Feb 24 (Tue)
13:00 MCS2068 APDEZoe Wyatt (University of Cambridge): Stability for relativistic fluids on slowly expanding cosmological spacetimes
On a background Minkowski spacetime, the Euler equations (both relativistic and not) are known to admit unstable homogeneous solutions with finite-time shock formation. Such shock formation can be suppressed on cosmological spacetimes whose spatial slices expand at an accelerated rate. However, situations with decelerated expansion, which are relevant in our early universe, are not as well understood. I will present some recent joint work in this direction, based on collaborations with David Fajman, Maciej Maliborski, Todd Oliynyk and Max Ofner.
Venue: MCS2068
14:00 MCS2068 ASGOleksiy Klurman (University of Bristol): Distribution of character sums and extremal problems of Littlewood
I will talk about the distribution of character sums twisted by exponentials. I will show how to use such results to make progress on an old problem of Mahler (constructing polynomials with coefficients -1 and +1 with large Mahler measure), as well as on minimizing the L_p norms of well-known Turyn and Fekete polynomials.
Venue: MCS2068
Feb 26 (Thu)
13:00 MCS2068 G&TBrendan Guilfoyle (Munster Technological University): Umbilic index bounds and holomorphic discs
In this talk I will outline the proof of a bound on the
index of isolated umbilic points on a convex surface in Euclidean
3-space. The proof involves an associated elliptic boundary value
problem for which the Fredholm index is related to the umbilic index.
The existence of holomorphic discs, established in a recently published
paper with Wilhelm Klingenberg, is shown to bound this index. The other
ingredients of the proof are the h-principle for Lagrangian surfaces and
a construction which attaches a cross-cap to a surface and cancels
hyperbolic points.
Venue: MCS2068
14:00 MCS2068 ProbChristina Goldschmidt (Department of Statistics, University of Oxford): The stable trees revisited
Consider the family tree of a branching process with offspring distribution (p_k)_{k \ge 0} of mean 1 and with a heavy tail such that p_k \sim c k^{-\alpha - 1} as k \to \infty, for some constant c > 0 and \alpha \in (1,2). (This implies that the offspring distribution is in the domain of attraction of an \alpha-stable distribution.) Now condition the tree to have exactly n vertices. It is a well-known theorem (originally due to Duquesne) that distances in the tree vary as n^{1/\alpha} and, on rescaling them by this factor, we obtain a limit in distribution as n \to \infty called the stable tree. In this talk, Ill discuss a new (simple) construction of the stable trees, and indicate how to give a proof of the scaling limit theorem using it. This is joint work with Liam Hill (https://arxiv.org/abs/2512.17533).
Venue: MCS2068
Feb 27 (Fri)
13:00 MCS0001 HEPMPaul Fendley (Oxford University): The uses of lattice non-invertible dualities and symmetries
I will describe a variety of applications of non-invertible symmetries and dualities. One use is to extend Kramers-Wannier duality to a large class of models, explaining exact degeneracies between non-(conventional) symmetry-related ground states as well as in the low-energy spectrum. For critical models, the universal behaviour under Dehn twists gives exact results for scaling dimensions, while gluing a topological defect to a boundary allows universal ratios of the boundary g-factor to be computed exactly on the lattice.
Venue: MCS0001
Mar 02 (Mon)
13:00 Teams StatHelen Ogden (Southampton): Adaptively-Structured Mixed Models for Simple Clustered Data
I will describe a new class of flexible mixed-effects models for simple clustered or longitudinal data. The idea of these Adaptively-Structured Mixed Models (AdaStruMMs) is to replace pre-specified random-effects structure by unknowns to be estimated. AdaStruMMs meet three requirements, at least one of which is unmet by all existing approaches I have considered:
1. Sufficient flexibility to represent individual trajectories as arbitrary smooth curves.
2. Information sharing between individuals to exploit structural similarities.
3. Accurate estimation of individual trajectories and population summaries across different data structures.
I will demonstrate the high-quality inference offered by AdaStruMMs through a range of simulations, and give some ideas about visualising and interpreting model fit through an example on changes in body composition in adolescent girls.
Venue: Teams
Mar 03 (Tue)
13:00 MCS2068 APDEHarry Wells (University College London): A posteriori error estimation for stabilised finite element method approximations of partial differential equations
Finite Element Methods (FEMs) are a popular numerical framework for solving partial differential equations (PDEs). Within the vast literature of FEMs exists a class of stabilised FEMs, designed to counteract the numerical artifacts and instabilities frequently introduced by standard methods. Classic examples of problems that require these stabilised methods include convection-dominated transport equations.
One way to assess the performance and accuracy of a FEM is through an a posteriori error bound. The primary benefit of this approach is the ability to bound the numerical error using an estimator function that requires no explicit knowledge of the exact, analytical solution. However, guaranteeing the reliability and efficiency of such estimators becomes a challenge when the numerical solution has been computed using stabilisation techniques.
In this talk, I will present theoretical results concerning the a posteriori error analysis of these stabilised schemes. In particular, I will detail how to design a stabilisation scheme such that it does not influence the reliability or efficiency of the a posteriori error bound whilst still enforcing the desired mathematical properties. The talk will conclude by applying this general a posteriori error analysis to the numerical approximation of Mean-Field Games (MFGs). The practical benefits of these results will be demonstrated through the implementation of Adaptive FEMs, showcasing how these estimators can be used to improve computational efficiency.
Venue: MCS2068
14:00 MCS2068 ASGHeejong Lee (KIAS (Korea Institute For Advanced Study)): Serre weight conjectures and modularity lifting for GSp4
Given a Galois representation attached to a regular algebraic cuspidal automorphic representation, the Hodge--Tate weight of the Galois representation is matched with the weight of the automorphic representation. Serre weight conjectures are mod p analogue of such a correspondence, relating ramification at p of a mod p Galois representation and Serre weights of mod p algebraic automorphic forms. In this talk, I will discuss how to understand Serre weight conjectures and modularity lifting as a relationship between representation theory of finite groups of Lie type (e.g. GSp4(Fp)) and the geometry of p-adic local Galois representations. Then I will explain the proof idea in the case of GSp4. This is based on a joint work with Daniel Le and Bao V. Le Hung.
Venue: MCS2068
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Usual Venue: MCS2068
Contact: yohance.a.osborne@durham.ac.uk
Feb 24 13:00 Zoe Wyatt (University of Cambridge): Stability for relativistic fluids on slowly expanding cosmological spacetimes
On a background Minkowski spacetime, the Euler equations (both relativistic and not) are known to admit unstable homogeneous solutions with finite-time shock formation. Such shock formation can be suppressed on cosmological spacetimes whose spatial slices expand at an accelerated rate. However, situations with decelerated expansion, which are relevant in our early universe, are not as well understood. I will present some recent joint work in this direction, based on collaborations with David Fajman, Maciej Maliborski, Todd Oliynyk and Max Ofner.
Venue: MCS2068
Mar 03 13:00 Harry Wells (University College London): A posteriori error estimation for stabilised finite element method approximations of partial differential equations
Finite Element Methods (FEMs) are a popular numerical framework for solving partial differential equations (PDEs). Within the vast literature of FEMs exists a class of stabilised FEMs, designed to counteract the numerical artifacts and instabilities frequently introduced by standard methods. Classic examples of problems that require these stabilised methods include convection-dominated transport equations.
One way to assess the performance and accuracy of a FEM is through an a posteriori error bound. The primary benefit of this approach is the ability to bound the numerical error using an estimator function that requires no explicit knowledge of the exact, analytical solution. However, guaranteeing the reliability and efficiency of such estimators becomes a challenge when the numerical solution has been computed using stabilisation techniques.
In this talk, I will present theoretical results concerning the a posteriori error analysis of these stabilised schemes. In particular, I will detail how to design a stabilisation scheme such that it does not influence the reliability or efficiency of the a posteriori error bound whilst still enforcing the desired mathematical properties. The talk will conclude by applying this general a posteriori error analysis to the numerical approximation of Mean-Field Games (MFGs). The practical benefits of these results will be demonstrated through the implementation of Adaptive FEMs, showcasing how these estimators can be used to improve computational efficiency.
Venue: MCS2068
Mar 10 13:00 Thomas Sales (University of Sussex): Fully nonlinear mean field games with nondifferentiable Hamiltonians
Mean field games are systems of partial differential equations modelling the Nash equilibria of dynamic differential games for large populations of players. In their full generality this system is fully nonlinear and may involve a nondifferentiable Hamiltonian - in which case not only is the analysis more involved than the usual quasilinear case (with a differentiable Hamiltonian), but even the statement of the problem is not so obvious. In this talk, we discuss a novel approach to studying this problem by introducing a non-standard variational inequality formulation. Under reasonable assumptions, such as assuming the Hamiltonian satisfies a uniform Cordes condition, we show that this variational inequality formulation admits a solution and moreover this solution is unique under the usual monotonicity assumptions. This talk is based on joint work with Iain Smears (UCL).
Venue: MCS2068
Usual Venue: MCS3070
Contact: andrew.krause@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS2068
Contact: herbert.gangl@durham.ac.uk
Feb 24 14:00 Oleksiy Klurman (University of Bristol): Distribution of character sums and extremal problems of Littlewood
I will talk about the distribution of character sums twisted by exponentials. I will show how to use such results to make progress on an old problem of Mahler (constructing polynomials with coefficients -1 and +1 with large Mahler measure), as well as on minimizing the L_p norms of well-known Turyn and Fekete polynomials.
Venue: MCS2068
Mar 03 14:00 Heejong Lee (KIAS (Korea Institute For Advanced Study)): Serre weight conjectures and modularity lifting for GSp4
Given a Galois representation attached to a regular algebraic cuspidal automorphic representation, the Hodge--Tate weight of the Galois representation is matched with the weight of the automorphic representation. Serre weight conjectures are mod p analogue of such a correspondence, relating ramification at p of a mod p Galois representation and Serre weights of mod p algebraic automorphic forms. In this talk, I will discuss how to understand Serre weight conjectures and modularity lifting as a relationship between representation theory of finite groups of Lie type (e.g. GSp4(Fp)) and the geometry of p-adic local Galois representations. Then I will explain the proof idea in the case of GSp4. This is based on a joint work with Daniel Le and Bao V. Le Hung.
Venue: MCS2068
Usual Venue: OC218
Contact: mohamed.anber@durham.ac.uk
For more information, see HERE.
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS3052
Contact: andrew.krause@durham.ac.uk
Mar 05 14:15 Jessica Banks (Liverpool): All Things to All Students
The new MSc in Applied Statistics and Data Science in the Department of Mathematical Sciences at the University of Liverpool is open to students from a diverse range of backgrounds. I lead the teaching of the first 6 weeks of the programme, which aim to establish a common foundation in mathematics, statistics and programming. In this talk I will discuss the practicalities of how I approached this in the technological world of mid-2025 and what I hope to adapt for 2026.
Venue: MCS2050
Usual Venue: MCS2068
Contact: fernando.galaz-garcia@durham.ac.uk
Feb 26 13:00 Brendan Guilfoyle (Munster Technological University): Umbilic index bounds and holomorphic discs
In this talk I will outline the proof of a bound on the
index of isolated umbilic points on a convex surface in Euclidean
3-space. The proof involves an associated elliptic boundary value
problem for which the Fredholm index is related to the umbilic index.
The existence of holomorphic discs, established in a recently published
paper with Wilhelm Klingenberg, is shown to bound this index. The other
ingredients of the proof are the h-principle for Lagrangian surfaces and
a construction which attaches a cross-cap to a surface and cancels
hyperbolic points.
Venue: MCS2068
Mar 05 13:00 Ben Lambert and Julian Scheuer (Leeds and Goethe University Frankfurt): Foliations of null hypersurfaces by surfaces of constant
spacetime mean curvature near MOTS
Recently, a new mean curvature flow in null hypersurfaces
was studied to prove the existence of MOTS under some relatively weak
assumptions on the null hypersurface. In a continuation of this
approach, together with Wilhelm Klingenberg we prove the existence of
foliations of null hypersurfaces near a stable MOTS by certain constant
curvature surfaces. In this talk we have a look at a modified null mean
curvature flow to construct such foliations.
Venue: MCS2068
Mar 12 13:00 Zhengyao Huang (Durham): A Sudakov decomposition of optimal transport in the Monge
problem on positively curved manifolds
We will cover Monge's problem on Riemannian manifolds with
positive sectional curvature. Assuming that the source and target
measures are absolutely continuous with respect to the Riemannian volume
measure, we generalize a variational method from the Euclidean setting
to establish the existence of a transport density and an explicit
disintegration of measures along optimal rays. These results extend the
approach of Bianchini-Gloyer-Caravenna to the Riemannian context.
Venue: MCS2068
Mar 19 13:00 Andy Wand (Glasgow): TBA
Apr 02 13:00 Thiago de Paiva (Peking University): A simpler braid description for all links in the 3-sphere
By Alexander's theorem, every link in the 3-sphere can be
represented as the closure of a braid. Lorenz links and twisted torus
links are two families that have been extensively studied and are well
described in terms of braids. In this talk, we present a natural
generalization of Lorenz links and twisted torus links that produces all
links in the 3-sphere, providing a simpler braid description for every
link in the 3-sphere.
Venue: MCS2068
Apr 30 13:00 Anthea Monod (Imperial): TBA
Usual Venue: MCS0001
Contact: p.e.dorey@durham.ac.uk,enrico.andriolo@durham.ac.uk,tobias.p.hansen@durham.ac.uk
Feb 27 13:00 Paul Fendley (Oxford University): The uses of lattice non-invertible dualities and symmetries
I will describe a variety of applications of non-invertible symmetries and dualities. One use is to extend Kramers-Wannier duality to a large class of models, explaining exact degeneracies between non-(conventional) symmetry-related ground states as well as in the low-energy spectrum. For critical models, the universal behaviour under Dehn twists gives exact results for scaling dimensions, while gluing a topological defect to a boundary allows universal ratios of the boundary g-factor to be computed exactly on the lattice.
Venue: MCS0001
Mar 06 13:00 Olalla Castro Alvaredo (City University London): Integrable Quantum Field Theories Perturbed by TTbar
In this talk I will review recent results on the development of a form factor program for integrable quantum field theories (IQFTs) perturbed by irrelevant operators. Under such deformations, integrability is preserved and the two-body scattering phase gets deformed in a simple manner. The consequences of such a deformation are theories that exhibit a Hagedorn transition and have no UV completion. In our work we have mainly asked the question of how the deformation of the S-matrix and the subsequent "pathologies" of the deformed theories affect the properties of the correlation functions of the deformed theory. In this talk I will a present a partial answer to this question, summarising work in collaboration with Stefano Negro, Fabio Sailis and István M. Szécsényi.
Venue: MCS0001
Mar 13 13:00 Costantinos Papageorgakis (Queen Mary University London): Deep Finite Temperature Bootstrap
We introduce a novel method to bootstrap crossing equations in Conformal Field Theory and apply it to finite temperature theories on S_1×R_d\u22121. Traditional bootstrap approaches relying on positivity constraints or truncation schemes are not applicable to this problem. Instead, we capture infinite towers of operators using suitable tail functions, which are bootstrapped numerically together with explicit CFT data. Our method employs three key ingredients: the Kubo-Martin-Schwinger (KMS) condition, thermal dispersion relations, and Neural Networks that model spin-dependent tail functions. We test the method on Generalized Free Fields and apply it to bootstrap double-twist thermal data in holographic CFTs.
Venue: MCS0001
Mar 20 13:00 Donal O'Connell (Edinburgh University): TBA
Mar 27 13:00 Sean Hartnoll (Cambridge University): TBA
Usual Venue: MCS2068
Contact: tyler.helmuth@durham.ac.uk,oliver.kelsey-tough@durham.ac.uk
Feb 26 14:00 Christina Goldschmidt (Department of Statistics, University of Oxford): The stable trees revisited
Consider the family tree of a branching process with offspring distribution (p_k)_{k \ge 0} of mean 1 and with a heavy tail such that p_k \sim c k^{-\alpha - 1} as k \to \infty, for some constant c > 0 and \alpha \in (1,2). (This implies that the offspring distribution is in the domain of attraction of an \alpha-stable distribution.) Now condition the tree to have exactly n vertices. It is a well-known theorem (originally due to Duquesne) that distances in the tree vary as n^{1/\alpha} and, on rescaling them by this factor, we obtain a limit in distribution as n \to \infty called the stable tree. In this talk, Ill discuss a new (simple) construction of the stable trees, and indicate how to give a proof of the scaling limit theorem using it. This is joint work with Liam Hill (https://arxiv.org/abs/2512.17533).
Venue: MCS2068
Usual Venue: MCS3070
Contact: joe.thomas@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS2068
Contact: hyeyoung.maeng@durham.ac.uk,andrew.iskauskas@durham.ac.uk
Mar 02 13:00 Helen Ogden (Southampton): Adaptively-Structured Mixed Models for Simple Clustered Data
I will describe a new class of flexible mixed-effects models for simple clustered or longitudinal data. The idea of these Adaptively-Structured Mixed Models (AdaStruMMs) is to replace pre-specified random-effects structure by unknowns to be estimated. AdaStruMMs meet three requirements, at least one of which is unmet by all existing approaches I have considered:
1. Sufficient flexibility to represent individual trajectories as arbitrary smooth curves.
2. Information sharing between individuals to exploit structural similarities.
3. Accurate estimation of individual trajectories and population summaries across different data structures.
I will demonstrate the high-quality inference offered by AdaStruMMs through a range of simulations, and give some ideas about visualising and interpreting model fit through an example on changes in body composition in adolescent girls.
Venue: Teams
Mar 09 13:00 Irini Moustaki (LSE): TBA
Mar 16 13:00 Mengchu Li (Birmingham): Segmenting Human–LLM Co-authored Text via Change Point Detection
The rise of large language models (LLMs) has created an urgent need to distinguish between human-written and machine-generated text to ensure authenticity and societal trust. Existing detectors typically provide a binary classification for an entire passage; however, this is insufficient for human-LLM co-authored text, where the objective is to localize specific segments authored by each. To bridge this gap, we propose algorithms to segment text into human- and machine-authored pieces. Our key observation is that such a segmentation task is conceptually similar to classical change point detection in time series analysis. Leveraging this analogy, we adapt change point detection to LLM-generated text detection, develop a weighted algorithm and a generalized algorithm to accommodate heterogeneous sentence lengths, and establish the minimax optimality of our procedure. Empirically, our approach substantially outperforms existing baseline algorithms, reducing localization errors by up to 50%.
Venue: MCS2068
Mar 23 13:00 Rasa Remenyte-Prescott (Nottingham): TBA
