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.