Date/Time : 08 Dec 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Yuta Takaya, Tokyo University

The relation between period integrals and L-functions, studied since the work of Hecke and Tate, has recently been reformulated by Ben-Zvi–Sakellaridis–Venkatesh as relative Langlands duality. In this talk, I will present a version of this duality, the normalized period conjecture, in the framework of the categorical local Langlands correspondence à la Fargues-Scholze. I will describe computations for the Iwasawa-Tate and Hecke periods that support this conjecture, and discuss how it leads to a relation between distinguished representations and distinguished L-parameters. This talk is based on joint work with Milton Lin.

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Date/Time : 03 Dec 2025 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Jose Carrillo, University of Oxford

Many phenomena in the life sciences, ranging from the microscopic to macroscopic level, exhibit surprisingly similar structures. Behaviour at the microscopic level, including ion channel transport, chemotaxis, and angiogenesis, and behaviour at the macroscopic level, including herding of animal populations, motion of human crowds, and bacteria orientation, are both largely driven by long-range attractive forces, due to electrical, chemical or social interactions, and short-range repulsion, due to dissipation or finite size effects. Various modelling approaches at the agent-based level, from cellular automata to Brownian particles, have been used to describe these phenomena. An alternative way to pass from microscopic models to continuum descriptions requires the analysis of the mean-field limit, as the number of agents becomes large. All these approaches lead to a continuum kinematic equation for the evolution of the density of individuals known as the aggregation-diffusion equation. This equation models the evolution of the density of individuals of a population, that move driven by the balances of forces: on one hand, the diffusive term models diffusion of the population, where individuals escape high concentration of individuals, and on the other hand, the aggregation forces due to the drifts modelling attraction/repulsion at a distance. The aggregation-diffusion equation can also be understood as the steepest-descent curve (gradient flow) of free energies coming from statistical physics. Significant effort has been devoted to the subtle mechanism of balance between aggregation and diffusion. In some extreme cases, the minimisation of the free energy leads to partial concentration of the mass. Aggregation-diffusion equations are present in a wealth of applications across science and engineering. Of particular relevance is mathematical biology, with an emphasis on cell population models. The aggregation terms, either in scalar or in system form, is often used to model the motion of cells as they concentrate or separate from a target or interact through chemical cues. The diffusion effects described above are consistent with population pressure effects, whereby groups of cells naturally spread away from areas of high concentration. This talk will give an overview of the state of the art in the understanding of aggregation-diffusion equations, and their applications in mathematical biology and machine learning.

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Date/Time : 01 Dec 2025 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Wenkui Du, Massachusetts Institute of Technology

In this talk, I will discuss the singularity theory of mean curvature flow. As the most natural evolution equation in extrinsic geometry, mean curvature flow has striking applications in geometry, topology and image processing. A central challenge for these applications is understanding the structure of singularities. This talk surveys recent progress on the classification of singularity models of mean curvature flow and their applications. In particular, ancient noncollapsed solutions naturally arise when we consider blow-up limits near singularities. Several results about classification of ancient noncollapsed solutions will be presented. I will also mention my future plan of singularity analysis in geometric variational problems. The talk is based on my joint works with collaborators B. Choi, Daskalopoulos, Haslhofer, Šešum, Zhao and Zhu.

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Date/Time : 28 Nov 2025 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Koulik Khamaru, Rutgers University

Modern decision-making increasingly relies on adaptive experimentation, particularly in settings such as A/B testing, multi-armed bandits, and reinforcement learning. While these methods enable more efficient learning and allocation of resources, they fundamentally challenge traditional statistical inference. Classical i.i.d.-based tools often break down under adaptive data collection, resulting in biased estimators and misleading confidence intervals.

This talk offers an overview of statistical inference in these adaptive environments. We highlight the pitfalls of naive inference through concrete examples and introduce the concept of stability—originally formulated by Lai and Wei (1982)—as a unifying principle for valid inference under adaptivity. A key advantage of stability is that it allows us to recover classical inferential guarantees—such as asymptotic normality and valid confidence intervals—even when the data arise from highly adaptive algorithms. In other words, stability serves as the bridge that lets i.i.d.-based tools remain valid in non-i.i.d. bandit settings.

Next, we discuss the stability properties of two widely used algorithms: the Upper Confidence Bound (UCB) and Thompson Sampling. We argue that while UCB is stable, Thompson Sampling is not. Finally, we propose a modification of Thompson Sampling that regains stability while maintaining near-optimal regret. Key illustrations include quantitative central limit theorems of empirical mean in stochastic bandits and least square estimators in contextual bandits. We also present a new proof technique for analyzing regret and establishing stability, which we believe has broader applicability and may be of independent interest.

The talk is based on a series of joint works with Cunhui Zhang, Qiyang Han, Budhaditya Halder, Subhayan Pan, and Samya Praharaj.

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Date/Time : 26 Nov 2025 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Leonardo Nagami Coregliano, University of Chicago

In the Netflix Prize Competition (2006–2009), we are given a finite set $U$ of users, a finite set $M$ of movies and a partial function $f: U\times M\rightharpoonup R$, where $f(u,m)$ indicates how user $u$ rates movie $m$ and we are tasked with completing $f$ to a total function to predict how all users $U$ rate all movies in $M$. Although some algorithms did fairly well in the competition, giving a satisfactory theoretical explanation for their success has been difficult.

In this talk I will discuss how this learning problem can be seen as an instance of a framework that we call “sample completion learning” and how sample completion learning is completely characterized by the model-theoretic notion of $k$-dependence introduced by Shelah (which can be seen as a high-dimensional version of the Vapnik–Chervonenkis dimension). In turn, this gives a full theoretical characterization of when the Netflix problem is “solvable”.

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Date/Time : 26 Nov 2025 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Bjoern Bringmann, Princeton University

Gibbs measures were first introduced in statistical mechanics, where they have been used to describe statistical equilibria of physical systems. Over the last decades, Gibbs measures have also become central objects in probability theory, partial differential equations, and mathematical physics. In this talk, we are interested in the heat, wave, and Schrödinger dynamics corresponding to Gibbs measures. In the first part of the talk, we discuss the invariance of the $\Phi^4_3$-measure under the three-dimensional cubic nonlinear wave equation. In the second part, we then discuss the global well-posedness of the stochastic Abelian-Higgs model, which is the Langevin equation for the Abelian-Higgs measure.

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Date/Time : 25 Nov 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Davide Ravotti, Université de Lille

Translation flows are a simple kind of motion on geometric surfaces built by gluing polygons edge-to-edge. In certain special cases, called self-similar, the flow repeats its behavior in a precise way when the surface is stretched and folded by a symmetry known as a pseudo-Anosov map. When this happens, we can understand the flow by studying this symmetry. A powerful method for doing this, pioneered in a work by Giulietti and Liverani, uses a tool called transfer operator. By analyzing how the transfer operator acts on a carefully chosen space of distributions, it is possible to deduce fine dynamical and statistical properties of self-similar flows on compact surfaces. This strategy was successfully carried out by Faure, Gouëzel, and Lanneau.

In this talk, I will describe how we extend this approach to self-similar translation flows on certain non-compact surfaces, namely Abelian covers. By introducing a family of weighted transfer operators, we obtain precise formulas describing the long-term behavior of time averages of observables, for points that are typical with respect to the natural measure lifted to the cover (joint work with Henk Bruin, Charles Fougerons, and Dalia Terhesiu). If time allows, I will also discuss ongoing work (with Mauro Artigiani, Roberto Castorrini, and Yuriy Tumarkin) that goes beyond the natural area measure and treats a broader class of ergodic invariant measures, known as Maharam measures.

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Date/Time : 25 Nov 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Bjoern Bringmann, Princeton University

There has been much recent progress on the local solution theory for geometric singular SPDEs. However, the global theory is still largely open. In this talk, we discuss the global well-posedness of the stochastic Abelian-Higgs model in two dimension, which is a geometric singular SPDE arising from gauge theory. The proof is based on a new covariant approach, which consists of two parts: First, we introduce covariant stochastic objects, which are controlled using covariant heat kernel estimates. Second, we control nonlinear remainders using a covariant monotonicity formula, which is inspired by earlier work of Hamilton.

This is joint work with S. Cao.

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Date/Time : 25 Nov 2025 10:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Lo Chi-Heng , National University of Singapore

In this talk, I will discuss Jiang’s Conjecture, which predicts an upper bound for the wavefront set of any representation of Arthur type in terms of the local Arthur packet containing it. I will then describe its generalization to ABV-packets and to arbitrary irreducible representations (not necessarily of Arthur type), and show that all these formulations of Jiang’s Conjecture are in fact equivalent. Moreover, I will explain that these conjectures can be further reduced to the case of anti-tempered representations.

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