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표현론 집중 강연 안내 (9월 15일 ~ 9월 17일)
by 이승빈 14 Aug '26

14 Aug '26

표현론 세미나 메일 구독자 분들께 안녕하세요. 다가오는 9월에 있을 표현론 집중강연에 대해서 안내드립니다. ---------------------------------------------------------------------- Lecture Series on Representation Theory Lecture 1: Geometric Crystals and Integral Polytopes Associated with Kirillov-Reshetikhin Modules Speaker: Masato Okado (Osaka Metropolitan University) Place and Dates: 129-406 (SNU) Talk 1: 09.15. (Tue) 10:00~11:30 Talk 2: 09.16. (Wed) 10:00~11:30 Talk 3: 09.17. (Thu) 10:00~11:30 Abstract: Among the finite-dimensional representations of quantum affine algebras, there exists a family of modules with desirable properties known as Kirillov-Reshetikhin (KR) modules. KR modules are parameterized by a vertex $r$ of the Dynkin diagram and a positive integer $l$, and they possess crystal structures in the sense of Kashiwara. Meanwhile, Berenstein and Kazhdan introduced the concept of "geometric crystals" as an algebraic-geometric analogue of crystals; it is conjectured that these exist in correspondence with sequences of KR modules where $r$ is fixed. Recently, we have obtained the "decoration functions" (in the sense of Berenstein and Kazhdan) for cases where the corresponding affine Lie algebra is of ADE type and $r$ corresponds to a minuscule weight representation. By applying ultradiscretization (tropicalization) to these geometric crystals with decoration functions, one obtains an integral convex polytope representation of the KR crystal—the crystal structure associated with the KR module—for any value of $l$. In the talk, I will illustrate the construction procedures for crystals, geometric crystals, and integral convex polytopes using basic examples. For root systems of type A, these correspond respectively to (rectangular) Young tableaux, Grassmannians, and Gelfand-Tsetlin polytopes (corresponding to specific highest weight representations). This conjecture can be extended to all root systems, yet the area remains almost entirely unexplored for types other than type A. Lecture 2: Representation theory of quantum symmetric pairs and related combinatorics Speaker: Hideya Watanabe (Rikkyo University) Place and Dates: 129-406 (SNU) Talk 1: 09.15. (Tue) 15:00~16:30 Talk 2: 09.16. (Wed) 15:00~16:30 Talk 3: 09.17. (Thu) 15:00~16:30 Abstract: Given a symmetric pair (g,k), a pair of complex reductive Lie algebras, one has its quantum deformation (U_q(g), U^i(k)), called a quantum symmetric pair (QSP for short). A QSP consists of a quantum group U_q(g) and its certain coideal subalgebra U^i(k), called an i-quantum group. Although the i-quantum group U^i(k) is a quantum deformation of the Lie algebra k, it is different from the quantum group U_q(k), in general. As a result, the representation theory of i-quantum groups has a different flavor than that of quantum groups. In these lectures, we focus on non-Levi branching rules, i.e., the k-module structure of various g-modules. Such problems cannot be solved by means of quantum groups because U_q(k) is not a subalgebra of U_q(g). In the first part of the lectures, we review representation theory of quantum groups quickly. Then, we introduce QSPs and their integrable modules. We show that the integrable modules for a QSP leads us to a Peter-Weyl type decomposition of the dual of the i-quantum group. In the remaining parts, we introduce some interesting type-dependent results. We focus on type AI, AII, BII, and DII; the corresponding symmetric pairs are (gl_n, so_n), (gl_2n, sp_2n), (so_2n+1, so_2n), and (so_2n, so_2n-1). For these pairs, we can understand the branching rules in terms of some combinatorial objects. Such combinatorial objects include semistandard Young tableaux, King's symplectic tableaux, Kashiwara-Nakashima's orthogonal tableaux, and Gelfand-Tsetlin patterns. -------------------------------------------------------------------------------------- 감사합니다. 이승빈 올림.

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Jacobian conjecture 강연
by 이승빈 23 Jul '26

23 Jul '26

표현론 세미나 메일 구독자 분들께 7월 30일에 예정되어 있는 Jacobian conjecture 강연의 안내 메일 드립니다. ----------------------------------------------------------------------------------------------------- 일정 : 2026-07-30(목) 10:30~12:00 장소 : 129동 406호 강연자 : Kyungyong Lee (University of Alabama) On 7/20/2026, the counterexample to the Jacobian conjecture was discovered with the help of Claude Fable. We give an overview of the past, present, and future of the Jacobian conjecture. https://www.math.snu.ac.kr/bbs/board.php?bo_table=Math_Seminar&wr_id=46508&… -------------------------------------------------------------------------------------------------------------------- 감사합니다. 이승빈 올림.

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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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Kias 세미나 (Anna Romanov, Geordie Williamson)
by 이승빈 29 May '26

29 May '26

표현론 세미나 메일 구독자 분들께 Kias 에서 6월 30일(화), 7월 6일(월)에 표현론 세미나가 예정되어 있습니다. 발표 내용이 아직 정해지지 않았는데, 날짜/시간을 우선 안내드립니다. Anna Romanov (University of New South Wales, Australia) Jun. 30 (Tue), 2026, 10:30-12:00 (Korea time, UTC+9) in person, Room 1423, KIAS Geordie Williamson (University of Sydney, Australia) Jul. 6 (Mon), 2026, 10:30-12:00 (Korea time, UTC+9) in person, Room 1423, KIAS 감사합니다. 이승빈 올림.

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'표현론 집중 강연 일정 안내' 메일 중복 발송에 따른 양해 부탁의 건
by 이승빈 25 Apr '26

25 Apr '26

표현론 세미나 메일 구독자 분들께 어제와 오늘에 걸쳐 발송해 드린 '표현론 집중 강연 일정 안내' 메일이 발송 시스템의 일시적인 오류로 인해 중복 전달되었습니다. 발송 상태를 확인하고 재시도하는 과정에서 동일한 내용의 메일이 여러 차례 발송된 것으로 파악되었습니다. 수신된 메일들은 모두 동일한 내용이오니, 번거로우시겠지만 하나를 제외한 나머지 중복된 메일은 무시해 주시기를 부탁드립니다. 이용에 불편을 드려 대단히 죄송합니다. 감사합니다. 이승빈 올림

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표현론 집중 강연 일정 안내
by 이승빈 25 Apr '26

25 Apr '26

표현론 세미나 메일 구독자 분들께 안녕하세요. 서울대학교에서 진행될 표현론 집중 강연에 대해 안내 드립니다. 6월8일~12일: 집중강연 2개 Satoshi Naito (IST): 안내예정(crystal base theory: LS path models) 홍재현(IBS): 안내예정 9월14일~18일: 집중강연 2개 Masato Okado (OMU): 안내예정( Finite affine crystals) Hideya Watanabe (Rikkyo): 안내예정 (iquantum groups ans crystal base) 각 강연별로 주제 및 구체적인 장소, 세부 일정은 추후 공지드리도록 하겠습니다. 감사합니다. 이승빈 올림.

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표현론 집중 간연 일정 안내
by 이승빈 24 Apr '26

24 Apr '26

표현론 세미나 메일 구독자 분들께 안녕하세요. 서울대학교에서 진행될 표현론 집중 강연에 대해 안내 드립니다. 6월8일~12일: 집중강연 2개 Satoshi Naito (IST): 안내예정(crystal base theory: LS path models) 홍재현(IBS): 안내예정 9월14일~18일: 집중강연 2개 Masato Okado (OMU): 안내예정( Finite affine crystals) Hideya Watanabe (Rikkyo): 안내예정 (iquantum groups ans crystal base) 각 강연별로 주제 및 구체적인 장소, 세부 일정은 추후 공지드리도록 하겠습니다. 감사합니다. 이승빈 올림.

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표현론 집중 간연 일정 안내
by 이승빈 24 Apr '26

24 Apr '26

표현론 세미나 메일 구독자 분들께 안녕하세요. 서울대학교에서 진행될 표현론 집중 강연에 대해 안내 드립니다. 6월8일~12일: 집중강연 2개 Satoshi Naito (IST): 안내예정(crystal base theory: LS path models) 홍재현(IBS): 안내예정 9월14일~18일: 집중강연 2개 Masato Okado (OMU): 안내예정( Finite affine crystals) Hideya Watanabe (Rikkyo): 안내예정 (iquantum groups ans crystal base) 각 강연별로 주제 및 구체적인 장소, 세부 일정은 추후 공지드리도록 하겠습니다. 감사합니다. 이승빈 올림.

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표현론 집중 간연 일정 안내
by 이승빈 24 Apr '26

24 Apr '26

표현론 세미나 메일 구독자 분들께 안녕하세요. 서울대학교에서 진행될 표현론 집중 강연에 대해 안내 드립니다. 6월8일~12일: 집중강연 2개 Satoshi Naito (IST): 안내예정(crystal base theory: LS path models) 홍재현(IBS): 안내예정 9월14일~18일: 집중강연 2개 Masato Okado (OMU): 안내예정( Finite affine crystals) Hideya Watanabe (Rikkyo): 안내예정 (iquantum groups ans crystal base) 각 강연별로 주제 및 구체적인 장소, 세부 일정은 추후 공지드리도록 하겠습니다. 감사합니다. 이승빈 올림.

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