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.

 

Wed, 28 Sep 2022 09:00 -
Tue, 30 Jun 2026 17:00
Mathematical Institute

Cascading Principles - a major mathematically inspired art exhibition by Conrad Shawcross - extended until June 2026

Further Information

Oxford Mathematics is delighted to be hosting one of the largest exhibitions by the artist Conrad Shawcross in the UK. The exhibition, Cascading Principles: Expansions within Geometry, Philosophy, and Interference, brings together over 40 of Conrad's mathematically inspired works from the past seventeen years. Rather than in a gallery, they are placed in the working environment of the practitioners of the subject that inspired them, namely mathematics.

Conrad Shawcross models scientific thought and reasoning within his practice. Drawn to mathematics, physics, and philosophy from the early stages of his artistic career, Shawcross combines these disciplines in his work. He places a strong emphasis on the nature of matter, and on the relativity of gravity, entropy, and the nature of time itself. Like a scientist working in a laboratory, he conceives each work as an experiment. Modularity is key to his process and many works are built from a single essential unit or building block. If an atom or electron is a basic unit for physicists, his unit is the tetrahedron.

Unlike other shapes, a tetrahedron cannot tessellate with itself. It cannot cover or form a surface through its repetition - one tetrahedron is unable to fit together with others of its kind. Whilst other shapes can sit alongside one another without creating gaps or overlapping, tetrahedrons cannot resolve in this way. Shawcross’ Schisms are a perfect demonstration of this failure to tessellate. They bring twenty tetrahedrons together to form a sphere, which results in a deep crack and ruptures that permeate its surface. This failure of its geometry means that it cannot succeed as a scientific model, but it is this very failure that allows it to succeed as an art work, the cracks full of broad and potent implications.

The show includes all Conrad's manifold geometric and philosophical investigations into this curious, four-surfaced, triangular prism to date. These include the Paradigms, the Lattice Cubes, the Fractures, the Schisms, and The Dappled Light of the Sun. The latter was first shown in the courtyard of the Royal Academy and subsequently travelled all across the world, from east to west, China to America.

The show also contains the four Beacons. Activated like a stained-glass window by the light of the sun, they are composed of two coloured, perforated disks moving in counter rotation to one another, patterning the light through the non-repeating pattern of holes, and conveying a message using semaphoric language. These works are studies for the Ramsgate Beacons commission in Kent, as part of Pioneering Places East Kent.

The exhibition Cascading Principles: Expansions within Geometry, Philosophy, and Interference is curated by Fatoş Üstek, and is organised in collaboration with Oxford Mathematics. 

The exhibition is open 9am-5pm, Monday to Friday. Some of the works are in the private part of the building and we shall be arranging regular tours of that area. If you wish to join a tour please email @email.

The exhibition runs until 30 June 2026. You can see and find out more here.

Watch the four public talks centred around the exhibition (featuring Conrad himself).

The exhibition is generously supported by our longstanding partner XTX Markets.

Images clockwise from top left of Schism, Fracture, Paradigm and Axiom

Schism Fracture

Axiom Paradigm

Fri, 28 Feb 2025 09:00 -
Wed, 31 Dec 2025 00:00
Mezzanine

Kathleen Hyndman - Nature+Maths=Art

Further Information

The Mathematical Institute is delighted to be hosting a major exhibition of artist Kathleen Hyndman's mathematically inspired work.

The exhibition of drawings and paintings illustrate Hyndman’s desire to see nature and the world around her in mathematical sequences and geometrical patterns. Golden Section proportions and angles, prime numbers as well as Fibonacci numbers and eccentric constructions are all used to create works achieving a calm and balanced unity.

Born in Essex, Hyndman trained at Kingston-upon-Thames School of Art and exhibited widely in the UK and abroad, including MOMA Oxford and the Hayward Annual in London. As well as a full time artist, she was also a teacher and mother of two. She lived and had her studio in Kingston Bagpuize in Oxfordshire and had exhibitions at Zuleika Gallery in Woodstock until her death in 2022.

Open Monday to Friday 9am to 5pm.

The exhibition is curated by Zuleika Gallery and Professor Martin Kemp FBA, and will run until the end of the year.

Exhibition brochure

Bottom from left:  Hot Breeze, 1994; Heat, 1976; Exit (a seventeen sided work), 1993; Straight Line Rotation, White on Black. Forest, 1986

Below: film of the exhibition by Evan Nedyalkov

Mon, 20 Oct 2025
14:15
L4

Einstein constants and differential topology

Claude LeBrun
(Stony Brook University)
Abstract

A Riemannian metric is said to be  Einstein if it has constant Ricci curvature. In dimensions 2 or 3, this is actually equivalent to requiring the metric to have constant sectional curvature. However,  in dimensions 4 and higher, the Einstein condition becomes significantly weaker than constant sectional curvature, and this has rather dramatic consequences. In particular, it turns out that there are  high-dimensional smooth closed manifolds that admit pairs of Einstein metrics with Ricci curvatures of opposite signs. After explaining how one constructs such examples, I will then discuss some recent results exploring the coexistence of Einstein metrics with zero and positive Ricci curvatures.

Mon, 20 Oct 2025
15:30
L5

Skein modules are holonomic 

David Jordan
(University of Edinburgh)
Abstract
Abstract:  Skein modules capture vector spaces of line operators in 3D Chern-Simons, equivalently line operators constrained to a 3-dimensional boundary in the Kapustin-Witten twist of 4D N=4 gauge theory.  They have an elementary mathemical definition via representation theory of quantum groups.
 
In recent work with Iordanis Romaidis we proved that when the quantum parameter is generic, the skein module of a 3-manifold is finitely generated relative to the skein algebra of its boundary and that moreover the resulting singular support variety is Lagrangian, hence that skein modules are holonomic. Our results confirm and strengthen a conjecture of Detcherry, and imply a conjecture of Frohman, Gelca and LoFaro from 2002 (the latter independently established this year by Beletti and Detcherry using other methods).
 
In the talk I will give an outline of the key ingredients of the proof, which recreate elements of the classical theory of differential operators in the skein setting. 

 
Mon, 20 Oct 2025
15:30
L3

Identifying Bass martingales via gradient descent

Walter Schachermayer
(University of Vienna)
Abstract

Brenier’s theorem and its Benamou-Brenier variant play a pivotal role
in optimal transport theory. In the context of martingale transport
there is a perfect analogue, termed stretched Brownian motion. We
show that under a natural irreducibility condition this leads to the
notion of Bass martingales.
For given probability measures µ and ν on Rn in convex order, the
Bass martingale is induced by a probability measure α. It is the min-
imizer of a convex functional, called the Bass functional. This implies
that α can be found via gradient descent. We compare our approach
to the martingale Sinkhorn algorithm introduced in dimension one by
Conze and Henry-Labordere.

Mon, 20 Oct 2025
16:00
C3

TBC

Zachary Feng
(University of Oxford)
Abstract

TBC

Mon, 20 Oct 2025

16:30 - 17:30
L4

On non-isothermal flows of dilute incompressible polymeric fluids

Prof Josef Málek
(Faculty of Mathematics and Physics Charles University Prague)
Abstract

 In the first part of the talk, after revisiting some classical models for dilute polymeric fluids, we show that thermodynamically 
consistent models for non-isothermal flows of such fluids can be derived in a very elementary manner. Our approach is based on identifying the 
energy storage mechanisms and entropy production mechanisms in the fluid of interest, which in turn leads to explicit formulae for the Cauchy 
stress tensor and for all the fluxes involved. Having identified these mechanisms, we first derive the governing system of nonlinear partial 
differential equations coupling the unsteady incompressible temperature-dependent Navier–Stokes equations with a 
temperature-dependent generalization of the classical Fokker–Planck equation and an evolution equation for the internal energy. We then 
illustrate the potential use of the thermodynamic basis on a rudimentary stability analysis—specifically, the finite-amplitude (nonlinear) 
stability of a stationary spatially homogeneous state in a thermodynamically isolated system.

In the second part of the talk, we show that sequences of smooth solutions to the initial–boundary-value problem, which satisfy the 
underlying energy/entropy estimates (and their consequences in connection with the governing system of PDEs), converge to weak 
solutions that satisfy a renormalized entropy inequality. The talk is based on joint results with Miroslav Bulíček, Mark Dostalík, Vít Průša 
and Endré Süli.

Mon, 20 Oct 2025

16:30 - 17:30
L3

How to choose a model? A consequentialist approach

Prof. Thaleia Zariphopoulou
(University of Texas at Austin)
Abstract

Mathematical modelling and stochastic optimization are often based on the separation of two stages: At the first stage, a model is selected out of a family of plausible models and at the second stage, a policy is chosen that optimizes an underlying objective as if the chosen model were correct. In this talk, I will introduce a new approach which, rather than completely isolating the two stages, interlinks them dynamically. I will first introduce the notion of “consequential performance” of each  model and, in turn, propose a “consequentialist criterion for model selection” based on the expected utility of consequential performances. I will apply the approach to continuous-time portfolio selection and derive a key system of coupled PDEs and solve it for representative cases. I will, also, discuss the connection of the new approach with the popular methods of robust control and of unbiased estimators.   This is joint work with M. Strub (U. of Warwick)

Tue, 21 Oct 2025
12:30
C3

Mathematical modelling of a mass-conserving electrolytic cell

Georgina Ryan, OCIAM
Abstract

The electrochemical processes in electrolytic cells are the basis for modern energy technology such as batteries. Electrolytic cells consist of an electrolyte (an salt dissolved in solution), two electrodes, and a battery. The Poisson–Nernst–Planck equations are the simplest mathematical model of steady state ionic transport in an electrolytic cell. We find the matched asymptotic solutions for the ionic concentrations and electric potential inside the electrolytic cell with mass conservation and known flux boundary conditions. The mass conservation condition necessitates solving for a higher order solution in the outer region. Our results provide insight into the behaviour of an electrochemical system with a known voltage and current, which are both experimentally measurable quantities.

Tue, 21 Oct 2025
14:00
L6

Profinite Rigidity, Noetherian Domains, and Solvable Groups

Julian Wykowski
(Cambridge)
Abstract

The question of profinite rigidity asks whether the isomorphism type of a group Γ can be recovered entirely from its finite quotients. In this talk, I will introduce the study of profinite rigidity in a different setting: the category of modules over a Noetherian domain Λ. I will explore properties of Λ-modules that can be detected in finite quotients and present two profinite rigidity theorems: one for free Λ-modules under a weak homological assumption on Λ, and another for all Λ-modules in the case when Λ is a Dedekind domain. Returning to groups, I will explain how these algebraic results yield new answers to profinite rigidity for certain classes of solvable groups. Time permitting, I will conclude with a sketch of future directions and ongoing collaborations that push these ideas further.

Tue, 21 Oct 2025

14:00 - 15:00
L4

TBA

Omer Angel
(University of British Columbia)
Tue, 21 Oct 2025

14:00 - 15:00
L3

Optimal control of the Dyson equation and large deviations for Hermitian random matrices

Prof Panagiotis E. Souganidis
(University of Chicago)
Abstract

Using novel arguments as well as techniques developed over the last  twenty years to study mean field games, in this paper (i) we investigate the optimal control of the Dyson equation, which is the mean field equation for the so-called Dyson Brownian motion, that is, the stochastic particle system satisfied by the eigenvalues of large random matrices, (ii) we establish the well-posedness of the resulting infinite dimensional Hamilton-Jacobi equation, 
(iii) we provide a complete and direct proof for the large deviations for the spectrum of large random matrices, and (iv) we study the asymptotic behavior of the transition probabilities of the Dyson Brownian motion.  Joint work with Charles Bertucci and Pierre-Louis Lions.

Tue, 21 Oct 2025
15:30
L4

Vector fields on intrinsic mirrors

Mark Gross
(Cambridge)
Abstract
Siebert and I gave a general construction of mirror partners to log
Calabi-Yau pairs, we called these mirror partners "intrinsic mirrors". This talk
is about a small part of a larger project with Pomerleano and Siebert aimed
at understanding this construction at a deeper level. I will explain how to
construct vector fields on the mirror using enumerative geometry of the original
log Calabi-Yau pair.
Tue, 21 Oct 2025
16:00
C3

On dense subalgebras of the singular ideal in groupoid C*-algebras

Julian Gonzales
(University of Glasgow)
Abstract

Groupoids provide a rich supply of C*-algebras, and there are many results describing the structure of these C*-algebras using properties of the underlying groupoid. For non-Hausdorff groupoids, less is known, largely due to the existence of 'singular' functions in the reduced C*-algebra. This talk will discuss two approaches to studying ideals in non-Hausdorff groupoid C*-algebras. The first uses Timmermann's Hausdorff cover to reduce certain problems to the setting of Hausdorff groupoids. The second will restrict to isotropy groups. For amenable second-countable étale groupoids, these techniques allow us to characterise when the ideal of singular functions has dense intersection with the underlying groupoid *-algebra. This is based on joint work with K. A. Brix, J. B. Hume, and X. Li, as well as upcoming work with J. B. Hume.

Tue, 21 Oct 2025

16:00 - 17:00
L6

Randomness in the spectrum of the Laplacian: from flat tori to hyperbolic surfaces of high genus

Jens Marklof
(University of Bristol)
Further Information

(Joint seminar with OxPDE) 

Abstract

I will report on recent progress on influential conjectures from the 1970s and 1980s (Berry-Tabor, Bohigas-Giannoni-Schmit), which suggest that the spectral statistics of the Laplace-Beltrami operator on a given compact Riemannian manifold should be described either by a Poisson point process or by a random matrix ensemble, depending on whether the  geodesic flow is integrable or “chaotic”. This talk will straddle aspects of analysis, geometry, probability, number theory and ergodic theory, and should be accessible to a broad audience. The two most recent results presented in this lecture were obtained in collaboration with Laura Monk and with Wooyeon Kim and Matthew Welsh. 

Tue, 21 Oct 2025

16:00 - 17:00
L6

Randomness in the Spectrum of the Laplacian: From Flat Tori to Hyperbolic Surfaces of High Genus

Prof. Jens Marklof
(University of Bristol )
Abstract

I will report on recent progress on influential conjectures from the 1970s and 1980s (Berry-Tabor, Bohigas-Giannoni-Schmit), which suggest that the spectral statistics of the Laplace-Beltrami operator on a given compact Riemannian manifold should be described either by a Poisson point process or by a random matrix ensemble, depending on whether the  geodesic flow is integrable or “chaotic”. This talk will straddle aspects of analysis, geometry, probability, number theory and ergodic theory, and should be accessible to a broad audience. The two most recent results presented in this lecture were obtained in collaboration with Laura Monk and with Wooyeon Kim and Matthew Welsh. 

Wed, 22 Oct 2025

13:00 - 14:00
Quillen Room N3.12

Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity

Tabea Sieper
Abstract

Just as parallel threebranes on a smooth manifold are related to string theory on AdS_5 \times S^5, parallel threebranes near a conical singularity are related to string theory on AdS_5 \times X_5 for a suitable X_5. For the example of the conifold singularity Klebanov and Witten conjectured that a string theory on AdS_5 \times X^5 can be described by a certain \mathcal{N}=1 supersymmetric gauge theory. Based primarily on their work (arXiv:hep-th/9807080), I describe the gravitational setup of this correspondence as well as their construction of the field theory, allowing for various checks of the duality.

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.


 

Wed, 22 Oct 2025

14:30 - 15:30
N3.12

Mathematrix Book Club

(Mathematrix)
Abstract

Join us for the inaugural session of Mathematrix book club! Have you heard that office workplaces often have the thermostat set at a temperature that is too cold for women to work comfortably? This month we will be discussing the academic articles behind concepts that often come up in conversations about gender inequality in the workplace. The goal of book club is to develop an evidence-based understanding of diversity in mathematics and academia. 

 

Thu, 23 Oct 2025

12:00 - 13:00
L3

Master Stability for Traveling Waves on Networks

Stefan Ruschel
(University of Leeds)

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

Further Information

Stefan Ruschel’s research focuses on dynamical systems theory and its applications to nonlinear optics and mathematical biology, among others. He specialises in analytical and numerical methods for delay differential and functional differential equations when the delay is large compared to other time scales of the system. His specific contributions include work on the fixed point spectrum for large delay, as well as the characterisation of slowly oscillating solutions such as travelling pulses and waves.

His future research is dedicated to applying these techniques to delay and lattice dynamical systems arising from coupled excitable and coupled bi-stable systems in laser dynamics and neuroscience, where such solutions play an important role in data transmission and neural signal propagation.

He is currently a research fellow at the University of Leeds (UK), funded by UKRI in recognition of a Horizon Europe MSCA award post-Brexit.

Abstract

 I will present a new framework for determining effectively the spectrum and stability of traveling waves on networks with symmetries, such as rings and lattices, by computing master stability curves (MSCs). Unlike traditional methods, MSCs are independent of system size and can be readily used to assess wave destabilization and multi-stability in small and large networks.

 

 

 

Thu, 23 Oct 2025

12:00 - 12:30
Lecture Room 4

Stabilisation of the Navier⁠–Stokes equations on under-resolved meshes via enstrophy preservation

Boris Andrews
(Mathematical Institute (University of Oxford))
Abstract

The typical energy estimate for the Navier-Stokes equations provides a bound for the gradient of the velocity; energy-stable numerical methods that preserve this estimate preserve this bound. However, the bound scales with the Reynolds number (Re) causing solutions to be numerically unstable (i.e. exhibit spurious oscillations) on under-resolved meshes. The dissipation of enstrophy on the other hand provides, in the transient 2D case, a bound for the gradient that is independent of Re.

 

We propose a finite-element integrator for the Navier-Stokes equations that preserves the evolution of both the energy and enstrophy, implying gradient bounds that are, in the 2D case, independent of Re. Our scheme is a mixed velocity-vorticity discretisation, making use of a discrete Stokes complex. While we introduce an auxiliary vorticity in the discretisation, the energy- and enstrophy-stability results both hold on the primal variable, the velocity; our scheme thus exhibits greater numerical stability at large Re than traditional methods.

 

We conclude with a demonstration of numerical results, and a discussion of the existence and uniqueness of solutions.

Thu, 23 Oct 2025

13:00 - 14:00
Lecture Room 5

Markov α-potential games

Xinyu Li
(Mathematical Institute (University of Oxford))
Abstract

We propose a new framework of Markov α-potential games to study Markov games. 

We show that any Markov game with finite-state and finite-action is a Markov α-potential game, and establish the existence of an associated α-potential function. Any optimizer of an α-potential function is shown to be an α-stationary Nash equilibrium. We study two important classes of practically significant Markov games, Markov congestion games and the perturbed Markov team games, via the framework of Markov α-potential games, with explicit characterization of an upper bound for αand its relation to game parameters. 

Additionally, we provide a semi-infinite linear programming based formulation to obtain an upper bound for α for any Markov game. 

Furthermore, we study two equilibrium approximation algorithms, namely the projected gradient- ascent algorithm and the sequential maximum improvement algorithm, along with their Nash regret analysis.

 

This talk is part of the Erlangen AI Hub.

 

 

 

Thu, 23 Oct 2025

14:00 - 15:00
(This talk is hosted by Rutherford Appleton Laboratory)

TBA

Paul Goulart
(Oxford University)
Abstract

TBA

 

 

 

This talk is hosted by Rutherford Appleton Laboratory and will take place @ Harwell Campus, Didcot, OX11 0QX

Thu, 23 Oct 2025
14:00
L4

Multifold Schwinger-Keldysh EFT -- what I understand and what I don't

Akash Jain
Abstract

The organisers asked me to give a brief talk on what I’ve been thinking about lately. So, I’ll tell you about Schwinger-Keldysh EFTs: an EFT framework for non-equilibrium dissipative systems such as hydrodynamics. These are built on a closed-time contour that runs forward and backward in time, allowing access to a variety of non-equilibrium observables. However, these EFTs fundamentally miss a wider class of observables, called out-of-time-ordered correlators (OTOCs), which are closely tied to quantum chaos. In this talk, I’ll share some thoughts on extending Schwinger-Keldysh EFTs to multifold contours that capture such observables. I’ll also touch on the discrete KMS symmetry of thermal systems, which generalises from Z_2 in the single-fold case to the dihedral group in the -fold case. With any luck, I’ll reach the point where I’m stuck and you can help me figure it out.

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.