Date/Time : 05 Mar 2025 15:00
Venue : S17 #04-06 (SR1)
Speaker : James Farre, Max Planck Institute for Mathematics in the Sciences

The geodesic flow on the unit tangent bundle of a hyperbolic surface is a prototypical example of an Anosov flow, exhibiting rich, structurally stable dynamics. While invariant measures and closed sets for the geodesic flow can be quite complicated, the closely related horocycle flow exhibits striking rigidity. For example, on a closed surface, every horocycle is dense and equidistributed in its unit tangent bundle; this is very far from being true for geodesics.

Despite this rigidity, the behavior of horocycles remains mysterious in the setting of hyperbolic surfaces with infinite topology. In this talk, I will explore the dynamics of horocyclic trajectories for a particular class of infinite-area regular covers of closed hyperbolic surfaces. Surprisingly, these trajectories are intimately connected to an exceptional set for the geodesic flow: the distance-minimizing geodesic lamination. Both objects arise naturally in a geometric optimization problem: what does an optimal Lipschitz map to the circle in a given homotopy class look like?

This is joint work with Or Landesberg and Yair Minsky.

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Date/Time : 04 Mar 2025 14:00
Venue : S17 #05-11 (SR5)
Speaker : Xie Kaitao, The University of Hong Kong

The totally nonnegative part of flag varieties has been studied extensively for many years, and many remarkable properties have been established. Motivated by the study of higher Teichmuller theory, Guichard and Wienhard generalized Lusztig’s notion of total positivity and introduce theta positivity. In this talk, I will discuss the analogues for a family of theta nonnegative part of Lagrangian Grassmannian.

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Date/Time : 04 Mar 2025 15:00
Venue : S17 #04-05 (SR2)
Speaker : Anastasia Borovykh, Imperial College London

State-of-the-art foundation models are often seen as black boxes: we send a prompt in and we get out our – often useful – answer. But what happens inside the system as the prompt gets processed remains a bit of a mystery & our ability to control the processing into specific directions is limited.

In this walk we will discuss two concepts that can help us add additional controls into these models. First up, LogitLens, a method to gain more insight into the representations of hidden nodes. Second, steering vectors: by computing a vector that represents a particular feature or concept, we can use this to steer the model to include any property in the output we want. We end the talk by discussing whether the approach of ‘build a good model, then interpret it’ can work or whether we should shift our focus to ‘build an a priori interpretable model’ and discuss ways of potentially achieving this.

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Date/Time : 04 Mar 2025 15:00
Venue : S17 #05-11 (SR5)
Speaker : Max Gurevich, Technion - Israel Institute of Technology

For a split reductive p-adic group G, one can choose a hyperspecial maximal compact subgroup K and its Iwahori subgroup I. The resulting Hecke algebra H(I\K/I) is on one hand understood as a deformation of the Weyl group W of G; on the other, it acts on representations in the principal Bernstein block of G-representations.

With the p-adic story set aside, the geometric theory of Weyl group representations is expressed in the Springer correspondence, which parametrizes the spectrum of W in terms of local systems on unipotent conjugacy classes of the complex Langlands dual group to G.

When G is of classical type, the same local systems also arise as parameters in Arthur’s endoscopic approach to Langlands reciprocity. With Emile Okada, we explore the interplay between these two sets of parameters attached to irreducible representations, investigating their compatibility with natural restriction functors.

If time permits, I will explain one angle of broader motivation: an expectation relating local Arthur packets to the notion of ‘weak sphericity’ of representations. Interestingly, this property is most naturally analyzed through its specialization to the domain of Weyl group representations.

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Date/Time : 03 Mar 2025 16:00
Venue : S16 #03-06
Speaker : Li Zhuoyuan, Peking University

Data assimilation, as a key technique for merging physical models with observational to estimate state variables, has been widely explored in the fields of weather forecasting, oceanography, and ecology. However, conventional assimilation frameworks, such as variational methods (3D/4DVar) and sequential methods (EnKF), often struggle with the high dimensionality and pronounced nonlinearity inherent in both physical and observational models. In this talk, I will introduce our recent work on leveraging deep learning to address these challenges, focusing on data-driven reduced-order modeling and deep generative modeling.

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Date/Time : 26 Feb 2025 10:00
Venue : S17 #05-11 (SR5)
Speaker : Ma Jiajun, Xiamen University and Xiamen University Malaysia

This mini-course explores the fundamental aspects of local theta correspondence. The series consists of 5 lectures covering the following topics:

1. Models of the Heisenberg-Weil representation and the Metaplectic group
2. Dual pairs and general properties of theta correspondences
3. Theta correspondences over real fields
4. Theta correspondences over finite fields and p-adic fields
5. Geometric aspects of theta correspondence

This mini-course is designed for senior undergraduate students and graduate students.

This mini-course will live stream. Here is the zoom ID:
Meeting ID: 848 8485 0855
Passcode: 226224

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Date/Time : 24 Feb 2025 16:00
Venue : S17 #04-04 (SR3)
Speaker : Shota Osada, Kagoshima University

In this talk, we will consider the construction of $\mu$-reversible diffusion processes for a given point process $\mu$ on  $\mathbb{R}^d$. Specifically, we will discuss the Dirichlet form method to construct distorted Brownian motion on configuration spaces. For Poisson point processes, this corresponds to an infinite number of independent Brownian motions on $\mathbb{R}^d$. For correlated point processes, the interaction between particles is characterized by a function called the log-derivative, which describes the force exerted on one particle by the others. In previous results, the construction of diffusion processes using Dirichlet forms and their characterization using log-derivatives have been treated separately. In this talk, I will introduce that the existence of a logarithmic derivative implies the closability of the Dirichlet form. 

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Date/Time : 24 Feb 2025 16:00
Venue : S17 #04-04 (SR3)
Speaker : Shuhei Shibata, Kyushu University

We study the classical law of iterated logarithm for centered continuous Gaussian processes. Also, we introduce one of the asymptotic behavior of a non-Markovian stochastic process called elephant random walk as an application.

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Date/Time : 21 Feb 2025 13:00
Venue : S17 #04-04 (SR3)
Speaker : Weikun He, AMSS, Chinese Academy of Sciences

On homogeneous spaces such as SL_2(R)/SL_2(Z), there are interesting random walks which are driven by group action. We focus on asymptotic behaviour of such random walk, especially on the property of equidistribution in law. In this talk, I will present a method developed in a joint work with Timothée Bénard to estimate the rate of convergence of such equidistribution. It involves ideas from fractal geometry and it constitutes a crucial ingredient in the study of Diophantine approximation on fractal sets, presented in the YMLS talk.

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