sarkar (King's) -
*Brane sigma models and solutions in M, M*, and M' theories* - 17th October 2017 - Apostolos Vourdas (Bradford) -
*Renormalization of total sets of states into generalized bases with a resolution of the identity: a cooperative game theory approach* - 24th October 2017 - Alexander Altland (Cologne) -
*Large conformal golstone mode fluctuations in the SYK model* - 31th October 2017 -Tim Logvinenko (Cardiff) -
*Generalised braid category* - 14th November 2017 - Zlatko Papic (Leeds) -
*"Seeing" quantum integrability in the entraglement spectrum* - 21th November 2017 - Patrick Dorey (Durham) -
*Breaking integrability at the boundary* - 28th November 2017 - Andrey Morozov (Leicester) -
*Towards constructing a mathematically rigorous framework for modelling evolutionary fitness* - 5th December 2017 - David Vegh (QMUL) -
*Chaos, integrability, and weve-turbulence* - 12th December 2017 - Anotida Madzvamuse (Sussex) -
*Recent advances in mathematical modelling of cell migration*

### Winter 2018

- 30th January 2018 - Istvan Szecsenyi (City)
- 6th February 2018 - Rodolfo Russo (QMUL) -
*AdS3 holographic correlators with heavy states* - 13th February 2018 - Radu Tatar (Liverpool)
- 20th February 2018 - David Berman (QMUL) -
*A Review of Double and Exceptional Field Theory* - 27th February 2018 - Amir-Kian Kashani-Poo (ENS) -
*Topological strings and 6d SCFTs* - 13th March 2018 - Attila Csikasz-Nagy (KCL)
- 20th March 2018 - Nuno Freitas (Warwick and KCL)
- 3rd April 2018 - Luca Tagliacozzo (Strathclyde)

## Seminar series 2015-16

### Autumn 2015

- 29th September 2015 - Benjamin Doyon (King's) - Title: Thermalization and locality in quantum chains
- 3rd October 2015 - Nick Halmagyi (Jussieu) - Title: The Torsional Heterotic Conifold
- 6 October 2015 - Michael Levitin (Reading University) - Title: Indefinite Linear Pencils
- 20th October 2015 - Steve Baigent (UCL) - Title: Geometry in population modelling
- 27th October 2015 - Tobias Galla (Manchester University) - Title: Fixation and extinction dynamics in individual-based models: from evolutionary games to the initiation of cancer
- 10th November 2015 - Lucas Lacasa (QMUL) - Title: Time Series meet Network Science

### Winter 2016

- 26th January 2016 - Paul Fendley (Oxford)
- 2nd February 2016 - Dario Martelli (King's)
- 9th February 2016 - Anne Skeldon (Surrey)
- 23th February 2016 - Matt Fayers (QMUL)
- 8th March 2016 - Yasine Ikhlef (Jussieu)
- 15th March 2016 - Maciej Dunajski (Cambridge)
- 22th March 2016 - Rebecca Hoyle (Southampton)
- 29th March 2016 - Christian Korff (Glasgow)
- 5th April 2016 - Joe Bhaseen (King's)

## Seminar series 2014-15

### Autumn 2014

- 30/09/2014 - A. McKane (Manchester) - Title: Fast-mode elimination in stochastic metapopulation models
- 14/10/2014 - Ilke Canakci (Leicester) - Title: Clusters and triangulations: snake graphs and skein relations in surface cluster algebras, and their applications
- 21/10/2014 - David Evans (Cardiff) - Title: The search for the exotic: subfactors and conformal field theories
- 02/11/2014 - Dan Franks (York) - Title: Collective motion and animal sociality
- 11/11/2014 - Gabriele Travaglini (QMUL) - Title: Harmony of scattering amplitudes
- 18/11/2014 - Tomasz Lukowski (Oxford) - Title: Lessons from crossing symmetry at large N
- 09/12/2014 - David Jordan (Edinburgh) - Title: Quantizations of character varieties from a 4D TFT

### Winter 2015

- 27/01/2015 - Fabian Essler (Oxford) - Title: Generalized Gibbs Ensembles for Quantum Field Theories
- 03/02/2015 - Jean Avan (Cergy) - Title: Aspects of dynamical quantum algebras
- 10/02/2015 - George Papadopoulos (King's) - Title: Conformal symmetry and smoothness
- 17/02/2015 - Jan Plefka (Humboldt Universität Berlin) - Title: Yangian Symmetry of smooth supersymmetric Wilson Loops in N=4 SYM
- 24/02/2015 - Eva-Maria Graefe (Imperial College) - Title: The semiclassical limit of complexified quantum dynamics
- 17/03/2015 - Paolo Mattioli (QMUL) - Title: Quivers, Words and Fundamentals
- 24/03/2015 - Stefan Weigert (York) - Title: The Existence Problem of Mutually Unbiased Bases- or: "Why six is the first odd integer"
- 31/03/2015 - Jonathan Healey (Keele) - Title: On the origins of the viscous instability mechanism

## Seminar Series 2013-14

### Autumn 2013

**01/10/2013**

Andrea Baronchelli (City)

Title: Unconsciously rational: optimal strategies in human mental searches in online auctions

Abstract: Characterizing how we explore abstract spaces is key to understand our (ir)rational behavior and decision making. While some light has been shed on the navigation of semantic networks, however, little is known about the mental exploration of metric spaces, such as the one dimensional line of numbers, prices, etc. Here we address this issue by investigating the behavior of users exploring the "bid space" in online auctions.

We find that they systematically perform Lévy flights, i.e., random walks whose step lengths follow a power-law distribution. Interestingly, this is the best strategy that can be adopted by a random searcher looking for a target in an unknown environment, and has been observed in the foraging patterns of many species.

In the case of online auctions, we measure the power-law scaling over several decades, providing the neatest observation of Lévy flights reported so far. We also show that the histogram describing single individual exponents is well peaked, pointing out the existence of an almost universal behaviour. Furthermore, a simple model reveals that the observed exponents are nearly optimal, and represent a Nash equilibrium. We rationalize these findings through a simple evolutionary process, showing that the observed behavior is robust against invasion of alternative strategies.

Our results show that humans share with the other animals universal patterns in general searching processes, and raise fundamental issues in cognitive, behavioural and evolutionary sciences.

**08/10/2013**

L. Mason (Oxford University)

Title: Scattering amplitudes and holomorphic Wilson loops

Abstract: Scattering amplitudes and correlation functions can be reformulated in twistor space in terms of holomorphic objects. I'll explain how the amplitude Wilson-loop correspondence for planar N=4 super Yang-Mills can be reformulated in twistor space and proved at the level of the loop integrand.

If I have time I will discuss more recent work that shows that this leads to a simple representation of all-loop integrand in dlog form and how it can for examples be directly integrated without Feynman parameters.

**15/10/2013**

J. Simon (Edinburgh University)Title: Typicality in black hole physics

Abstract : In this talk we will review the connection between black holes and thermodynamics, motivating the need for a quantum theory of gravity as the corresponding quantum statistical mechanics behind its thermodynamical behaviour.

Using this perspective, we will explore the idea of quantum entanglement being responsible for the origin of thermalization. We will use our results on typicality, which are based on geometrical properties of large dimensional spheres, in quantum mechanics and 2d CFTs to give a further twist on the explanation for why Hawking's calculation is so robust.

**22/10/2013**

K. Sharkey (Liverpool University)

Title: Exact representations of Susceptible-Infectious-Removed (SIR) epidemic dynamics on networks

Abstract: The majority of epidemic models fall into two categories: 1) deterministic models represented by differential equations and 2) stochastic models which can be evaluated by simulation.

In this presentation I will discuss the precise connection between these models. Until recently, exact correspondence was only established in situations exhibiting large degrees of symmetry or for infinite populations. I will consider SIR dynamics on finite static contact networks. I will give an overview of two provably exact deterministic representations of the underlying stochastic model for tree-like networks. These are the message passing description of Karrer and Newman and my pair-based moment closure representation.

I will discuss the relationship between the two representations and the relative merits of both.

**29/10/2013**

A. Tseytlin (Imperial College London)

Title: On conformal higher spin models

**12/11/2013**

B Vicedo (Hertfordshire) cancelled

**19/11/2013**

A.-C. Davis (DAMTP, Cambridge) cancelled

Title: The Cosmological Chameleon

Abstract: Observations suggest the Universe is undergoing accelerated expansion today. One possible explanation for this acceleration is modified gravity. The chameleon mechanism is one such theory of modified gravity whereby potential deviations from standard can be screened in dense environments.

I will first discuss the accelerating Universe before introducing the chameleon mechanism. I will end with ways of detecting chameleon theories and some recent work on black holes in screened, modified gravity theories.

**26/11/2013**

Reinhold Egger (Düsseldorf University)

Title: Majorana fermions in mesoscopic quantum transportAbstract: Recent experiments have provided the first signatures of localized Majorana fermions through peculiar zero-bias anomalies in the conductance of semiconductor nanowires.

In this talk, from a theory perspective, a broad introduction to the physics of Majorana fermion induced quantum transport will be given. After a discussion of the mathematical properties of Majorana fermions and the physical conditions for their realization, the zero bias anomaly will be traced to the phenomenon of resonant Andreev reflection. In the final part of the talk, it will be shown that in settings where Coulomb interactions are pronounced, a novel topological Kondo effect characterized by the orthogonal symmetry group, and leading to non-Fermi liquid physics, can be realized.

**27/11/2013**

Eirik Eik Svanes (Oxford University)

Title: Manifolds with SU(3) structure

**29/11/2013**

Andrew Mathas (University of Sydney)

Title: Cyclotomic quiver Hecke algebras of type A

Abstract: Brundan and Kleshchev have shown that the cyclotomic Hecke algebras of type A are isomorphic to the cyclotomic quiver Hecke algebras of type A, which arose out of work of Khovanov and Lauda, and Rouquier. As a result these algebras, which include as special cases the group algebras of the symmetric groups, are Z-graded algebras.

I will describe some of the recent developments in the graded representation theory of these algebras and show how the grading is already implicit in their classical (ungraded) representation theory.

**04/12/2013**

Chis Braun (City)

Title: Noncommutative localisation of algebras and modules

Abstract: Localisation is, in its simplest form, a method of adding multiplicative inverses, for example constructing the rational numbers from the integers. Localisation permeates mathematics in increasingly sophisticated guises and lies at the centre of homotopy theory.

In this talk I will provide an introduction to these ideas and discuss a result connecting the localisation of an algebraic structure to the localisation of its representations. This general abstract result has a range of concrete applications, including the group completion theorem, characteristic classes of A-infinity algebras and a derived Riemann-Hilbert correspondence. This is joint work in progress with Joe Chuang and Andrey Lazarev.

**10/12/2013**

Toby Wood (Leeds University)

Title: No lights, no music: The pseudo-incompressible MHD equations

Abstract: Most fluid flows of interest in engineering, geophysics, and even astrophysics can be regarded as "pseudo-incompressible", in the sense that acoustic waves carry only a tiny fraction of the total energy. Numerical simulations of such flows therefore often use "wave-filtered" equations (e.g. incompressible, Boussinesq, anelastic, etc.) that are based on approximations to the fully compressible equations.

Such equations are always derived under very specific physical assumptions, but are often applied in situations where these assumptions are not appropriate. In this talk, we will describe how these approximations can be improved, and generalized, by using concepts from Lagrangian mechanics.

### Winter 2014

**14/01/2014**

Carl M. Bender (Washington University in St. Louis and City)

Title: Nonlinear eigenvalue problems

Abstract: We present an asymptotic study of the nonlinear differential equation y'(x)=cos[\pi xy(x)] subject to the initial condition y=y(0) at x=0.

Although the differential equation is nonlinear, the solutions to this initial-value problem are strikingly similar to solutions to the time-independent Schroedinger eigenvalue problem. As x increases from 0, y(x) oscillates and thus resembles a quantum wave function in a classically allowed region. At a critical value that depends on the initial condition y(0) the solution y(x) undergoes a transition; the oscillations abruptly cease and y(x) decays to 0 monotonically for large x.

This transition resembles the transition in a wave function that occurs at a turning point as one enters the classically forbidden region. The initial conditions y(0) fall into discrete classes; in the nth class of initial conditions, a_{n-1}<y(0)<a_n (n=1, 2, 3, ...), y(x) exhibits exactly n maxima in the oscillatory region. The boundaries a_n of these classes are the analogs of quantum-mechanical eigenvalues.

We give an asymptotic calculation of a_n for large n; this calculation corresponds to a semiclassical (WKB) calculation in quantum mechanics of high-energy eigenvalues. Our principal result is that for large n, a_n is asymptotic to A n^{1/2}$, where A=2^{1/3}. The work presented here was done by C. M. Bender, A. Fring, and J. Komijani.

**28/01/2014**

Chris Bowman (City)

Title: The Partition algebra and the Kronecker Problem

Abstract: The Kronecker problem asks for a combinatorial understanding of the tensor products of simple modules for the symmetric group. We shall introduce the partition algebra as a natural setting in which to study this problem and discuss new results concerning its representation theory. This is based on joint work with M. De Visscher, O. King, and R. Orellana.

**04/02/2014**

Ginestra Bianconi (QMUL)

Title: Statistical mechanics of multiplex networks

Abstract: A large variety of complex systems, from the brain to the weather networks and complex infrastructures, are formed by several networks that coexist, interact and coevolve forming a "network of networks". Modeling such multilayer structures and characterizing the rich interplay between their structure and their dynamical behavior is crucial in order to understand and predict complex phenomena.

In this talk I will present recent works on statistical mechanics of multiplex networks. Multiplex networks are formed by N nodes linked in different layers by different networks. I will present models that generate multiplexes with different types of correlations between the layers, and characterize new percolation phenomena on multiplex networks, showing first order phase transitions, bistability or a complex phase diagram with tricriticals points and higher order critical points.

**18/02/2014**

Steven Donkin (University of York)

Title: Some Remarks on Gill's Theorems On Young Modules.

Abstract: In a recent paper C. Gill proves some results on the tensor product of Young modules for symmetric groups. Gill uses methods from the modular representation theory of finite groups.

We here take a different point of view by first working in the context of representations of general linear groups and then applying the Schur functor (a point of view pioneered by J. A. Green). Our results are valid too (and no more difficult to obtain) in the quantised situation (of representation of quantum general linear groups and Hecke algebras). For the purposes of exposition we shall describe the situation in the classical context and then compare and contrast with the quantised context if time permits.

**25/02/2014**

Paul Martin (Leeds University)

Title: "Fun with partition categories"

Abstract: The Brauer category sits inside the partition category - both having elementary set-theoretic constructions. The Temperley-Lieb category sits inside these categories (in at least two different ways), but it's construction has a more geometrical flavour.

We will consider geometrically defined extensions of the TL category in the Brauer and partition categories. These constructions are motivated in part by applications in computational physics, but here we will consider them from a representation theory perspective.)

**11/03/2014**

Giuseppe Mussardo (Sissa)

**18/03/2014**

Anne Davis (Cambridge)

**25/03/2014**

John McNamara (Bristol)

**01/04/2014**

Peter Hydon (Surrey)

Title: "Difference equations by differential equation methods"

Abstract: Around twenty years ago, I heard an eminent numerical analyst say, "Any problem involving difference equations is an order of magnitude harder than the corresponding problem for differential equations." Research since that time has transformed our understanding of difference equations and their solutions. The basic geometric structures that underpin difference equations are now known.

From these, it has been possible to develop systematic techniques for finding solutions, first integrals or conservation laws of a given difference equation. These look a little different to their counterparts for differential equations, mainly because the solutions of difference equations are not continuous. However, they are widely applicable and most of them do not require the equation to have special properties such as linearizability or integrability.

## Seminar Series 2012-13

### Autumn 2012

**02/10/2012**

Evgeny Sklyanin (York)

**09/10/2012**

Roland Frederick (Humboldt)

Title: Novel algebraic directions in Free Probability Theory

Abstract: Free probability theory, a species of non-commutative probability theory, is amazing for several reasons. Not only has it nice combinatorial features underlying it but also profound connections with other fields, in particular physics. Recently, we established a priori unexpected relations with some very prominent algebraic objects, in particular Hopf algebras. In this talk we will carefully introduce some of the basic features and give a glance at future directions.

**16/10/2012**

Marcus Linkelmann (City)

Title: On Hochschild cohomology of algebras

Abstract: Hochschild cohomology is a sophisticated invariant which can be associated with any algebra over a commutative ring. The structural connections between an algebra and its Hochschild cohomology are far from being well understood. We describe some aspects of this relationship, with a particular view to applications in modular representation theory.

**23/10/2012**

Andrey Morozov (Leicester)

**30/10/2012**

Jerome Gauntlett (Imperial)

Title: Holography, black holes and superconductors

Abstract: The AdS/CFT correspondence in string theory is a powerful ``holographic" tool to study strongly coupled quantum systems using weakly coupled gravitational techniques. It is possible that it can provide valuable insight into poorly understood systems arising in condensed matter such as high temperature superconductors. We will explain how superconducting phases can be described using holography via the construction of novel black hole solutions. We also describe the dynamical evolution of holographic superconductor via the construction of dynamical black holes. This reveals a new emergent temperature scale in the superconducting phase that also exists outside of the context of holography and could be experimentally tested.

**31/10/2012**

Tamara Rogers (Arizona)

**13/11/2012**

Tina Davies (Leeds)

Title: Short-wavelength magnetic buoyancy instability

Abstract: We consider the magnetic buoyancy instability in the short-wavelength limit of Gilman (1970). In this limit the perturbation equations (a system of coupled ODEs) can be reduced to a single algebraic dispersion relation, with coefficients depending on height. Put otherwise it seems that, in this limit, a problem that would have been treated as an eigenvalue problem requiring a set of boundary conditions can be reduced to a single equation for which the boundary conditions are unimportant. Here I present asymptotics and numerical calculations to illustrate the link between the two systems, which can be viewed as being analogous to the more familiar problem of the quantum harmonic oscillator.

**20/11/2012**

Gerard Watts (King's)

**27/11/2012**

David B Penman (Essex)

Title: Sums, Restricted Sums and Differences

Abstract: Given a (nonempty) set $A$ of integers, two of the most obvious things to do with it are to form the sumset $A+A=\{a+b:\,a,b\in A\}$ and the difference set $A-A=\{a-b:\,a,b\in A\}$. One might also wish to consider the restricted sumset $A\hat{+}A=\{a+b:\,a,b\in A,\,a\neq b\}$. One can then ask various obvious questions about the relationships between the sizes of various of these sets and what this implies about structure, and I shall discuss some known results on this, including generalisations to more general contexts, e.g. in group theory. An intuition one might have is that the sumset/restricted sumset will be smaller than the difference set as addition is commutative but subtraction isn't: I shall survey various known results showing that this intuition is non-trivially wrong. At the end I shall discuss some recent constructions of sets $A$ which give new record large values of $\log(|A+A|)/\log(|A-A|)$. The original part of the talk is based on joint work with my research student Matthew Wells.

**04/12/2012**

Nick Dorey (DAMTP)

**11/12/2012**

Anne Kandler (City)

Title: Modelling cultural evolution: A differential equation-based framework

Abstract: Over the last three decades, cultural evolution has evolved from a useful metaphor to a legitimate scientific field. Going hand in hand with the emergence of this new field of study, mathematical and computational modelling approaches have been developed to describe the phenomenon of cultural evolution. In this talk I will show on the examples of (i) the application of the concept of neutral evolution to the archeological record and (ii) the process of language shift how such models can be constructed and how they can enhance our understanding of the process of cultural evolution

### Winter 2013

**29/01/2013**

David Tong (DAMTP)

**12/02/2013**

Chris Hull (Imperial)

**19/02/2013**

Friedrich Lenz (QMUL)

**26/02/2013**

Alexander Veselov (Loughborough University)

Title: Universal formulae in Lie algebras and Chern-Simons theory

Abstract: In 1990s Vogel introduced an interesting parametrisation of simple Lie algebras by 3 parameters defined up to common multiple and permutations. Numerical characteristic of Lie algebra is universal if it can be expressed rationally in terms of Vogel's parameters (example - dimension of Lie algebra). I will present new universal formulae for certain Casimir eigenvalues as well as for some quantities in Chern-Simons theory on a 3D sphere, found jointly with Mkrtchyan and Sergeev.

**12/03/2013**

Alessandro de-Martino (City)

Title: A short trip in carbon flatland

Abstract: The exceptional properties of graphene, a new two-dimensional carbon crystal first isolated in 2004, have triggered an extraordinary amount of experimental and theoretical research. One of the reasons for the popularity of graphene is that its electronic properties are very different from those of conventional two-dimensional electronic systems and very intriguing from a fundamental point of view. In this talk I will give an introduction to the electronic properties of graphene and illustrate some of my work in this field.

**18/03/2013**

Inna Polichtchouk

Title: Intercomparison of General Circulation Models for Hot Extrasolar Planets

Abstract: We compare five general circulation models (GCMs), which have been recently used to study hot extrasolar planet atmospheres, under three test cases useful for assessing model convergence and accuracy. The models considered all solve the traditional primitive equations, but employ different numerical algorithms or grids. The test cases are chosen to cleanly address specific aspects of the behaviours typically reported in hot extrasolar planet simulations: 1) steady-state, 2) non-linearly evolving baroclinic wave and 3) response to fast thermal relaxation. When initialised with a steady jet, all models maintain the steadiness - except MITgcm in cubed-sphere grid. A very good agreement is obtained for a baroclinic wave evolving from an initial instability in spectral models only (see Figure 1). However, exact numerical convergence is not achieved across the spectral models: amplitudes and phases are observably different. When subject to a typical 'hot-Jupiter'-like forcing, all five models show quantitatively different behaviour - although qualitatively similar, time-variable, quadrupole-dominated flows are produced. Overall, in the tests considered here, spectral models in pressure coordinate (BOB and PEQMOD) perform the best and MITgcm in cubed-sphere grid with Shapiro filter performs the worst.

**20/03/2013**

Shigeo Koshitani (Chiba University)

Title: Source algebras version of Z*-theorem for odd primes

**26/03/2013**

Benjamin Favier (DAMTP)

Titile: Large-scale dynamos in compressible convection

**09/04/2013**

Andrei Bytsko (Geneva)