Feb 19 (Thu)
13:00 MCS2068 G&TRaphael Zentner (Durham): The Montesinos trick and proper rational tangle replacement
Recently Iltgen, Lewark and Marino introduced the concept of
a proper rational tangle replacement and the corresponding notion of the
proper rational unknotting number. They obtained lower bounds on it from
Khovanov homology. However, using the Montesinos trick and classical
3-manifold topology, one can also derive some lower bounds on the proper
rational unknotting number. We will explain this, and derive conclusions
about alternating knots and Montesinos knots. This is joint work with
Duncan McCoy.
Venue: MCS2068
14:00 MCS2068 ProbGiorgos Vasdekis (School of Mathematics, Statistics and Physics, Newcastle University): Skew-symmetric schemes for robust SDE sampling
We propose a new simple and explicit numerical scheme for
time-homogeneous stochastic differential equations (SDEs), focusing on
the case where the drift does not satisfy the Lipschitz property. The
scheme is based on sampling increments at each time step from a
skew-symmetric probability distribution, with the level of skewness
determined by the drift and volatility of the underlying process. We
show that as the step-size decreases the scheme converges weakly to the
SDE of interest. We then consider the problem of simulating from the
limiting distribution of an ergodic SDE using the numerical scheme with
a fixed step-size. We establish conditions under which the numerical
scheme converges to equilibrium at a geometric rate, and quantify the
bias between the equilibrium distributions of the scheme and of the
true diffusion process. Our results are supported via numerical
simulations, which indicate that the schemes possess a robustness
property with respect to different step-sizes.
This is joint work with Y. Iguchi, S. Livingstone, N. Nusken and R. Zhang.
Venue: MCS2068
Feb 20 (Fri)
13:00 MCS0001 HEPMCarlos Nunez (Swansea University): Aspects of gauge-strings duality
I will discuss some recent progress in the duality between gauge fields and strings, with a focus on models of confining dynamics. The talk will hopefully be of pedagogical character and is based on the papers I wrote in the last eight months.
Venue: MCS0001
Feb 23 (Mon)
13:00 MCS2068 StatLong Tran-Thanh (Warwick): Pruning at Initialisation through the lens of Graphon Limits, or How to Prune Neural Networks in a Principled Way
Sparse neural networks promise inference-time efficiency, yet training them effectively remains a fundamental challenge. Despite advances in pruning methods that create sparse architectures, understanding why some sparse structures are better trainable than others with the same level of sparsity remains poorly understood. Aiming to develop a systematic approach to this fundamental problem, we propose a novel theoretical framework based on the theory of graph limits, particularly graphons, that characterises sparse neural networks in the infinite-width regime. Our key insight is that connectivity patterns of sparse neural networks induced by pruning methods converge to specific graphons as networks' width tends to infinity, which encodes implicit structural biases of different pruning methods. Based on this, we derive a Graphon Neural Tangent Kernel (Graphon NTK) to study the training dynamics of sparse networks in the infinite width limit. Graphon NTK provides a general framework for the theoretical analysis of sparse networks. We empirically show that the spectral analysis of Graphon NTK correlates with observed training dynamics of sparse networks, explaining the varying convergence behaviours of different pruning methods. In addition, we also prove two fundamental theoretical results: (i) a Universal Approximation Theorem for sparse networks that depends only on the intrinsic dimension of active coordinate subspaces; and (ii) a Graphon-NTK generalisation bound demonstrating how the limit graphon modulates the kernel geometry to align with informative features. Overall, our framework provides theoretical insights into the impact of connectivity patterns on the trainability of various sparse network architectures. As such, it transforms the study of sparse neural networks from combinatorial graph problems into a rigorous framework of continuous operators, offering a new mechanism for analysing expressivity and generalisation in sparse neural networks.
Venue: MCS2068
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):
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
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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 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):
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
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS2068
Contact: fernando.galaz-garcia@durham.ac.uk
Feb 19 13:00 Raphael Zentner (Durham): The Montesinos trick and proper rational tangle replacement
Recently Iltgen, Lewark and Marino introduced the concept of
a proper rational tangle replacement and the corresponding notion of the
proper rational unknotting number. They obtained lower bounds on it from
Khovanov homology. However, using the Montesinos trick and classical
3-manifold topology, one can also derive some lower bounds on the proper
rational unknotting number. We will explain this, and derive conclusions
about alternating knots and Montesinos knots. This is joint work with
Duncan McCoy.
Venue: MCS2068
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 20 13:00 Carlos Nunez (Swansea University): Aspects of gauge-strings duality
I will discuss some recent progress in the duality between gauge fields and strings, with a focus on models of confining dynamics. The talk will hopefully be of pedagogical character and is based on the papers I wrote in the last eight months.
Venue: MCS0001
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 19 14:00 Giorgos Vasdekis (School of Mathematics, Statistics and Physics, Newcastle University): Skew-symmetric schemes for robust SDE sampling
We propose a new simple and explicit numerical scheme for
time-homogeneous stochastic differential equations (SDEs), focusing on
the case where the drift does not satisfy the Lipschitz property. The
scheme is based on sampling increments at each time step from a
skew-symmetric probability distribution, with the level of skewness
determined by the drift and volatility of the underlying process. We
show that as the step-size decreases the scheme converges weakly to the
SDE of interest. We then consider the problem of simulating from the
limiting distribution of an ergodic SDE using the numerical scheme with
a fixed step-size. We establish conditions under which the numerical
scheme converges to equilibrium at a geometric rate, and quantify the
bias between the equilibrium distributions of the scheme and of the
true diffusion process. Our results are supported via numerical
simulations, which indicate that the schemes possess a robustness
property with respect to different step-sizes.
This is joint work with Y. Iguchi, S. Livingstone, N. Nusken and R. Zhang.
Venue: MCS2068
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
Feb 23 13:00 Long Tran-Thanh (Warwick): Pruning at Initialisation through the lens of Graphon Limits, or How to Prune Neural Networks in a Principled Way
Sparse neural networks promise inference-time efficiency, yet training them effectively remains a fundamental challenge. Despite advances in pruning methods that create sparse architectures, understanding why some sparse structures are better trainable than others with the same level of sparsity remains poorly understood. Aiming to develop a systematic approach to this fundamental problem, we propose a novel theoretical framework based on the theory of graph limits, particularly graphons, that characterises sparse neural networks in the infinite-width regime. Our key insight is that connectivity patterns of sparse neural networks induced by pruning methods converge to specific graphons as networks' width tends to infinity, which encodes implicit structural biases of different pruning methods. Based on this, we derive a Graphon Neural Tangent Kernel (Graphon NTK) to study the training dynamics of sparse networks in the infinite width limit. Graphon NTK provides a general framework for the theoretical analysis of sparse networks. We empirically show that the spectral analysis of Graphon NTK correlates with observed training dynamics of sparse networks, explaining the varying convergence behaviours of different pruning methods. In addition, we also prove two fundamental theoretical results: (i) a Universal Approximation Theorem for sparse networks that depends only on the intrinsic dimension of active coordinate subspaces; and (ii) a Graphon-NTK generalisation bound demonstrating how the limit graphon modulates the kernel geometry to align with informative features. Overall, our framework provides theoretical insights into the impact of connectivity patterns on the trainability of various sparse network architectures. As such, it transforms the study of sparse neural networks from combinatorial graph problems into a rigorous framework of continuous operators, offering a new mechanism for analysing expressivity and generalisation in sparse neural networks.
Venue: MCS2068
Mar 02 13:00 Helen Ogden (Southampton): TBA
Mar 09 13:00 Irini Moustaki (LSE): TBA
Mar 16 13:00 Mengchu Li (Birmingham): TBA
Mar 23 13:00 Rasa Remenyte-Prescott (Nottingham): TBA
