Speaker Lucas Theis will talk about: 'What makes an image realistic ?'

The last decade has seen tremendous progress in our ability to generate realistic-looking data, be it images, text, audio, or video. 
In this presentation, we will look at the closely related problem of quantifying realism, that is, designing functions that can reliably tell realistic data from unrealistic data. This problem turns out to be significantly harder to solve and remains poorly understood, despite its prevalence in machine learning and recent breakthroughs in generative AI. Drawing on insights from algorithmic information theory, we discuss why this problem is challenging, why a good generative model alone is insufficient to solve it, and what a good solution would look like. In particular, we introduce the notion of a universal critic, which unlike adversarial critics does not require adversarial training. While universal critics are not immediately practical, they can serve both as a North Star for guiding practical implementations and as a tool for analyzing existing attempts to capture realism.

In this talk, I will present a result proved in my recent paper arXiv:2502.13580. I will discuss biharmonic maps between (and submanifolds of) conformally compact manifolds, a large class of complete manifolds generalizing hyperbolic space. After an introduction to conformally compact geometry, I will discuss one of the main results of the paper: if S is a properly embedded sub-manifold of a conformally compact manifold (N,h), and moreover S is transverse to the boundary and (N,h) has non-positive curvature, then S must be minimal. This result confirms a conjecture known as the Generalized Chen’s Conjecture, in the conformally compact context.

TBA

We study a very general class of first-order linear hyperbolic
systems that both become weakly hyperbolic and contain singular
lower-order coefficients at a single time t = 0. In "critical" weakly
hyperbolic settings, it is well-known that solutions lose a finite
amount of regularity at t = 0. Here, we both improve upon the analysis
in the weakly hyperbolic setting, and we extend this analysis to systems
containing critically singular coefficients, which may also exhibit
modified asymptotics and regularity loss at t = 0.

In particular, we give precise quantifications for (1) the asymptotics
of solutions as t approaches 0, (2) the scattering problem of solving
the system with asymptotic data at t = 0, and (3) the loss of regularity
due to the degeneracies at t = 0. Finally, we discuss a wide range of
applications for these results, including weakly hyperbolic wave
equations (and equations of higher order), as well as equations arising
from relativity and cosmology (e.g. at big bang singularities).

This is joint work with Bolys Sabitbek (Ghent).

In this talk, I will examine the dynamics of the fermion–rotor system, originally introduced by Polchinski as a toy model for monopole–fermion scattering. Despite its simplicity, the system is surprisingly subtle, with ingoing and outgoing fermion fields carrying different quantum numbers. I will show that the rotor acts as a twist operator in the low-energy theory, changing the quantum numbers of excitations that have previously passed through the origin to ensure scattering consistent with all symmetries, thereby resolving the long-standing Unitarity puzzle. I will then discuss generalizations of this setup with multiple rotors and unequal charges, and demonstrate how the system can be viewed as a UV-completion of boundary states for chiral theories, establishing a connection to the proposed resolution of the puzzle using boundary conformal field theory.

to follow

In this talk, I will introduce the nilpotent cohomological Hall algebra COHA(S, Z) of coherent sheaves on a smooth quasi-projective complex surface S that are set-theoretically supported on a closed subscheme Z. This algebra can be viewed as the "largest" algebra of cohomological Hecke operators associated with modifications along a subscheme Z of S. When S is the minimal resolution of an ADE singularity and Z is the exceptional divisor, I will describe how to characterize COHA(S, Z) in terms of the Yangian of the corresponding affine ADE quiver Q (based on joint work with Emanuel Diaconescu, Mauro Porta, Oliver Schiffmann, and Eric Vasserot, arXiv:2502.19445). More generally, I will discuss nilpotent COHAs arising from Bridgeland stability conditions on the bounded derived category of nilpotent representations of the preprojective algebra of Q, following joint work with Olivier Schiffmann and Parth Shimpi (arXiv:2511.08576).

to follow

Join us to discuss x+y: A Mathematician’s Manifesto for Rethinking Gender by Eugenia Cheng.

I will discuss old and new results about the distribution of zeros of modular forms, and relation to Quantum Unique Ergodicity. It is known that a modular form of weight k has about k/12 zeros in the fundamental domain . A classical question in the analytic theory of modular forms is “can we locate the zeros of a distinguished family of modular forms?”. In 1970, F. Rankin and Swinnerton-Dyer proved that the zeros of the Eisenstein series all lie on the circular part of the boundary of the fundamental domain. In the beginning of this century, I discovered that for cuspidal Hecke eigenforms, the picture is very different - the zeros are not localized, and in fact become uniformly distributed in the fundamental domain. Very recently, we have investigated other families of modular forms, such as the Miller basis (ZR 2024, Roei Raveh 2025, Adi Zilka 2026), Poincare series (RA Rankin 1982, Noam Kimmel 2025) and theta functions (Roei Raveh 2026),  finding a variety of possible distributions of the zeroes.

(Joint seminar with Random Matrix Theory)

I will discuss old and new results about the distribution of zeros of modular forms, and relation to Quantum Unique Ergodicity. It is known that a modular form of weight k has about k/12 zeros in the fundamental domain . A classical question in the analytic theory of modular forms is “can we locate the zeros of a distinguished family of modular forms?”. In 1970, F. Rankin and Swinnerton-Dyer proved that the zeros of the Eisenstein series all lie on the circular part of the boundary of the fundamental domain. In the beginning of this century, I discovered that for cuspidal Hecke eigenforms, the picture is very different - the zeros are not localized, and in fact become uniformly distributed in the fundamental domain. Very recently, we have investigated other families of modular forms, such as the Miller basis (ZR 2024, Roei Raveh 2025, Adi Zilka 2026), Poincare series (RA Rankin 1982, Noam Kimmel 2025) and theta functions (Roei Raveh 2026),  finding a variety of possible distributions of the zeroes.

The mitigation of bacterial adhesion to surfaces and subsequent biofilm formation is a key challenge in healthcare and manufacturing processes. To accurately predict biofilm formation you must determine how changes to bacteria behaviours and dynamics alter their ability to adhere to surfaces. In this talk, I will present a framework for incorporating microscale behaviour into continuum models using techniques from statistical mechanics at the microscale combined with boundary-layer theory at the macroscale.

We will examine the flow of a dilute suspension of motile bacteria over a flat absorbing surface, developing an effective model for the bacteria density near the boundary inspired by the classical Lévêque boundary layer problem. We use our effective model to derive analytical solutions for the bacterial adhesion rate as a function of fluid shear rate and individual motility parameters of the bacteria, validating against stochastic numerical simulations of individual bacteria. We find that bacterial adhesion is greatest at intermediate flow rates, since at higher flow rates shear-induced upstream swimming limits adhesion.

TBA

Professor Ana Djurdjevac will talk about; 'The Dean–Kawasaki Equation: Theory, Numerics, and Applications'

The Dean–Kawasaki equation provides a stochastic partial differential equation description of interacting particle systems at the level of empirical densities and has attracted considerable interest in statistical physics, stochastic analysis, and applied modeling. In this work, we study analytical and numerical aspects of the Dean–Kawasaki equation, with a particular focus on well-posedness, structure preservation, and possible discretization strategies. In addition, we extend the framework to the Dean–Kawasaki equation posed on smooth hypersurfaces. We discuss applications of the Dean–Kawasaki framework to particle-based models arising in biological systems and modeling social dynamics.

TBA

Specialist species thrive under specific environmental conditions in narrow geographic ranges and are widely recognized as heavily threatened by climate deregulation. Many might rely on both their potential to adapt and to disperse towards a refugium to avoid extinction. It is thus crucial to understand the influence of environmental conditions on the unfolding process of adaptation. I will present a PDE model of the eco-evolutionary dynamics of a specialist species in a two-patch environment with moving optima. The transmission of the adaptive trait across generations is modelled by a non-linear, non-local operator of sexual reproduction. In an asymptotic regime of small variance, I justify that the local trait distributions are well approximatted by Gaussian distributions with fixed variances, which allows to report the analysis on the closed system of moments. Thanks to a separation of time scales between ecology and evolution, I next derive a limit system of moments and analyse its stationary states. In particular, I identify the critical environmental speed for persistence, which reflects how both the existence of a refugium and the cost of dispersal impact extinction patterns. Additionally, the analysis provides key insights regarding the path towards this refugium. I show that there exists a critical environmental speed above which the species crosses a tipping point, resulting into an abrupt habitat switch from its native patch to the refugium. When selection for local adaptation is strong, this habitat switch passes through an evolutionary ‘‘death valley’’ that can promote extinction for lower environmental speeds than the critical one.

A (saturated) fusion system on a p-group P contains data about conjugacy within P, the typical case being the system induced by a group on its Sylow p-subgroup. Fusion systems are completely determined by looking at their essential subgroups, which must admit an automorphism of order coprime to p. For p=2, we describe two new methods that address the question: given an essential subgroup $E<P$ of a fusion system on P, what can we say about P? In particular, one method gives us sufficient conditions to deduce that $E\triangleleft P$, while the other explores cases where we have strong control over the normaliser tower of E in P.

I will discuss an ongoing joint work with Luigi Appolloni and Andrea Malchiodi concerning the above objects. Minimal surfaces are critical points of the area functional, which is analytic in this case, so we should expect critical points (minimal surfaces) to be either isolated or to belong to smooth nearby minimal foliations. On the other hand, the flat plane of multiplicity two in $\mathbb{R}^3$ can be (in compact regions) approximated by a blown-down catenoid, which will converge back to the plane with multiplicity two in the limit. Hence a plane of multiplicity two cannot be thought of as being isolated, or belonging solely to a smooth family, because there are “nearby” minimal surfaces of distinct topology weakly converging to it. We will nevertheless prove that, when the ambient manifold is closed and analytic, this type of local degeneration is impossible amongst closed and embedded minimal surfaces of bounded topology: such surfaces, even with multiplicity are either isolated or belong to smooth families of nearby minimal surfaces.  

I will introduce the Polchinski dynamics, a general framework to study asymptotic properties of statistical mechanics and field theory models inspired by renormalisation group ideas. The Polchinski dynamics has appeared recently under different names, such as stochastic localisation, and in very different contexts (Markov chain mixing, optimal transport, functional inequalities...) Here I will motivate its construction from a physics point of view and mention a few applications. In particular, I will explain how the Polchinski dynamics can be used to generalise Bakry and Emery’s Γ2 calculus to obtain functional inequalities (e.g. Poincaré, log-Sobolev) in physics models which are typically high-dimensional and non-convex. 

The aim of this talk is to discuss a finite-volume scheme for the aggregation-diffusion family of equations with non-linear mobility
∂tρ = ∇ · (m(ρ)∇(U′(ρ) + V + W ∗ ρ)) in bounded domains with no-flux conditions. We will present basic properties of the scheme: existence, decay of a free, and comparison principle (where applicable); and a convergence-by-compactness result for the saturation case where m(0) = m(1) = 0, under general assumptions on m,U, V , and W. The results are joint works published in [1, 2]. At the end of the talk, we will discuss an extension to the Porous-Medium Equation with non-local pressure that corresponds to m(ρ) = ρm, U, V = 0 and W(x) = c|x|^−d−2s.

This project is joint work with Jose Carrillo (University of Oxford). 
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to follow

Given a quantum Hamiltonian, represented as an $N \times N$ Hermitian matrix $H$, we derive an expression for the largest Lyapunov exponent of the classical trajectories in the phase space appropriate for the dynamics induced by $H$. To this end we associate to $H$ a graph with $N$ vertices and derive a quantum map on functions defined on the directed edges of the graph. Using the semiclassical approach in the reverse direction we obtain the corresponding classical evolution (Liouvillian) operator. Using ergodic theory methods (Sinai, Ruelle, Bowen, Pollicott\ldots) we obtain closed expressions for the Lyapunov exponent, as well as for its variance. Applications for random matrix models will be presented.

to follow

TBA

Speaker Yongho Park will talk about 'Subspace Correction Methods for Convex Optimization: Algorithms, Theory, and Applications'

This talk considers a framework of subspace correction methods for convex optimization, which provides a unified perspective for the design and analysis of a wide range of iterative methods, including advanced domain decomposition and multigrid methods. We first develop a convergence theory for parallel subspace correction methods based on the observation that these methods can be interpreted as nonlinearly preconditioned gradient descent methods. This viewpoint leads to a simpler and sharper analysis compared with existing approaches. We further show how the theory can be extended to semicoercive and nearly semicoercive problems. In addition, we explore connections between subspace correction methods and other classes of iterative algorithms, such as alternating projection methods, through the lens of convex duality, thereby enabling a unified treatment. Several applications are presented, including nonlinear partial differential equations, variational inequalities, and mathematical imaging problems. The talk concludes with a discussion of relevant and emerging research directions.

Conventional data feeds from exchanges, even L3 feeds, generally only tell one what happened: accepted submissions of maker and taker orders,  cancellations, and the evolution of the order book and the best bid and ask prices. However, by analyzing a dataset derived from the blockchain of the highly liquid cryptocurrency exchange Hyperliquid, we are able to see all messages (4.5 bn in our one-month sample), including rejections. Unexpectedly, almost 60% of message traffic is generated by submission and subsequent rejection of a single order type: post-only limit orders sent to the 'wrong' (aggressive) side of the book, for example a buy limit order at a price at or above the best ask. Such orders are automatically rejected on arrival except in the (rare) case that the price moves up while the order is in transit. Nearly 30% of message traffic relates to cancellations, leaving a small fraction for all other messages.

I shall describe this order flow in detail, then address the question of why message traffic is dominated by rejected submissions which, by their nature, do not influence the order book in any way at all, and are invisible to all traders except the submitter. We propose that the reason lies in a market-making strategy whose aim is to gain queue priority immediately after any price change, and I shall show how the evidence supports this hypothesis. I shall also discuss the risk/return characteristics of the strategy, and finally discuss its pivotal role in replenishing liquidity following a price move.

Joint work with Jakob Albers, Mihai Cucuringu and Alex Shestopaloff.

Normal heart function relies of the fine-tuned synchronization of cellular components. In healthy hearts, calcium oscillations and physical contractions are coupled across a synchronised network of 3 billion heart cells. When the process of functional isolation of rogue cells isn’t successful, the network becomes maladapted, resulting in cardiovascular diseases, including heart failure and arrythmia. To advance knowledge on this normal-to-disease transition we must first address the lack of a mechanistic understanding of the plastic readaptation of these networks. In this talk I will explore coupling and loss of synchronisation using a mathematical model of calcium oscillations informed by experimental data. I will show some preliminary results pointing at the heterogeneity hidden behind seemingly uniform cell populations, as a causative mechanism behind disrupted dynamics in maladapted networks.

We consider a class of Lagrangian sections L contained in certain Calabi-Yau Lagrangian fibrations (mirrors of toric weak Fano manifolds). We prove that a form of the Thomas-Yau conjecture holds in this case: L is isomorphic to a special Lagrangian section in this class if and only if a stability condition holds, in the sense of a slope inequality on objects in a set of exact triangles in the Fukaya-Seidel category. This agrees with general proposals by Li. On
surfaces and threefolds, under more restrictive assumptions, this result can be used to show a precise relation with Bridgeland stability, as predicted by Joyce. Based on arXiv:2505.07228 and arXiv:2508.17709.