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seminar-announce@snurep.crystalline.site

June 2026

1 participants
2 discussions

Kias 세미나 안내 (Anna Romanov, Kyu-Hwan Lee, Geordie Williamson)
by 이승빈 30 Jun '26

30 Jun '26

표현론 세미나 메일 구독자 분들께 Kias 에서 예정된 표현론 세미나 안내 메일 드립니다. 6/30, 7/6 강연은 이전에 안내드렸었지만, 발표 초록과 Zoom link 등을 포함해서 다시 안내 드립니다. speaker : *Anna Romanov* (University of New South Wales, Australia) date and time : *Jun. 30 (Tue), 2026, 10:30-12:00 (Korea time, UTC+9)* place : *Room 1423, KIAS *(in person) Zoom: Meeting ID: 822 3428 6796, Passcode: 760129, link: https://kias-re-kr.zoom.us/j/82234286796?pwd=JHofNUjsg3npLrFObNApbf6dKf704R… title: *Lusztig-Vogan categories and a categorial approach to real reductive groups* abstract: Soergel bimodules were introduced to tackle hard questions about the representation theory of complex semisimple Lie algebras. Similar (but harder) questions also exist about the representation theory of real reductive Lie groups. Can a Soergel-esque approach be taken in this world? I’ve been thinking about this question for many years. In this talk, I’ll tell you about my perspective. More specifically, I’ll introduce a collection of module categories over Soergel bimodules which encode information about the admissible representation theory of a real reductive group, with a focus on examples. --------- speaker : *Kyu-Hwan Lee* (University of Connecticut, USA) date and time : *Jul. 2 (Thu), 2026, 10:30-12:00 (Korea time, UTC+9)* place : *Room 1424, KIAS *(in person) (different room) Zoom: Meeting ID: 811 9263 1241, Passcode: 047201, link: https://kias-re-kr.zoom.us/j/81192631241?pwd=Ihc1VK2NG3pGRHygrOJG5DQwBreC0Q… title: *Auto-correlation functions of Sato-Tate distributions and identities of symplectic characters* abstract: The Sato--Tate distributions for genus 2 curves describe the statistics of the numbers of rational points on these curves. In this talk, we explicitly compute the autocorrelation functions of Sato--Tate distributions for genus 2 curves as sums of irreducible characters of symplectic groups. Our computations yield families of identities involving irreducible characters of the symplectic groups Sp(2m) for all m, which are of independent interest. The proofs use combinatorial objects, in particular crystals. This is a joint work with Se-jin Oh. --------- speaker : *Geordie Williamson* (University of Sydney, Australia) date and time : *Jul. 6 (Mon), 2026, 10:30-12:00 (Korea time, UTC+9)* place : *Room 1423, KIAS *(in person) Zoom : Meeting ID: 850 9457 8742, Passcode: 324001, link: https://kias-re-kr.zoom.us/j/85094578742?pwd=8edh0bmChHB3jKphDdiJNRxKZOLIDq… title: *Can we describe canonical bases as the solutions of optimization problems?* abstract: Canonical bases (e.g. of representations of quantum groups, of quantum groups themselves, of Hecke algebras, and of their representations) are mysterious and fundamental objects. Their definition typically involves the quantum parameter q in a critical way, via some form of "bar invariance" or "self-duality". Typically, their definition is elementary and combinatorial, and yet they have many deep properties — e.g. positivity and connections to representation theory or geometry. In the story I would like to tell one inverts the picture: one asks for the “simplest” or “smallest” basis which has positive structure constants. Remarkably, in many small examples, there is a unique solution and one recovers the canonical basis (often after specialising q->1) in an elementary way. This is typically not the case in large examples though, and the failure is tied to subtle geometry / representation theoretic behaviour. I would also like to advertise this problem as a place where Reinforcement Learning methods might find an interesting application (this was the original motivation for this project, but has not yet been pursued). This is joint work with Tom Goertzen (https://arxiv.org/abs/2604.18894). 감사합니다. 이승빈 올림.

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집중강연 안내 (CoHAs and Quantum Groups)
by 이승빈 19 Jun '26

19 Jun '26

표현론 세미나 메일 구독자분들께 7월과 8월에 Cohomological Hall algebra와 quantum group과 관련된 집중강연이 예정되어 있어 안내 메일 드립니다. 1) 강연자: Wenjun Niu 소속: Perimeter Institute 장소: 서울대학교 129동 406호 시간: 2026-07-27(월) 10:00~11:30 2026-07-27(월) 14:00~15:30 2026-07-29(수) 10:00~11:30 Title: Defects of 4d N=2 field theories and representation theory Abstract: 4d N=2 field theories is a rich source of new mathematics. In this series of talks, I will focus on the holomorphic-topological twist of these theories, and explore the (higher) algebra of defects, particularly the category of line defects. Along the way, I will report on work in progress/to appear with various collaborators on the representation-theoretic aspects of these defects. The following is a break-down of the plan of the lectures. The lectures will be mildly connected to each other. 1. This lecture will be mostly about background materials. I will start with reviewing the HT twist of 4d N=2 gauge theories in the BV formalism. Using this, I will explain how to give a systematic yet abstract definition of defects of various dimensions, and highlight the algebraic structures they carry. I will also discuss compactifications of the theory and what happens to defects under these compactifications. 2. In the second lecture, I will consider boundary conditions of the 4d pure gauge theories given by linear representations of the gauge group, possibly deformed by a potential. I will explain how the action of bulk lines on such boundary lines realizes the chiral ring relations of Nekrasov-Shatashivili. This is based on joint work to appear with J. Hilburn. 3. I will explore possibly non-Lagrangian 4d HT theories using cohomological Hall algebras. After reviewing the definition and properties of these algebras, as well as their string-theoretic interpretation, I will explain a proposal to define the category of line operators of the 4d HT theory using these algebras. This is based on joint work to appear with S. DeHority and A. Latyntsev. When the CoHA corresponds to a Lagrangian gauge theory, we formulate a conjecture relating our proposed category and the category of Cautis-Williams. I will discuss an idea to tackle this conjecture using the results of the second lecture. This is a work very much in progress with D. Gaiotto and J. Hilburn. 2) 강연자: Dylan Butson 소속: UCLA 장소: 서울대학교 129동 406호 시간: 2026-08-10(월) 10:00~11:30 2026-08-10(월) 14:00~15:30 2026-08-12(수) 10:00~11:30 Title: Yangians, W-algebras, and Hall algebras of toric Calabi-Yau threefolds Abstract: I will explain how various moduli spaces of (framed) sheaves on certain toric Calabi-Yau threefolds admit concrete descriptions as spaces of representations of certain (framed) quivers with potential. I will then explain that these (framed) quivers determine cohomological Hall algebras (and representations thereof), and that these algebras and representations are closely related to affine Yangians and W-algebras in type A. Time permitting, I will outline a partially conjectural dictionary relating generalized coproducts on shifted affine Yangians, partial free-field realizations of affine W-algebras, and the geometry of toric divisors in this class of threefolds. 감사합니다. 이승빈 올림.

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