Date/Time : 25 Nov 2024 14:00
Venue : S17 #04-06 (SR1)
Speaker : Tomasz Przebinda, University of Oklahoma

We describe an integral kernel operator which should map a Harish-Chandra character of a representation of one member of a dual pair to a distribution on the other member of the dual pair. A well founded hope is that this distribution coincides with the character of the big theta lift. In part this is a joint work with Hung Yean Loke.

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Date/Time : 14 Nov 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Finn Wiersig, National University of Singapore

The Riemann-Hilbert correspondence establishes a profound connection between certain differential equations on a given complex analytic manifold and its topology. This result had numerous interesting applications; for example, it was applied by Beilinson-Bernstein and Brylinski-Kashiwara in the 1980s to study the representation theory of semisimple algebraic groups. This talk explores ongoing research leveraging these concepts to investigate representation theory appearing in the p-adic local Langlands program, focusing on progress towards a p-adic analytic Riemann-Hilbert correspondence.

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Date/Time : 07 Nov 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Euiyong Park, University of Seoul

Let $C$ be a generalized Cartan matrix and $U_q(\mathfrak{g})$ the quantum group associated with $C$. In this talk, I am going to talk about the PBW theory for the bosonic extension $\widehat{A}_{\mathfrak{g}}$ of the negative half $U_q^-(\mathfrak{g})$. When $U_q(\mathfrak{g})$ is of finite simply-laced type, the algebra $\widehat{A}_{\mathfrak{g}}$ is isomorphic to the quantum Grothendieck ring of the Hernandez-Leclerc category over a quantum affine algebra. The PBW theory allows us to define a new family of subalgebras, denoted by $\widehat{A}_{\mathfrak{g}}(b)$, for any element $b$ in the (generalized) Braid group associated with $C$. I will explain why this algebra $\widehat{A}_{\mathfrak{g}}(b)$ can be viewed as a natural extension of the quantum unipotent coordinate ring $A_q(n(w))$ for a Weyl group element $w$. This talk is based on arXiv:2401.04878 (with Se-jin Oh) and arXiv:2408.07312 (with Masaki Kashiwara, Myungho Kim and Se-jin Oh).

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Date/Time : 30 Oct 2024 16:00
Venue : S17 #04-05 (SR2)
Speaker : Jimmy He, Ohio State University

The study of quantum groups and integrable systems have long been connected through the Yang-Baxter equation. Recently, these ideas have been introduced in probability to study integrable stochastic models. I will discuss a similar story for models with boundary, which are connected to quantum symmetric spaces through the reflection equation, as well as some applications to probability. The focus will be on illustrating the connections through illustrative examples and applications for a specific model called the six vertex model.

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Date/Time : 24 Oct 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Michael Pevzner, Université de Reims-Champagne-Ardenne

Inspired by classical concepts of generating functions for orthogonal polynomials, this talk will explore “generating operators” for a family of differential operators acting between two manifolds.

We will present a formula for these generating operators associated with Rankin–Cohen brackets and discuss their connection to infinite-dimensional representation theory. Joint work with T. Kobayashi.

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Date/Time : 24 Oct 2024 17:00
Venue : S17 #05-12 (SR4)
Speaker : Jimmy He, Ohio State University

The study of quantum groups and integrable systems have long been connected through the Yang-Baxter equation. Recently, these ideas have been introduced in probability to study integrable stochastic models. I will discuss a similar story for models with boundary, which are connected to quantum symmetric spaces through the reflection equation, as well as some applications to probability. The focus will be on illustrating the connections through illustrative examples and applications for a specific model called the six vertex model.

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Date/Time : 23 Oct 2024 16:00
Venue : S17 #04-05 (SR2)
Speaker : Jimmy He, Ohio State University

The study of quantum groups and integrable systems have long been connected through the Yang-Baxter equation. Recently, these ideas have been introduced in probability to study integrable stochastic models. I will discuss a similar story for models with boundary, which are connected to quantum symmetric spaces through the reflection equation, as well as some applications to probability. The focus will be on illustrating the connections through illustrative examples and applications for a specific model called the six vertex model.

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Date/Time : 03 Oct 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Dihua Jiang, University of Minnesota

I will discuss relations between non-abelian Fourier transforms and the Langlands conjecture on automorphic L-functions and associated local factors in the framework of Braverman-Kazhdan-Ngo.

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Date/Time : 03 Oct 2024 17:00
Venue : S17 #05-12 (SR4)
Speaker : Meng Fai Lim, Central China Normal University

In this talk, we begin reviewing the non-commutative Iwasawa theory as developed by Coates, Fukaya, Kato, Sujatha and Venjakob which is concerned with attaching suitable characteristic elements to modules of arithmetic interest (for instance, Selmer groups). By their construction, these characteristic elements are realized as element in an appropriate localized K_1 group. We then introduce a notion of “taking modulo p” of these characteristic elements and discuss some of its properties. This is an ongoing work with Chao Qin.

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