Feb 04 (Wed)
13:00 MCS3070 S&MCarsten Peterson (Sorbonne Université): Resonances on geometrically finite graphs
Compact Riemannian manifolds admit an orthonormal basis of $L^2$-eigenfunctions of the Laplacian. The shape of these eigenfunctions and the distribution of the eigenvalues are central questions in spectral geometry. In the non-compact setting we no longer have discrete $L^2$-spectrum. However, an analogous theory arises when one instead studies the poles of the meromorphic continuation of the resolvent of the Laplacian, which are known as resonances. These objects have been particularly well-studied in the setting of geometrically finite hyperbolic surfaces. We discuss analogous results for certain infinite regular graphs which are analogous to geometrically finite hyperbolic surfaces; in fact, as we shall explain, the objects we study are most properly understood not as graphs, but as "graphs of groups". We prove the meromorphic continuation of the resolvent of the adjacency operator and describe geometrically the corresponding resonant states, which are certain (non-$L^2$) eigenfunctions associated to the resonances. This is based on joint work with Christian Arends and Tobias Weich.
Venue: MCS3070
14:00 MCS3070 HEPJRodrigo Olea (PUCV, Chile): Conformal Renormalization, Holographic Entanglement Entropy and Willmore Energy
Conformal Renormalization provides the required counterterms for Einstein-AdS gravity action to be finite in even bulk dimensions. This is done by embedding the Einstein theory in a particular type of Conformal Gravity. Indeed, in the Einstein sector of this Conformal Gravity, the action is equivalent to the one given by holographic techniques within the AdS/CFT framework. In this talk, we show that the evaluation of the action of this Conformal Gravity in 6D on manifolds with conical defects leads to a surface functional which is also a conformal invariant. This codimension-2 energy functional reduces to a renormalized form of Holographic Entanglement Entropy for minimal surfaces. For arbitrary surfaces, in turn, it recovers the notions of Hawking Mass and Willmore energy in higher dimensions.
Venue: MCS3070
16:00 zoom A&CRowan Wright (University of Southampton): Correlators of light-like loop operators in N=4 super Yang-Mills theory
Feb 05 (Thu)
13:00 MCS2068 G&TSarah Whitehouse (Sheffield): Homotopy theory and geometry related to multicomplexes
A multicomplex is a variant of a bicomplex and these
structures arise naturally in many geometric, topological and algebraic
contexts; for example, from filtered simplicial sets. I will explain
some recent joint work with Joana Cirici and Muriel Livernet which
explores homotopy theories related to the two spectral sequences of a
truncated multicomplex. There are potential applications to the study of
homotopy types of almost and generalized complex manifolds.
Venue: MCS2068
14:00 MCS2068 ProbJannis Dause (TU Berlin): Duality in Non-Markovian Stochastic Control problems using Rough Stochastic Differential Equations
The classical stochastic optimal control framework is heavily based on the
Markovianity of the underlying dynamics e.g., through the use of the
dynamic programming principle and the subsequent derivation of the
Hamilton-Jacobi-Bellman equation. In this talk we will focus on a certain
class of non-Markovian stochastic control problem arising e.g., from optimal
control under stochastic volatility.
In particular we will consider controlled doubly-stochastic differential
equations driven by two independent Brownian noises B and W, where the
coefficients depend progressively on the noise W. Extending previous work
of [Diehl, Friz,Gassiat '17] by methods from BS(P)DE-theory, we are then
able to relate this stochastic control problem to a penalized version of
the original control problem, where W can now be treated as a
'frozen', i.e., deterministic (but irregular) path. Most importantly
this 'dual problem' is now Markovian and may thus be treated by
classical methods.
The main technical tool allowing us handle the dual problem will be the
recently introduced theory of Rough Stochastic Differential Equations
(RSDEs) [Friz, Hoquet, Lê '21], which provides a generalized framework of
classical SDE Theory and Lyons' Rough Differential Equations.
This is joint work with Peter Bank, Peter K. Friz and Filippo de Feo.
Venue: MCS2068
14:00 MCS3070 ASGDavid Helm (Imperial College, London): Uniqueness of supercuspidal support for generic representations
Let G be a connected reductive group. Supercuspidal support is an invariant attached to irreducible mod \ell representations of G(k), where k is a p-adic field or finite field of characteristic p. Vigneras showed in the mid-'90s that when G=GL_n, the supercuspidal support of any irreducible representation of G consists of a single conjugacy class, and posed the question of whether this held for other reductive groups; Dudas and Dat gave examples showing that this need not be the case. We prove that for k finite, and G arbitrary, this question has an affirmative answer for a large class of representations called the generic representations of G(k). If time permits we will also discuss how our approach (partially) generalizes to the p-adic setting, and completely generalizes conditionally on certain well-known conjectures in the Langlands correspondence. (This is joint work with Jean-Francois Dat, Rob Kurinczuk, and Gil Moss.)
Venue: MCS3070
Feb 06 (Fri)
13:00 MCS0001 HEPMFiona Seibold (Ecole Polytechnique Lausanne): Integrable deformations of AdS3 strings
Free strings on backgrounds such as AdS3xS3xT4 and AdS3xS3xS3xS1 can be described by integrable sigma models, which admit a very rich landscape of integrable deformations. In this talk I will focus on TsT, trigonometric and elliptic deformations which preserve some amount of supersymmetry and interpolate between well-known integrable setups, including AdS2 backgrounds. I will present the deformed geometry and check that the S-matrix encoding the scattering of excitations on the string worldsheet is compatible with factorisation.
Venue: MCS0001
Feb 09 (Mon)
13:00 MCS2068 StatJuraj Medzihorsky (Durham): Selecting treatments and estimating effects with partial identification midpoints
The fundamental difficulty in comparing the efficacies of two treatments based on observational data is that those who actually selected or received a particular treatment may give different responses to it than those who did not select or receive it. Robins (1989) and Manski (1990) showed that also in this situation, one may derive bounds for the effect sizes. Then, a natural procedure is to prefer the treatment with the higher midpoint of the bounds, which can be interpreted in terms of minimizing maximum regret. This paper shows the decision to be immune to Simpson’s paradox in the sense that it will never select different treatments when applied to the whole data and to its strata separately, as it is equivalent to Rudas’s (2014) selection rule. Furthermore, comparing the midpoints yields estimators of average treatment effects in the whole population or its subsets such as the treated units. Such estimators can be interpreted as regularized, and unlike the conventional risk difference estimators are decomposable and free of Simpson’s paradox. The paper connects these properties to Chattopadhyay and Zubizarreta’s (2023) implied weights of effect estimators based on Gaussian linear regression. The paper also discusses some of the statistical properties of the decision process and the estimators.
Venue: MCS2068
14:00 MCS2068 PureJoni Teravainen (Cambridge): Patterns in prime factors
The number of prime factors of an integer is one of the simplest arithmetic quantities, yet it exhibits surprisingly random behaviour. In this talk I will describe recent work resolving several classic problems of Paul Erdős concerning patterns in prime factorisations, including on how the number of prime factors of neighbouring integers interact and whether long strings of integers can have unusually few prime factors. The proofs combine probabilistic ideas with recent advances in analytic number theory. This is based on joint work with Terence Tao.
Venue: MCS2068
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Contact: arthur.lipstein@durham.ac.uk
Feb 04 16:00 Rowan Wright (University of Southampton): Correlators of light-like loop operators in N=4 super Yang-Mills theory
Planar scattering amplitudes in N=4 super Yang-Mills theory are famously dual to the expectation values of null polygonal Wilson loops, and there has been much recent interest in studying closely related objects, such as a Wilson loop with a Lagrangian operator insertion.
After presenting some motivation for studying such objects and reviewing amplitude-Wilson loop duality, I will present evidence that much of the same mathematical structure is also enjoyed by correlators of multiple loop operators and their supersymmetric extensions. This includes very natural generalisations of the Q-bar equation and BCFW recursion relations, and expressions for one-loop leading singularities in terms of tree-level objects.
Venue: zoom
Usual Venue: MCS2068
Contact: yohance.a.osborne@durham.ac.uk
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 05 14:00 David Helm (Imperial College, London): Uniqueness of supercuspidal support for generic representations
Let G be a connected reductive group. Supercuspidal support is an invariant attached to irreducible mod \ell representations of G(k), where k is a p-adic field or finite field of characteristic p. Vigneras showed in the mid-'90s that when G=GL_n, the supercuspidal support of any irreducible representation of G consists of a single conjugacy class, and posed the question of whether this held for other reductive groups; Dudas and Dat gave examples showing that this need not be the case. We prove that for k finite, and G arbitrary, this question has an affirmative answer for a large class of representations called the generic representations of G(k). If time permits we will also discuss how our approach (partially) generalizes to the p-adic setting, and completely generalizes conditionally on certain well-known conjectures in the Langlands correspondence. (This is joint work with Jean-Francois Dat, Rob Kurinczuk, and Gil Moss.)
Venue: MCS3070
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 05 13:00 Sarah Whitehouse (Sheffield): Homotopy theory and geometry related to multicomplexes
A multicomplex is a variant of a bicomplex and these
structures arise naturally in many geometric, topological and algebraic
contexts; for example, from filtered simplicial sets. I will explain
some recent joint work with Joana Cirici and Muriel Livernet which
explores homotopy theories related to the two spectral sequences of a
truncated multicomplex. There are potential applications to the study of
homotopy types of almost and generalized complex manifolds.
Venue: MCS2068
Feb 12 13:00 Tom Nye (Newcastle): Metric geometry for statistics in spaces of trees, forests and
graphs
Feb 19 13:00 Raphael Zentner (Durham): TBA
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: MCS3070
Contact: mendel.t.nguyen@durham.ac.uk
Feb 04 14:00 Rodrigo Olea (PUCV, Chile): Conformal Renormalization, Holographic Entanglement Entropy and Willmore Energy
Conformal Renormalization provides the required counterterms for Einstein-AdS gravity action to be finite in even bulk dimensions. This is done by embedding the Einstein theory in a particular type of Conformal Gravity. Indeed, in the Einstein sector of this Conformal Gravity, the action is equivalent to the one given by holographic techniques within the AdS/CFT framework. In this talk, we show that the evaluation of the action of this Conformal Gravity in 6D on manifolds with conical defects leads to a surface functional which is also a conformal invariant. This codimension-2 energy functional reduces to a renormalized form of Holographic Entanglement Entropy for minimal surfaces. For arbitrary surfaces, in turn, it recovers the notions of Hawking Mass and Willmore energy in higher dimensions.
Venue: MCS3070
Usual Venue: MCS0001
Contact: p.e.dorey@durham.ac.uk,enrico.andriolo@durham.ac.uk,tobias.p.hansen@durham.ac.uk
Feb 06 13:00 Fiona Seibold (Ecole Polytechnique Lausanne): Integrable deformations of AdS3 strings
Free strings on backgrounds such as AdS3xS3xT4 and AdS3xS3xS3xS1 can be described by integrable sigma models, which admit a very rich landscape of integrable deformations. In this talk I will focus on TsT, trigonometric and elliptic deformations which preserve some amount of supersymmetry and interpolate between well-known integrable setups, including AdS2 backgrounds. I will present the deformed geometry and check that the S-matrix encoding the scattering of excitations on the string worldsheet is compatible with factorisation.
Venue: MCS0001
Feb 13 13:00 Ayan Kumar Patra (Durham University): TBA
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 05 14:00 Jannis Dause (TU Berlin): Duality in Non-Markovian Stochastic Control problems using Rough Stochastic Differential Equations
The classical stochastic optimal control framework is heavily based on the
Markovianity of the underlying dynamics e.g., through the use of the
dynamic programming principle and the subsequent derivation of the
Hamilton-Jacobi-Bellman equation. In this talk we will focus on a certain
class of non-Markovian stochastic control problem arising e.g., from optimal
control under stochastic volatility.
In particular we will consider controlled doubly-stochastic differential
equations driven by two independent Brownian noises B and W, where the
coefficients depend progressively on the noise W. Extending previous work
of [Diehl, Friz,Gassiat '17] by methods from BS(P)DE-theory, we are then
able to relate this stochastic control problem to a penalized version of
the original control problem, where W can now be treated as a
'frozen', i.e., deterministic (but irregular) path. Most importantly
this 'dual problem' is now Markovian and may thus be treated by
classical methods.
The main technical tool allowing us handle the dual problem will be the
recently introduced theory of Rough Stochastic Differential Equations
(RSDEs) [Friz, Hoquet, Lê '21], which provides a generalized framework of
classical SDE Theory and Lyons' Rough Differential Equations.
This is joint work with Peter Bank, Peter K. Friz and Filippo de Feo.
Venue: MCS2068
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: MCS2068
Contact: michael.r.magee@durham.ac.uk
Feb 09 14:00 Joni Teravainen (Cambridge): Patterns in prime factors
The number of prime factors of an integer is one of the simplest arithmetic quantities, yet it exhibits surprisingly random behaviour. In this talk I will describe recent work resolving several classic problems of Paul Erdős concerning patterns in prime factorisations, including on how the number of prime factors of neighbouring integers interact and whether long strings of integers can have unusually few prime factors. The proofs combine probabilistic ideas with recent advances in analytic number theory. This is based on joint work with Terence Tao.
Venue: MCS2068
Usual Venue: MCS3070
Contact: joe.thomas@durham.ac.uk
Feb 04 13:00 Carsten Peterson (Sorbonne Université): Resonances on geometrically finite graphs
Compact Riemannian manifolds admit an orthonormal basis of $L^2$-eigenfunctions of the Laplacian. The shape of these eigenfunctions and the distribution of the eigenvalues are central questions in spectral geometry. In the non-compact setting we no longer have discrete $L^2$-spectrum. However, an analogous theory arises when one instead studies the poles of the meromorphic continuation of the resolvent of the Laplacian, which are known as resonances. These objects have been particularly well-studied in the setting of geometrically finite hyperbolic surfaces. We discuss analogous results for certain infinite regular graphs which are analogous to geometrically finite hyperbolic surfaces; in fact, as we shall explain, the objects we study are most properly understood not as graphs, but as "graphs of groups". We prove the meromorphic continuation of the resolvent of the adjacency operator and describe geometrically the corresponding resonant states, which are certain (non-$L^2$) eigenfunctions associated to the resonances. This is based on joint work with Christian Arends and Tobias Weich.
Venue: MCS3070
Usual Venue: MCS2068
Contact: hyeyoung.maeng@durham.ac.uk,andrew.iskauskas@durham.ac.uk
Feb 09 13:00 Juraj Medzihorsky (Durham): Selecting treatments and estimating effects with partial identification midpoints
The fundamental difficulty in comparing the efficacies of two treatments based on observational data is that those who actually selected or received a particular treatment may give different responses to it than those who did not select or receive it. Robins (1989) and Manski (1990) showed that also in this situation, one may derive bounds for the effect sizes. Then, a natural procedure is to prefer the treatment with the higher midpoint of the bounds, which can be interpreted in terms of minimizing maximum regret. This paper shows the decision to be immune to Simpson’s paradox in the sense that it will never select different treatments when applied to the whole data and to its strata separately, as it is equivalent to Rudas’s (2014) selection rule. Furthermore, comparing the midpoints yields estimators of average treatment effects in the whole population or its subsets such as the treated units. Such estimators can be interpreted as regularized, and unlike the conventional risk difference estimators are decomposable and free of Simpson’s paradox. The paper connects these properties to Chattopadhyay and Zubizarreta’s (2023) implied weights of effect estimators based on Gaussian linear regression. The paper also discusses some of the statistical properties of the decision process and the estimators.
Venue: MCS2068
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
