Feb 10 (Tue)
13:00 MCS2068 APDEFrancisco Silva (University of Limoges): Optimal Control of Sweeping Processes: Theoretical Framework and Numerical Approximation
In this talk, based on joint work with J. Gianatti and E. Vilches, we first provide a theoretical framework for finite-horizon optimal control problems in which the state is governed by a controlled sweeping process, and we show that the value function is the unique viscosity solution of the associated HamiltonJacobiBellman equation. We then introduce a semi-Lagrangian scheme to approximate the value function and establish its convergence. Finally, we present numerical experiments for two-dimensional problems and discuss some promising extensions.
Venue: MCS2068
14:00 MCS2068 ASGJohannes Girsch (Durham University): Representations of GL_n over a p-adic field
I will give a basic introduction to the representation theory of GL_n(\Q_p) and describe some phenomena that do not appear in the complex representation theory of finite groups. In particular, I will introduce the so-called Bernstein block decomposition. I will then explain how one can use the theory of Bernstein-Zelevinsky derivatives and the notion of « highest derivative partition » to study Bernstein blocks. This is joint work with David Helm.
Venue: MCS2068
Feb 12 (Thu)
13:00 MCS2068 G&TTom Nye (Newcastle): Metric geometry for statistics in spaces of trees, forests and
graphs
I will describe the construction and geometry of three
related spaces of graphs which arise from applications in statistics:
(i) the "classical" Billera-Holmes-Vogtmann (BHV) space of evolutionary
trees;
(ii) the wald space of evolutionary forests; and
(iii) a space of graphs/networks called "pipeworks".
All three are manifold-stratified geodesic metric spaces. A number of
geometric-statistical methods have been developed in BHV space, which I
will briefly cover. The latter two spaces are my own work (with
collaborators): there are several open problems.
Venue: MCS2068
14:00 MCS2068 ProbJulian Ransford (University of Cambridge): On the $L^2$ distortion of random triangulations
How well can a planar map be embedded in a Hilbert space? A theorem of Rao states that there is a universal constant $C$ such that every planar graph with $n$ vertices can be embedded in $\ell^2$ in a way that distances do not get distorted by more than a factor of $C \sqrt{\log n}$. Raos bound is known to be sharp, however the graphs that achieve it are pathological and fractal-like. On the other hand, trees can be embedded in $\ell^2$ whilst not distorting distances by more than a factor of $C\sqrt{\log \log n}$. It is therefore natural to ask what happens for a typical planar graph: are they usually more tree-like, or fractal-like? In this talk, I will discuss a recent result where we show that a uniformly random triangulation with $n$ vertices achieves $L^2$ distortion of at least $(\log n)^{1/4}$ with probability tending to 1 as $n \to \infty$. This is joint work with Jason Miller.
Venue: MCS2068
Feb 13 (Fri)
13:00 MCS0001 HEPMAyan Kumar Patra (Durham University): BKL dynamics and Trans-IR flows in AdS black holes
The interior of an asymptotically AdS black hole provides a natural setting where one can extend the notion of holographic RG flows past their conventional infrared fixed points. In this talk, I will explain how these extended “trans-IR” flows offer a natural framework for capturing gravitational dynamics behind the horizon, especially in the approach to a spacelike singularity. Close to the singularity, the geometry enters a regime governed by the BKL conjecture and characterized by a sequence of Kasner epochs and eras. I will first show how mixmaster (chaotic) dynamics can be realized for any higher-dimensional AdS black hole. I will then introduce a monotonic thermal a-function – derived from the null energy condition – which provides a measure of the effective degrees of freedom along the trans-IR flow. Using this quantity, I will show that the full sequence of Kasner epochs and eras can be effectively captured, and the degrees of freedom thin out and ultimately vanish at the trans-IR fixed point.
Venue: MCS0001
Feb 16 (Mon)
13:00 MCS2068 StatVanda Inacio (Edinburgh): The underlap coefficient as a measure of a biomarker’s discriminatory ability
The first step in evaluating a potential diagnostic biomarker is to examine how biomarker values vary across disease stages. In a three-class disease setting, the volume under the receiver operating characteristic surface and the three-class Youden index are commonly used summary measures of a biomarker’s discriminatory ability. However, these measures rely on a stochastic ordering assumption for the distributions of biomarker outcomes across the three groups. This assumption can be restrictive and its violation may lead to incorrect conclusions about a biomarker’s discriminatory ability. Moreover, even when a stochastic ordering exists, it may differ across biomarkers, complicating automated ranking in studies involving multiple biomarkers. To address these challenges, we propose the underlap coefficient, a summary index free from stochastic ordering assumptions, to quantify a biomarker's ability to distinguish between three (or more) disease groups. To account for patient heterogeneity, we also develop the covariate-specific underlap coefficient. We further introduce Bayesian nonparametric estimators for both the unconditional underlap coefficient and its covariate-specific counterpart. An extensive simulation study reveals a good performance of the proposed estimators. We illustrate the proposed methodology by assessing how four Alzheimer’s disease biomarkers distinguish between individuals with normal cognition, mild impairment, and dementia, examining the impact of age and gender on discriminatory ability.
Venue: MCS2068
Feb 17 (Tue)
13:00 MCS2068 APDEDavid Villringer (Imperial College London): Alpha-unstable flows and the fast dynamo problem
The fast dynamo problem concerns the amplification of magnetic fields by the motion of an electrically charged fluid. In the linear approximation, this manifests as exponential growth of the magnetic energy, at a resistivity-independent rate. In this talk, I will provide a construction of a Lipschitz, divergence-free and time-independent velocity field that is a fast dynamo on the whole space. The talk is based on joint work with Michele Coti Zelati and Massimo Sorella.
Venue: MCS2068
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Usual Venue: MCS2068
Contact: yohance.a.osborne@durham.ac.uk
Feb 10 13:00 Francisco Silva (University of Limoges): Optimal Control of Sweeping Processes: Theoretical Framework and Numerical Approximation
In this talk, based on joint work with J. Gianatti and E. Vilches, we first provide a theoretical framework for finite-horizon optimal control problems in which the state is governed by a controlled sweeping process, and we show that the value function is the unique viscosity solution of the associated HamiltonJacobiBellman equation. We then introduce a semi-Lagrangian scheme to approximate the value function and establish its convergence. Finally, we present numerical experiments for two-dimensional problems and discuss some promising extensions.
Venue: MCS2068
Feb 17 13:00 David Villringer (Imperial College London): Alpha-unstable flows and the fast dynamo problem
The fast dynamo problem concerns the amplification of magnetic fields by the motion of an electrically charged fluid. In the linear approximation, this manifests as exponential growth of the magnetic energy, at a resistivity-independent rate. In this talk, I will provide a construction of a Lipschitz, divergence-free and time-independent velocity field that is a fast dynamo on the whole space. The talk is based on joint work with Michele Coti Zelati and Massimo Sorella.
Venue: MCS2068
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
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 10 14:00 Johannes Girsch (Durham University): Representations of GL_n over a p-adic field
I will give a basic introduction to the representation theory of GL_n(\Q_p) and describe some phenomena that do not appear in the complex representation theory of finite groups. In particular, I will introduce the so-called Bernstein block decomposition. I will then explain how one can use the theory of Bernstein-Zelevinsky derivatives and the notion of « highest derivative partition » to study Bernstein blocks. This is joint work with David Helm.
Venue: MCS2068
Feb 24 14:00 Oleksiy Klurman (University of Bristol):
Mar 03 14:00 Heejong Lee (KIAS):
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 12 13:00 Tom Nye (Newcastle): Metric geometry for statistics in spaces of trees, forests and
graphs
I will describe the construction and geometry of three
related spaces of graphs which arise from applications in statistics:
(i) the "classical" Billera-Holmes-Vogtmann (BHV) space of evolutionary
trees;
(ii) the wald space of evolutionary forests; and
(iii) a space of graphs/networks called "pipeworks".
All three are manifold-stratified geodesic metric spaces. A number of
geometric-statistical methods have been developed in BHV space, which I
will briefly cover. The latter two spaces are my own work (with
collaborators): there are several open problems.
Venue: MCS2068
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): TBA
Mar 06 13:00 Julian Scheuer (Goethe University Frankfurt): TBA
Mar 12 13:00 Zhengyao Huang (Durham): TBA
Mar 19 13:00 Andy Wand (Glasgow): TBA
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 13 13:00 Ayan Kumar Patra (Durham University): BKL dynamics and Trans-IR flows in AdS black holes
The interior of an asymptotically AdS black hole provides a natural setting where one can extend the notion of holographic RG flows past their conventional infrared fixed points. In this talk, I will explain how these extended “trans-IR” flows offer a natural framework for capturing gravitational dynamics behind the horizon, especially in the approach to a spacelike singularity. Close to the singularity, the geometry enters a regime governed by the BKL conjecture and characterized by a sequence of Kasner epochs and eras. I will first show how mixmaster (chaotic) dynamics can be realized for any higher-dimensional AdS black hole. I will then introduce a monotonic thermal a-function – derived from the null energy condition – which provides a measure of the effective degrees of freedom along the trans-IR flow. Using this quantity, I will show that the full sequence of Kasner epochs and eras can be effectively captured, and the degrees of freedom thin out and ultimately vanish at the trans-IR fixed point.
Venue: MCS0001
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): TBA
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): TBA
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 12 14:00 Julian Ransford (University of Cambridge): On the $L^2$ distortion of random triangulations
How well can a planar map be embedded in a Hilbert space? A theorem of Rao states that there is a universal constant $C$ such that every planar graph with $n$ vertices can be embedded in $\ell^2$ in a way that distances do not get distorted by more than a factor of $C \sqrt{\log n}$. Raos bound is known to be sharp, however the graphs that achieve it are pathological and fractal-like. On the other hand, trees can be embedded in $\ell^2$ whilst not distorting distances by more than a factor of $C\sqrt{\log \log n}$. It is therefore natural to ask what happens for a typical planar graph: are they usually more tree-like, or fractal-like? In this talk, I will discuss a recent result where we show that a uniformly random triangulation with $n$ vertices achieves $L^2$ distortion of at least $(\log n)^{1/4}$ with probability tending to 1 as $n \to \infty$. This is joint work with Jason Miller.
Venue: MCS2068
Feb 19 14:00 Giorgios Vaskedis (Newcastle University): TBA
Usual Venue: MCS3070
Contact: joe.thomas@durham.ac.uk
Feb 18 13:00 Renan Gross (University of Cambridge): Converging surfaces, log determinants, and small eigenvalues
The Laplacian is a central operator in the analysis of surfaces (and life in general). In this talk, we investigate the log determinant of the Laplacian of converging surfaces (in the Benjamini-Schramm sense), showing that the log-det converges when the short geodesics are not too short. In fact, this short geodesic condition gives a lower bound on how small the small eigenvalues can be, which can in turn be used to bound the heat-kernel for large times. The techniques involve extremal length, spectral embedding, and volume arguments.
Joint work with Guy Lachman and Asaf Nachmias.
Venue: MCS2068
Usual Venue: MCS2068
Contact: hyeyoung.maeng@durham.ac.uk,andrew.iskauskas@durham.ac.uk
Feb 16 13:00 Vanda Inacio (Edinburgh): The underlap coefficient as a measure of a biomarker’s discriminatory ability
The first step in evaluating a potential diagnostic biomarker is to examine how biomarker values vary across disease stages. In a three-class disease setting, the volume under the receiver operating characteristic surface and the three-class Youden index are commonly used summary measures of a biomarker’s discriminatory ability. However, these measures rely on a stochastic ordering assumption for the distributions of biomarker outcomes across the three groups. This assumption can be restrictive and its violation may lead to incorrect conclusions about a biomarker’s discriminatory ability. Moreover, even when a stochastic ordering exists, it may differ across biomarkers, complicating automated ranking in studies involving multiple biomarkers. To address these challenges, we propose the underlap coefficient, a summary index free from stochastic ordering assumptions, to quantify a biomarker's ability to distinguish between three (or more) disease groups. To account for patient heterogeneity, we also develop the covariate-specific underlap coefficient. We further introduce Bayesian nonparametric estimators for both the unconditional underlap coefficient and its covariate-specific counterpart. An extensive simulation study reveals a good performance of the proposed estimators. We illustrate the proposed methodology by assessing how four Alzheimer’s disease biomarkers distinguish between individuals with normal cognition, mild impairment, and dementia, examining the impact of age and gender on discriminatory ability.
Venue: MCS2068
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
