Date/Time : 19 Nov 2025 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Siqing Zhang, Yale University

The Hodge Theorem reveals a fundamental phenomenon in algebraic geometry: the de Rham cohomology can often be identified with the Dolbeault cohomology. The Non Abelian version of this phenomenon “identifies” the moduli of flat connections with the moduli of Higgs bundles. The arithmetic version of this phenomenon echoes these identifications in prime characteristics. In this talk, I will introduce recent advances on the interplay among the Non Abelian Hodge Theories in different characteristics. By bringing moduli theory into the prime characteristic version, we reveal new structures over the complex numbers.

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Date/Time : 19 Nov 2025 15:00
Venue : S16 #05-17
Speaker : Ely Sandine, University of California, Berkeley

The Euler-Poisson system describes the evolution of a self-gravitating compressible fluid. I will present recent work proving the existence of certain self-similar implosion profiles for this system. These solutions belong to a family numerically conjectured by Hunter. I will discuss related PDEs, previous results for this system and aspects of the proof.

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Date/Time : 19 Nov 2025 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Seonwoo Kim, Yonsei University

The main purpose of this lecture course is to introduce the recently-developed resolvent approach [Landim-Marcondes-Seo, JEMS ’25] to metastability and beyond. First, I will review the historical developments in the treatment of the metastability phenomenon and summarize the pros/cons of the previous methods. Next, I will state and prove the resolvent approach in a simple setting, focusing especially on its strength, along with some real-model applications. Finally, I will summarize my recent work with Jungkyoung Lee (KIAS) to extend and generalize this approach to non-compact metastable transitions.

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Date/Time : 19 Nov 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Srecko Durasinovic, Nanyang Technological University

Mixture models, such as Gaussian mixture models (GMMs), are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the mixture parameters. We study the problem of approximating a target measure, available only through finitely many of its moments, by a mixture of distributions from a parametric family (e.g., Gaussian, exponential, Poisson), with approximation quality measured by the 2-Wasserstein ($\was$) or the total variation ($\tv$) distance. Unlike many existing approaches, the parameter set is not assumed to be finite; it is modeled as a compact basic semi-algebraic set. We introduce a hierarchy of semidefinite relaxations with asymptotic convergence to the desired optimal value. In addition, when a certain rank condition is satisfied, the convergence is even finite and recovery of an optimal mixing measure is obtained. We also present an application to clustering, where our framework serves either as a stand-alone method or as a preprocessing step that yields both the number of clusters and strong initial parameter estimates, thereby accelerating convergence of standard (local) clustering algorithms.

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Date/Time : 19 Nov 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Arpan Kabiraj, Indian Institute of Technology Palakkad

In 80’s, Goldman introduced a Lie bracket on the linear span of the free homotopy classes of directed closed curves on a surface called the Goldman Lie bracket. In this talk we will discuss some properties of Goldman Lie bracket using hyperbolic geometry. We will use these properties to give characterizations of simple closed curves. This is a joint work with Moira Chas.

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Date/Time : 18 Nov 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Fernando Camacho Cadena, Strasbourg University

A hyperbolic structure on a surface S can be deformed by cutting along a curve c without self—intersections, twisting, and re-gluing. Such a deformation can also be seen as the Hamiltonian flow of the length function of c on the Teichmüller space of S, equipped with the Weil—Petersson symplectic form. In this talk, I will discuss Hamiltonian flows associated to length functions of self—intersecting curves, and their generalizations to higher rank Teichmüller spaces. This is partially joint work with J. Farre and A. Wienhard.

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Date/Time : 17 Nov 2025 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : He Xuhua, University of Hong Kong

Lusztig’s theory of canonical bases reveals a remarkably rigid and positive algebraic structure on quantum groups and their modules. A fundamental result in symmetric types establishes that the structure constants for multiplication in the negative part $U^-$, as well as for the action of Chevalley generators $E_i$ and $F_i$ on a single simple module, all belong to $\mathbb{N}[v, v^{-1}]$.

Lusztig conjectured that this strong positivity holds for the multiplication within the modified quantum group and the action on the tensor product of modules. In this talk, I will present recent joint work with my postdoc, Jiepeng Fang. Our main result establishes that the structure constants for both the multiplication with arbitrary canonical basis elements in $\dot{\mathbf{U}}$ and the action on the canonical basis elements of arbitrary tensor products of simple lowest and highest weight modules by canonical basis elements arising from spherical parabolic subalgebras belong to $\mathbb{N}[v,v^{-1}]$.

A key innovation in our proof is the “thickening philosophy”, an algebraic technique inspired by geometric ideas from total positivity, building on my earlier work with Huanchen Bao. This method embeds a suitable approximation of the tensor product into the negative part $\tilde{U}^-$ of a larger quantum group, constructed via a framed
quiver. This allows us to inherit the desired positivity directly from the well-established positivity of the canonical basis of $\tilde{U}^-$. This approach demonstrates how wild Kac-Moody groups can provide a powerful framework for elucidating the representation theory of quantum groups beyond finite and affine types.

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Date/Time : 17 Nov 2025 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Seonwoo Kim, Yonsei University

The main purpose of this lecture course is to introduce the recently-developed resolvent approach [Landim-Marcondes-Seo, JEMS ’25] to metastability and beyond. First, I will review the historical developments in the treatment of the metastability phenomenon and summarize the pros/cons of the previous methods. Next, I will state and prove the resolvent approach in a simple setting, focusing especially on its strength, along with some real-model applications. Finally, I will summarize my recent work with Jungkyoung Lee (KIAS) to extend and generalize this approach to non-compact metastable transitions.

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Date/Time : 17 Nov 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Wang Weiqiang, University of Virginia

As a degeneration of affine quantum groups, Yangians quantize current algebras. It is known that truncated shifted Yangians quantize affine Grassmannian slices of type ADE; the latter are Coulomb branches of framed quiver gauge theories, and in type A, they can be identified with nilpotent Slodowy slices. As a degeneration of affine iquantum groups, twisted Yangians quantize twisted current algebras. We explain the Poisson geometry of [truncated shifted] twisted Yangians in terms of fixed point loci of affine Grassmannian slices by Poisson involutions; in split type A, the latter are identified will nipotent Slodowy slices of type BCD. This is joint work with Kang Lu and Alex Weekes.

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