Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

 

Thu, 23 Oct 2025
16:00
Lecture Room 4

On the generic part of the cohomology of Shimura varieties of abelian type

Xiangqian Yang
(Peking University)
Abstract

The cohomology of Shimura varieties plays an important role in Langlands program, serving as a link between automorphic forms and Galois representations. In this talk, we prove a vanishing result for the cohomology of Shimura varieties of abelian type with torsion coefficients, generalizing the previous results of Caraiani-Scholze, Koshikawa, Hamann-Lee, and others. Our proofs utilize the unipotent categorical local Langlands correspondence developed by Zhu and the Igusa stacks constructed by Daniels-van Hoften-Kim-Zhang. This is a joint work with Xinwen Zhu.

Thu, 23 Oct 2025
16:00
L5

An 𝛼-Potential Game Framework for Dynamic Games

XinYu Li
(Mathematical Insitute, Oxford)
Abstract

We study  dynamic -player noncooperative games called -potential games, where the change of a player’s objective function upon her unilateral deviation from her strategy is equal to the change of an -potential function up to an error . Analogous to the static potential game (which corresponds to ), the -potential game framework is shown to reduce the challenging task of finding -Nash equilibria for a dynamic game to minimizing the -potential function. Moreover, an analytical characterization of -potential functions is established, with  represented in terms of the magnitude of the asymmetry of objective functions’ second-order derivatives. For stochastic differential games in which the state dynamic is a controlled diffusion,  is characterized in terms of the number of players, the choice of admissible strategies, and the intensity of interactions and the level of heterogeneity among players. Two classes of stochastic differential games, namely, distributed games and games with mean field interactions, are analyzed to highlight the dependence of  on general game characteristics that are beyond the mean field paradigm, which focuses on the limit of  with homogeneous players. To analyze the -NE (Nash equilibrium), the associated optimization problem is embedded into a conditional McKean–Vlasov control problem. A verification theorem is established to construct -NE based on solutions to an infinite-dimensional Hamilton–Jacobi–Bellman equation, which is reduced to a system of ordinary differential equations for linear-quadratic games.

Fri, 24 Oct 2025

11:00 - 12:00
L4

Evolutionary dynamics of extra-chromosomal DNA

Dr Weini Huang
(School of Mathematical Sciences Queen Mary University of London)
Abstract

Extra-chromosomal DNA (ecDNA) is a genetic error found in more than 30% of tumour samples across various cancer types. It is a key driver of oncogene amplification promoting tumour progression and therapeutic resistance, and is correlated to the worse clinical outcomes. Different from chromosomal DNA where genetic materials are on average equally divided to daughter cells controlled by centromeres during mitosis, the segregation of ecDNA copies is random partition and leads to a fast accumulation of cell-to-cell heterogeneity in copy numbers.  I will present our analytical and computational modeling of ecDNA dynamics under random segregation, examining the impact of copy-number-dependent versus -independent fitness, as well as the maintenance and de-mixing of multiple ecDNA species or variants within single cells. By integrating experimental and clinical data, our results demonstrate that ecDNA is not merely a by-product but a driving force in tumor progression. Intra-tumor heterogeneity exists not only in copy number but also in genetic and phenotypic diversity. Furthermore, ecDNA fitness can be copy-number dependent, which has significant implications for treatment.

Fri, 24 Oct 2025
12:00
L3

Gravitational Instantons, Weyl Curvature, and Conformally Kaehler Geometry

Claude LeBrun
(SUNY at Stony Brook)
Abstract

In this talk, I will discuss my joint paper with Olivier Biquard and Paul Gauduchon on ALF Ricci-flat Riemannian  4-manifolds. My collaborators had previously classified all such spaces that are toric and Hermitian, but not Kaehler. Our main result uses an open curvature condition to prove a rigidity result of the following type: any Ricci-flat metric that is sufficiently close to a non-Kaehler, toric, Hermitian ALF solution (with respect to a norm that imposes reasonable fall-off at infinity) is actually  one of the  known Hermitian toric  solutions. 
 

Fri, 24 Oct 2025
13:00
L6

Generalized Persistent Laplacians and Their Spectral Properties

Arne Wolf
(Imperial College)
Abstract
Laplacian operators are classical objects that are fundamental in both pure and applied mathematics and are becoming increasingly prominent in modern computational and data science fields such as applied and computational topology and application areas such as machine learning and network science. In our recent paper, we introduce a unifying operator-theoretic framework of generalized Laplacians as invariants that encompasses and extends all existing constructions, from discrete combinatorial settings to de Rham complexes of smooth manifolds. Within this framework, we introduce and study a generalized notion of persistent Laplacians. While the classical persistent Laplacian fails to satisfy the desirable properties of monotonicity and stability - both crucial for robustness and interpretability - our framework allows to isolate and analyze these properties systematically.  We demonstrate that their component maps, the up- and down-persistent Laplacians, satisfy these properties individually. Moreover, we provide a condition for full monotonicity and show that the spectra of these separate components fully determine the spectra of the full Laplacians, making them not only preferable but sufficient for analysis. We study these questions comprehensively, in both the finite and infinite dimensional settings. Our work expands and strengthens the theoretical foundation of generalized Laplacian-based methods in pure, applied, and computational mathematics.


 

Fri, 24 Oct 2025

14:00 - 15:00
L1

Making the most of intercollegiate classes

Abstract

What should you expect in intercollegiate classes?  What can you do to get the most out of them?  In this session, experienced class tutors will share their thoughts, and a current student will offer tips and advice based on their experience.

All undergraduate and masters students welcome, especially Part B and MSc students attending intercollegiate classes. (Students who attended the Part C/OMMS induction event will find significant overlap between the advice offered there and this session!)

Mon, 27 Oct 2025
14:15
L4

Hurwitz-Brill-Noether Theory via K3 Surfaces

Sohelya Feyzbakhsh
(Imperial College London)
Abstract

I will discuss the Brill-Noether theory of a general elliptic $K3$ surface using wall-crossing with respect to Bridgeland stability conditions. As an application, I will provide an example of a general $k$-gonal curve from the perspective of Hurwitz-Brill-Noether theory. This is joint work with Gavril Farkas and Andrés Rojas.

Mon, 27 Oct 2025
14:15
L4

Hurwitz-Brill-Noether Theory via K3 Surfaces

Sohelya Feyzbakhsh
(Imperial College London)
Abstract

I will discuss the Brill-Noether theory of a general elliptic 𝐾3 surface using wall-crossing with respect to Bridgeland stability conditions. As an application, I will provide an example of a general 𝑘-gonal curve from the perspective of Hurwitz-Brill-Noether theory. This is joint work with Gavril Farkas and Andrés Rojas.

Mon, 27 Oct 2025
15:30
L3

Stochastic optimal control and large deviations in the space of probability measures

(Centre de Mathématiques Appliquées, École polytechnique )
Abstract

I will present problems a stochastic variant of the classic optimal transport problem as well as a large deviation question for a mean field system of interacting particles. We shall see that those problems can be analyzed by means of a Hamilton-Jacobi equation on the space of probability measures. I will then present the main challenge on such equations as well as the current known techniques to address them. In particular, I will show how the notion of relaxed controls in this setting naturally solve an important difficulty, while being clearly interpretable in terms of geometry on the space of probability measures.

Mon, 27 Oct 2025

16:30 - 17:30
L4

Spatially-extended mean-field PDEs as universal limits of large, heterogeneous networks of spiking neurons

Dr Valentin Schmutz
(University College London)
Abstract

The dynamics of spatially-structured networks of N interacting stochastic neurons can be described by deterministic population equations in the mean-field limit. While this is known, a general question has remained unanswered: does synaptic weight scaling suffice, by itself, to guarantee the convergence of network dynamics to a deterministic population equation, even when networks are not assumed to be homogeneous or spatially structured? In this work, we consider networks of stochastic integrate-and-fire neurons with arbitrary synaptic weights satisfying a O(1/N) scaling condition. Borrowing results from the theory of dense graph limits, or graphons, we prove that, as N tends to infinity, and up to the extraction of a subsequence, the empirical measure of the neurons' membrane potentials converges to the solution of a spatially-extended mean-field partial differential equation (PDE). Our proof requires analytical techniques that go beyond standard propagation of chaos methods. In particular, we introduce a weak metric that depends on the dense graph limit kernel and we show how the weak convergence of the initial data can be obtained by propagating the regularity of the limit kernel along the dual-backward equation associated with the spatially-extended mean-field PDE. Overall, this result invites us to reinterpret spatially-extended population equations as universal mean-field limits of networks of neurons with O(1/N) synaptic weight scaling. This work was done in collaboration with Pierre-Emmanuel Jabin (Penn State) and Datong Zhou (Sorbonne Université).

Tue, 28 Oct 2025
14:00
L6

The representation type of a finite tensor category

Petter Bergh
(NTNU)
Abstract

A finite tensor category is a suitably nice abelian category with a compatible monoidal structure. It makes perfect sense to define the representation type of such a category, as a measure of how complicated the category is in terms of its indecomposable objects. For example, finite representation type means that the category contains only finitely many indecomposable objects, up to isomorphism.  

In this talk, we shall see that if a finite tensor category has finitely generated cohomology, and the Krull dimension of its cohomology ring is at least three, then the category is of wild representation type. This is a report on recent joint work with K. Erdmann, J. Plavnik, and S. Witherspoon. 

Tue, 28 Oct 2025
15:30
L4

TBA

Jakob Stein
(State University of Campinas and University of Oxford)
Tue, 28 Oct 2025
16:00
C3

TBC

Sophie Zegers
(TU Delft)
Abstract

to follow

Wed, 29 Oct 2025

17:00 - 18:00
L5

Will mechanisation change research mathematics?

Ursula Martin
Abstract

A 2024 collection of articles in the Bulletin of the AMS asked "Will machines change mathematics?", suggesting that  "Pure mathematicians are used to enjoying a great degree of research autonomy and intellectual freedom, a fragile and precious heritage that might be swept aside by a mindless use of machines." and challenging readers to  "decide upon our subject’s future direction.”

This was a response to growing awareness of the mathematical capabilities of emerging technologies, alone or in combination. These techniques include  software such as LEAN for  providing formal proofs; use of LLMs to produce credible, if derivative, research papers with expert human guidance; specialist algorithms such as AlphaGeometry; and sophisticated use of machine learning to search for examples.  Their development (at huge cost in compute power and energy) has been accompanied by an unfamiliar and exuberant level of hype from well-funded start-ups claiming to “solve mathematics” and the like.

To try and understand what’s going on we look at the factors,  whether technical, social or economic, leading to the ongoing adoption and impact, or otherwise, of previous computational interventions in mathematical practice. As an example we consider key decisions made in the early days of computational group theory.

Thu, 30 Oct 2025

12:00 - 13:00
L3

Growth, tissue regeneration and active process

Prof. Martine Ben Amar
(Laboratoire de Physique Statistique, École Normale Supérieure, Paris, France)

The join button will be published 30 minutes before the seminar starts (login required).

Further Information

Professor Martine Ben Amar is a theoretical physicist whose work explores the physics and mechanics of soft matter, with applications ranging from fundamental instabilities in solids and fluids to biological growth processes. Her research has addressed phenomena such as dendritic growth, Saffman–Taylor instability, elastic singularities, and morphogenesis in vegetal and animal tissues. More recently, she has focused on the interface between physics and biology, modelling the growth of cancerous tumours through reaction–diffusion equations and studying the role of mechanical stresses in tissue development—work that connects directly with medical applications in collaboration with clinicians.

A graduate in atomic physics, she has taught at UPMC since 1993 and was elected a senior member of the Institut Universitaire de France in 2011. She held the McCarthy Chair at MIT in 1999–2000 and has led the federation Dynamics of Complex Systems, uniting over 200 researchers across Paris institutions. Passionate about science, she describes her vocation as “understanding, showing, and predicting the laws of the universe and life.”

Abstract

When a specimen of non-trivial shape undergoes deformation under a dead load or during an active process, finite element simulations are the only technique for evaluating the deformation. Classical books describe complicated techniques for evaluating stresses and strains in semi-infinite, circular or cylindrical objects.  However, the results obtained are limited, and it is well known that elasticity (linear or nonlinear) is strongly intertwined with geometry. For the simplest geometries, it is possible to determine the exact deformation, essentially for low loading values, and prove that there is a threshold above which the specimen loses stability. The next step is to apply perturbation techniques (linear and nonlinear bifurcation theory).
 

In this talk, I will demonstrate how many aspects can be simplified or revealed through the use of complex analysis and conformal mapping techniques for shapes, strains, and active stresses in thin samples. Examples include leaves and embryonic jellyfish.

 

Thu, 30 Oct 2025

12:00 - 12:30
Lecture Room 4

TBA

Umberto Zerbinati
(Mathematical Institute (University of Oxford))
Abstract

TBA

Thu, 30 Oct 2025

14:00 - 15:00
Lecture Room 3

Sparse Graphical Linear Dynamical Systems

Emilie Chouzenoux
(INRIA Saclay, France)
Abstract

Time-series datasets are central in numerous fields of science and engineering, such as biomedicine, Earth observation, and network analysis. Extensive research exists on state-space models (SSMs), which are powerful mathematical tools that allow for probabilistic and interpretable learning on time series. Estimating the model parameters in SSMs is arguably one of the most complicated tasks, and the inclusion of prior knowledge is known to both ease the interpretation but also to complicate the inferential tasks. In this talk, I will introduce a novel joint graphical modeling framework called DGLASSO (Dynamic Graphical Lasso) [1], that bridges the static graphical Lasso model [2] and the causal-based graphical approach for the linear-Gaussian SSM in [3]. I will also present a new inference method within the DGLASSO framework that implements an efficient block alternating majorization-minimization algorithm. The algorithm's convergence is established by departing from modern tools from nonlinear analysis. Experimental validation on synthetic and real weather variability data showcases the effectiveness of the proposed model and inference algorithm.

 

[1] E. Chouzenoux and V. Elvira. Sparse Graphical Linear Dynamical Systems. Journal of Machine Learning Research, vol. 25, no. 223, pp. 1-53, 2024

[2] J. Friedman, T. Hastie, and R. Tibshirani. Sparse inverse covariance estimation with the graphical LASSO. Biostatistics, vol. 9, no. 3, pp. 432–441, Jul. 2008.

[3] V. Elvira and E. Chouzenoux. Graphical Inference in Linear-Gaussian State-Space Models. IEEE Transactions on Signal Processing, vol. 70, pp. 4757-4771, Sep. 2022.

 

 

Thu, 30 Oct 2025
16:00
L6

TBC

Mikael de la Salle
(CNRS)
Abstract

to follow

Thu, 30 Oct 2025
16:00
L5

A rough path approach to pathwise stochastic integration a la Follmer

Anna Kwossek
(University of Vienna)
Abstract

We develop a general framework for pathwise stochastic integration that extends Follmer's classical approach beyond gradient-type integrands and standard left-point Riemann sums and provides pathwise counterparts of Ito, Stratonovich, and backward Ito integration. More precisely, for a continuous path admitting both quadratic variation and Levy area along a fixed sequence of partitions, we define pathwise stochastic integrals as limits of general Riemann sums and prove that they coincide with integrals defined with respect to suitable rough paths. Furthermore, we identify necessary and sufficient conditions under which the quadratic variation and the Levy area of a continuous path are invariant with respect to the choice of partition sequences.

Fri, 31 Oct 2025

11:00 - 12:00
L4

Approximations of systems of partial differential equations for nonlocal interactions

Professor Yoshitaro Tanaka
(Department of Complex and Intelligent Systems School of Systems Information Science Future University Hakodate)
Abstract

Motivated by pattern formations and cell movements, many evolution equations incorporating spatial convolution with suitable integral kernel have been proposed. Numerical simulations of these nonlocal evolution equations can reproduce various patterns depending on the shape and form of integral kernel.The solutions to nonlocal evolution equations are similar to the patterns obtained by reaction-diffusion system and Keller-Segel system models. In this talk, we classify nonlocal interactions into two types, and investigate their relationship with reaction-diffusion systems and Keller-Segel systems, respectively. In these partial differential equation systems, we introduce multiple auxiliary diffusive substances and consider the singular limit of the quasi-steady state to approximate nonlocal interactions. In particular, we introduce how the parameters of the partial differential equation system are determined by the given integral kernel. These analyses demonstrate that, under certain conditions, nonlocal interactions and partial differential equation systems can be treated within a unified framework.  
This talk is based on collaborations with Hiroshi Ishii of Hokkaido University and Hideki Murakawa of Ryukoku University. 

Fri, 31 Oct 2025

11:00 - 12:00
L1

What does a good maths solution look like?

Abstract

We'll discuss what mathematicians are looking for in written solutions.  How can you set out your ideas clearly, and what are the standard mathematical conventions?

This session is likely to be most relevant for first-year undergraduates, but all are welcome.

Fri, 31 Oct 2025

12:00 - 13:00
N2.37

Mathematrix: Mental Health as a Grad Student with Prof Ian Griffiths

Prof Ian Griffiths
(Mathematrix)
Abstract

Prof Ian Griffiths (a mental health first aider in the department) will lead a discussion about how to protect your mental health when studying an intense graduate degree and outline the support and resources available within the Mathematical Institute. 

Mon, 03 Nov 2025

14:00 - 15:00
Lecture Room 3

A Langevin sampler for quantum tomography

Dr Estelle Massart
(Université catholique de Louvain (Belgium))
Abstract

Quantum tomography involves obtaining a full classical description of a prepared quantum state from experimental results. We propose a Langevin sampler for quantum tomography, that relies on a new formulation of Bayesian quantum tomography exploiting the Burer-Monteiro factorization of Hermitian positive-semidefinite matrices. If the rank of the target density matrix is known, this formulation allows us to define a posterior distribution that is only supported on matrices whose rank is upper-bounded by the rank of the target density matrix. Conversely, if the target rank is unknown, any upper bound on the rank can be used by our algorithm, and the rank of the resulting posterior mean estimator is further reduced by the use of a low-rank promoting prior density. This prior density is a complex extension of the one proposed in [Annales de l’Institut Henri Poincaré Probability and Statistics, 56(2):1465–1483, 2020]. We derive a PAC-Bayesian bound on our proposed estimator that matches the best bounds available in the literature, and we show numerically that it leads to strong scalability improvements compared to existing techniques when the rank of the density matrix is known to be small.

 

Mon, 03 Nov 2025
14:15
L4

Intersection cohomology of symplectic implosions

Andrew Dancer
(Oxford University)
Abstract

Symplectic implosion is an abelianisation construction in symplectic geometry. The implosion of the cotangent bundle of a group K plays a universal role in the implosion of manifolds with a K-action.  This universal implosion, which is usually a singular variety, can also be viewed as the non-reductive Geometric Invariant Theory quotient of the complexification G of K by its maximal unipotent subgroup. 

In this talk, we describe joint work with Johan Martens and Nick Proudfoot which uses point-counting techniques to calculate the intersection cohomology of the universal implosion.