Our series of departmental seminars and colloquia will be of interest to all academic staff, postdoctoral researchers and PhD students. Contact Abhishek Pal Majumder for further information.

**6 December 2023**

15:00 to 16:00 Maths 314

**Speaker**: Prof. Ken McLaughlin

**Title:** Introduction to Soliton gasses

**Abstract:** In this presentation I will provide an introduction to solitons – fundamental solutions of nonlinear partial differential equations – with simple examples. Then we will consider more complicated solutions of the same pdes made up of many solitons, and construct a soliton gas by taking the limit as the number of solitons grows to infinity. A description of the history of the kinetic theory of soliton gasses will be encountered along the way. Time permitting, I will explain recent results in which random matrix theory techniques are being used to study fluctuations of random soliton gasses. The work presented will include joint work with Manuela Girotti (Emory University), Tamara Grava (SISSA and University of Bristol), Robert Jenkins (University of Central Florida), and Alexander Minakov (Charles University, Prague).

**Bio: **Ken McLaughlin grew up in Tucson, Arizona, removing cactus needles from baseballs and soccer balls, and peering through a homemade telescope at the dark skies of the desert. He earned his Bachelor’s degree and Ph.D. in Mathematics From New York University. He has been a faculty member at the University of North Carolina, Chapel Hill, The University of Arizona, the Universidad Federal de Brasília (Brazil), and Colorado State University, before joining Tulane University as the Evelyn and John G. Phillips Distinguished Chair in Mathematics. McLaughlin has served as the Head of the Mathematics Department at the University of Arizona, and as the Chair of the Mathematics Department at Colorado State University. He has held visiting research professorships at international research centers in France, Italy, Brazil, Belgium, the United Kingdom, and the United States. His research is in a field called “integrability”, where he and his friends discover new phenomena in complex systems and provides complete and mathematically precise descriptions of these phenomena, by integrating techniques from across many areas of mathematics.

**23 November 2023**

15:00 to 16:00 Maths 314

**Speaker**: Prof. Ashwin Seshadri (Indian Institute of Science)

**Title:** Glimpses of nonlinear dynamics in low-order climate model hierarchies

**Abstract:** We will provide a glimpse of a few different problems in nonlinear climate dynamics, all of which impinge on the design and use of model hierarchies to investigate problems of climate stability and climate change. We will first give a glimpse of nonlinear dynamics of monsoons, in context of questions about whether monsoons are tipping elements. We will show that, once the dominant balances are included in the equations, a range of models demonstrate the absence of tipping dynamics. We will consider a low-order model of coupled weather-climate interactions to study AMOC dynamics, which exhibits intermingled basins, to explore questions of initial condition sensitivity and model uncertainty, and implications for long-term prediction of slow climate variables. Lastly, we will discuss the nonlinear dynamics of Volterra gyrostats, which naturally give rise to coupled hierarchies of low order models obtained through model reduction techniques. We will discuss some results from recent work on low-dimensional chaos and briefly speculate on how these models might be used to probe a range of relevant topics related to uncertainty across modelling hierarchies.

**16 November 2023**

13:00 to 14:00 Maths 100

**Speaker**: Dr. Shixuan Wang (Department of Economics)

**Title:** Detection of a structural break in intraday volatility pattern

**Abstract:** We develop testing procedures for the presence of a change point in the intraday volatility pattern. Statistical methodology and theory are developed in the framework of Functional Data Analysis. They are based on a model akin to the stochastic volatility model for scalar point-to-point returns. In our context, we study intraday curves, one curve per trading day. After postulating a suitable model for such functional data, we present three tests focusing, respectively, on changes in the shape, the magnitude and arbitrary changes in the sequences of the curves of interest. We justify the respective procedures by showing that they have asymptotically correct size and by deriving consistency rates for all tests. These rates involve the sample size (the number of trading days) and the grid size (the number of observations per day). We also derive the corresponding change point estimators and their consistency rates. All procedures are additionally validated by a simulation study and an application to US stocks.

**17 October 2023**

13:00 to 14:00 Maths 212

**The event consists of three seminars and it will be chaired by Prof. Jennifer Scott. **

**Speaker**: Prof. Sue Todd

**Title:** REF 2028: What we know now and what is still to be decided

**Abstract:** This short presentation will outline the early decisions which have been taken regarding the format of REF2028, pointing out where the approach differs from last time. It will then be highlighted which elements are still to be determined and the timescales involved.

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**Speaker**: Dr. Calvin Smith

**Title:** 'Tilting' the classroom

**Abstract:** This talk describes my implementation of Alcock's 'Tilted classroom' approach and a series of activities designed to promote engagement with mathematics.

Alcock, Lara (2018). Tilting the classroom. Loughborough University. Journal contribution.

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**Speaker**: Dr. Chris Daw

**Title:** What is arithmetic geometry all about? (Or, at least, what does Chris do all day?)

**Abstract:** It's not so easy to explain arithmetic geometry in 20 minutes, but I'm going to try to give a gentle introduction to what it's all about. I'll do my best to give a sense of some of the most important results, ideas, and problems. At the least, I'll draw some pictures.

**15 March 2023**

16:00 to 17:00 Maths 113

**Speaker**: Prof. Roger Moser (University of Bath)

**Title:** p-harmonic functions out of their comfort zone

**Abstract:** For p strictly between 1 and infinity, p-harmonic functions are the solutions of a quintessential variational problem, which may be taught to undergraduates in a course on the calculus of variations. They enjoy very nice properties in terms of existence, uniqueness, regularity, etc. Many of these properties are lost, however, when we consider the case p=1 or the limit as p tends to infinity. I will discuss some geometric ideas that offer a better understanding of these extreme cases, nevertheless.

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**23 February 2023**

15.30 to 16.30 Maths 113

**Speaker**: Prof. Wael Bahsoun (Loughborough University)

**Title: **Statistical properties of mean-field coupled Anosov maps

**Abstract: **We will talk about infinite systems of globally coupled Anosov diffeomorphisms with weak coupling strength. Using transfer operators acting on anisotropic Banach spaces, we prove that the coupled system admits a unique physical equilibrium. Moreover, we prove exponential convergence to equilibrium for a suitable class of distributions. This is joint work with C. Liverani and F. M. Sélley.

**1 February 2023**

15.30 to 16.30 Maths 113

**The event consists of three seminars and it will be co-ordinated by Prof. Jennifer Scott. **

**Speaker**: Prof. Marcus Tindall (University of Reading)

**Title: **Mathematical Biology - What next?

**Abstract: **I will take a look at areas of recent activity for the Mathematical Biology Group, specifically around systems pharmacology and food systems, introducing general themes within the group, relevant projects and mathematical approaches. I will also outline the planned landscape of our activities for the next few years.

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**Speaker**: Prof. Jani Virtanen (University of Reading)

**Title: **Toeplitz matrices and operators

**Abstract:**An extraordinary variety of problems in mathematics, physics, and engineering can be expressed in terms of Toeplitz matrices (defined as matrices constant along the parallels to the main diagonal) and their infinite dimensional generalizations (viewed as operators on function spaces). The study of Toeplitz matrices was initiated by Otto Toeplitz in his Habilitationsschrift in 1907, who used them to give concrete examples of Hilbert’s general theory of functional analysis in Göttingen. I will discuss the Szego ̋- Widom limit theorem (which describes the asymptotic behavior of determinants of finite Toeplitz matrices), its recent generalizations, applications, and spectral properties of Toeplitz operators.

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**Speaker**: Prof. Amos Lawless (University of Reading)

**Title: **Conditioning and Preconditioning of Data Assimilation Problems.

**Abstract:**Data assimilation is used to estimate the state of a system from measurements of that system and some prior knowledge. When applied in environmental problems, such as weather and ocean forecasting, it is necessary to solve very large optimisation problems, often involving millions of variables. The accuracy to which we can solve the problem, and the speed of convergence of iterative minimisation methods, is dependent on the condition number of the problem, which in this case is equal to the ratio of the largest and smallest eigenvalues of the Hessian matrix. In this talk I will discuss a series of papers in which we have analysed what affects the conditioning of different formulations of the data assimilation problem and mention some recent work on using randomised methods to improve the conditioning.

#### 8 December 2022

15:30 to 16:30 Maths 113

**Speaker**: Dr. Greg Pavliotis (Imperial College London)

**Title: **Mean field limits for weakly interacting diffusions: phase transitions, multiscale analysis, metastability and inference

**Abstract:** We consider a system of N weakly interacting particles driven by white noise. The mean-field limit of this system is described by the (nonlinear and nonlocal) McKean-Vlasov-Fokker-Planck PDE. We present a detailed analysis of continuous and discontinuous phase transitions for the McKeanVlasov PDE on the torus. We study the combined diffusive/mean-field limit of systems of weakly interacting diffusions with a periodic interaction potential. We show that, in the presence of phase transitions, the two limits do not commute. We then show the equivalence between uniform propagation of chaos, a uniform-in-N Logarithmic Sobolev inequality, the absence of phase transitions for the mean-field limit, and of Gaussian fluctuations around the McKean-Vlasov PDE. We discuss about dynamical metastability for systems that exhibit discontinuous phase transitions. Finally, we develop inference methodologies for estimating parameters in the drift of the McKean SDE using either the stochastic gradient descent algorithm or eigenfunction martingale estimators.

**16 November** 2022

15:30 to 16:30 Maths 113

**Speaker**: Dr. Claudia Neves (King's College London)

**Title:** Extreme value statistics born out of domains of attraction

**Abstract:** Extreme value statistics is essentially concerned with the modelling of rare events which are hard to predict and occur with only little warning. In this talk, I will address a number of challenges highlighted in the literature and how these align with the domain of attraction characterisation for extremes. Such a characterisation stems from a suite of mildly restrictive conditions, qualitative in nature, which not only provide computational convenience but also furnish sharp approximations to asymptotically justified models for extreme values, a key aspect to any statistical testing procedure as well as interval estimation methodology in a nonparametric setting.

**19 October 2022**

15:30 to 16:30 Maths 113

**Speaker**: Prof. Simon Chandler-Wilde

**Title**: "How to write 4* papers: reflections on REF 2021"

**Abstract**: Having been an Output Assessor for the Mathematical Sciences panel for REF 2021, I will talk about how papers are assessed and reflect on what makes a 4* (and 3*, 2* paper), and lessons learned about how to write my papers. I will also, having served on the most recent EPSRC Mathematical Sciences small grant scheme panel, report on how that works and what makes a strong application.

**Speaker: **Dr.Zuowei Wang

**Title: **Mathematical Modelling in Soft Matter and Biological Physics

**Abstract: **In this talk, I will give a brief overview of our research activities on applying mathematical, computational and statistical methods in studying the structural, dynamic and rheological behaviors of various soft matter and biological systems, and also mention potential collaborations with colleagues in the M&S department and across the university.

**Speaker: **Dr.Nikos Katzourakis

**Title: **Who needs nonlinear PDE theory in the era of supercomputers?

**Abstract: **In this short talk for non-experts, I will try to explain the necessity in developing theory for nonlinear Partial Differential Equations, and why (unless the rise of the AI scenario of the Terminator movies materialises), Skynet is very unlikely to be able to prove theorems.

### 23 March 2021

16:00 (via Zoom Meeting ID: 615 8447 3398

**Speaker: **Christiane Tretter, University of Bern

**Title: **Challenges in non-selfadjoint spectral problems

**Abstract:** In this talk different techniques to address the challenges arising in spectral problems for non-selfadjoint linear operators will be presented. The methods and results will be illustrated by several applications from mathematical physics.

### 15 October 2020

11:00 (via Microsoft Teams, joining instructions will be circulated in due course)

**Speaker:** Björn Schmalfuss, Friedrich Schiller Universität Jena

**Title: **Random Dynamical Systems - an Overview

**Abstract:** The theory of random dynamical systems generalizes the theory of (deterministic) dynamical systems if the system is influenced by an (ergodic) noise. These systems are generated for instance by stochastic differential equations driven by a Brownian motion, or more generally by other kinds of noise, like a fractional Brownian motion. In this talk, we discuss some problems of generation of such a system. In addition, we introduce some special objects from this theory like random attractors, random invariant manifolds, and random fixed points. Finally, we will discuss some applications.

### 26 November 2019

13:00 - 14:00 (Slingo Lecture Theatre, JJ Thomson Building)

**Speaker:** Gordon Blower (Lancaster University)

**Title:** Algebraic Approaches to Integrable Operators in Random Matrix Theory

**Abstract:** In the context of random matrix theory, many of the fundamental ensembles are described by integrable operators, which are defined on intervals on the real line, or more generally cuts on a hyperelliptic Riemann surface. In this largely expository talk, I discuss how these operators can be understood algebraically in terms of commutative and noncommutative differentials. While these results are implicit in papers of Cuntz and Quillen from the 1990s, their relevance has not been fully realized in random matrix theory.

### 15 February 2019

16:00 - 17:00 (M314)

**Speaker:** Nicholas Young (Newcastle University)

**Title:** Newton-Girard and Waring-Lagrange theorems for two non-commuting variables

**Abstract:** In 1629 Albert Girard gave formulae for the power sums of several commuting variables in terms of the elementary symmetric functions; his result was subsequently often attributed to Newton. Over a century later Waring proved that an arbitrary symmetric polynomial in finitely many commuting variables can be expressed as a polynomial in the elementary symmetric functions of those variables.

In 1939 Margarete Wolf studied the analagous questions for non-commuting variables. She showed that there is no finite algebraic basis for the algebra of symmetric functions in d > 1 non-commuting variables, so there is no finite set of 'elementary symmetric functions' in the non-commutative case.

Nevertheless, Jim Agler, John McCarthy and I have recently proved analogues of Girard's and Waring's theorems for symmetric functions in two non-commuting variables. We find three free polynomials f, g, h in two non-commuting indeterminates x, y such that every symmetric polynomial in x and y can be written as a polynomial in f, g, h, and 1/g. In particular, power sums can be written explicitly in terms of f, g, and h.

### 9 November 2018

16:00 - 17:00 (M113)

**Speaker: **Carola-Bibiane Schönlieb (Cambridge)

**Title:** Deep and shallow learning approaches for regularised inversion in imaging

**Abstract:** In this talk we discuss the idea of data-driven regularisers for inverse imaging problems, investigating two parametrisation: total variation type regularisers and deep neural networks. This talk is based on joint works with J. C. De Los Reyes, L. Calatroni, C. Chung, T. Valkonen, S. Lunz and O. Oektem.

Carola-Bibiane works in image processing and PDE. She won the Whitehead prize in 2016 "for her spectacular contributions to the mathematics of image analysis", and the Philip Leverhulme Prize in 2017.

### 3 March 2017

13:00 - 14:00 (M113)

**Speaker:** Daniel Lawson (University of Bristol)

**Theme:** Genetics for Mathematicians

**Title:** The mathematics behind fine-scale personal ancestry inference, and what it can tell us

**Abstract: **Personal Genomics is a booming industry and allows people to go on a discovery process for their own history. The methods behind it allow for a discovery process for whole a population and can inform fields such as history[1], archaeology[2] and sociology. In this talk we discuss the underlying genetics models and how they are related to (but more complex than) the well-studied problem of clustering a graph.

We will compare two recent advances that allow extremely accurate personal ancestry inference. The first, recently released by Ancestry DNA [3] uses hundreds of thousands of samples with known location and uses graph heuristics to achieve geographical localisation. The second, developed by ourselves [4], uses careful algorithms on fewer samples to achieve similar clustering. This is based on the "Stochastic Block Model" which is a generative description of a graph. A number of approaches to inference are available, including Markov-Chain Monte Carlo and algorithmic approaches such as maximising modularity. We will discuss their relative merits, as well as extensions to the model to allow nodes to be mixtures of the blocks, called the mixed membership model. This has great importance in genetics because it describes admixture, i.e. what proportion of a genome is from different regions.

Scaling these models, and the improvements in accuracy that scale provides, is invaluable in genetics, and we will describe some of the very exciting consequences of having this methodology available, which range from the practical (personal genomics) to the bizarre (what we can learn about 1700s social class from the amorous congress of Captain Cook's crew in the Society Islands).

[1] Leslie et al 2015, Nature 519:309-314

[2] Pagani & Lawson et al 2016 Nature 538:238-242

[3] Han et al 2017 Nat Comms 8:14238

[4] Lawson et al 2012, PLoS Genet. 8:e1002453

### 21 February 2017

13:00 - 14:00 (RH Theatre, JJ Thomson Building)

**Speaker: **Lara Alcock (Loughborough)

**Title: **Tilting the Classroom: Engaging Students in Large Lectures

**Abstract:** There is much discussion currently about flipping the classroom or otherwise making dramatic adjustments to teaching. But for most lecturers, especially those with large classes, this is not practical. My view is that lectures are not inherently bad, and that there are numerous ways to make them more engaging without dramatic changes.

This talk will be about 18 approaches that I use - these work well together, but each can be implemented independently so they can be tried out according to personal taste. There will be lots of examples and some light-touch discussion of how this approach relates to evidence from psychological research on learning.