Geometry, Algebra and Physics Seminar at KIAS
Geometry, Algebra and Physics Seminar at KIAS
organizer : Hyun Kyu Kim (Korea Institute for Advanced Study, hkim@kias.re.kr)
since Fall 2022
This is a not-so-regular seminar. Please contact Hyun Kyu Kim if you want to be in the mailing list. For speakers outside Korea, the talks will be conducted via Zoom mostly. If we have an offline talk, we will try to broadcast it real-time by Zoom. If the speaker agrees, we will record the lecture videos and make them available.
youtube channel for the recorded videos: https://www.youtube.com/@geometryalgebraandphysicskias
Upcoming talks
Geordie Williamson (University of Sydney, Australia)
Jul. 6 (Mon), 2026, 10:30-12:00 (Korea time, UTC+9)
in person, Room 1423, KIAS
Zoom : Meeting ID: 850 9457 8742, Passcode: 324001, link: https://kias-re-kr.zoom.us/j/85094578742?pwd=8edh0bmChHB3jKphDdiJNRxKZOLIDq.1
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).
Michel van Garrel (University of Birmingham, UK)
Jul. 10 (Fri), 2026, 10:30-12:00 (Korea time, UTC+9)
in person, Room 1424, KIAS
title: The Rising Sea for Enumerative Mirror Symmetry
abstract:
Enumerative Mirror Symmetry predicts that each Calabi-Yau variety X admits a mirror-dual Calabi-Yau variety Y, so that the symplectic Gromov-Witten (GW) invariants of X are computed from period integrals on Y. Mirror Symmetry inspired calculations of GW invariants have been achieved in several large families of cases yielding lots of data, yet we are still lacking a general approach.
The rising sea is a metaphor introduced by Grothendieck to describe a mathematical framework that is set up in a way so that major results of the theory are an almost automatic consequence of the definitions.
Comes in Intrinsic Mirror Symmetry (Gross-Siebert, 2022), which provides a general construction of Y from X. I will talk about an ongoing joint project with Siebert, where we show that the generating function of GW invariants of X equals the expansion of an intrinsic period integral on the Intrinsic Mirror Y of X. This project is motivated by building a Rising Sea framework for Enumerative Mirror Symmetry. (https://sites.google.com/view/gapkias)
Upcoming speakers (schedule to be settled)
Subhojoy Gupta (Indian Institute of Science, India)
Past talks (<- click to see more information, including links for recorded videos)
2026.Jul.02, Kyu-Hwan Lee (University of Connecticut, USA): Auto-correlation functions of Sato-Tate distributions and identities of symplectic characters
2026.Jun.30, Anna Romanov (University of New South Wales, Australia): Lusztig-Vogan categories and a categorial approach to real reductive groups
2026.Jun.12, Mikhail Khovanov (Johns Hopkins University, USA): An introduction to sl(3) web categorification
2026.Jun.12, Lang Mou (UC Davis, USA): Modulated graphs with potentials and skew-symmetrizable cluster algebras
2026.Jun.10, Amanda Burcroff (MIT, USA): Eventual Sign Coherence for Quivers
2026.Apr.2, Manish Patnaik (University of Alberta, Canada): Hints of a double affine Kazhdan—Lusztig theory
2026.Jan.30, Rinat Kashaev (Université de Genève, Switzerland): Applications of the Quantum Dilogarithm
2025.Dec.23, Vijay Higgins (UCLA, US): Skein identities at roots of unity
2025.Dec.5, Ben Davison (The Univ. of Edinburgh, UK): Tutte polynomials of graphs and symplectic duality
2025.Sep.19, Zhihao Wang (KIAS, Korea): Centers and Representations of the SL(n) quantum Teichmüller Space
2024.Jun.27, Volker Genz (IBS-CGP, Korea): Crystals and Cluster Algebras
2024.May.24, Kyoung-Seog Lee (POSTECH, Korea): An introduction to moduli spaces of vector bundles on an algebraic curve
2024.May.03, Dmitriy Voloshyn (IBS-CGP, Korea): Cluster algebras and Poisson geometry
2024.Apr.30, Sunghyuk Park (Harvard University, US): 3d quantum trace map
2024.Apr.25, Valentin Buciumas (POSTECH, Korea): Hecke algebras, Whittaker functions and quantum groups
2023.Dec.5, Ben Davison (The Univ. of Edinburgh, UK): Strong positivity for quantum cluster algebras
2023.Oct.23, Sin-Myung Lee (KIAS, Korea): Representations of quantum affine (super)algebras from the R-matrix's point of view
2023.Oct.12, Hyunbin Kim (Yonsei Univ., Korea): Morse Superpotential and Blowups of Surfaces
2023.Jul.6, Yoosik Kim (Pusan National University, Korea): Infinitely many monotone Lagrangian tori in flag manifolds
2023.Jun.29, Wataru Yuasa (Division of Mathematics and Mathematical Sciences, Kyoto University, Japan): State-clasp correspondence for skein algebras
2023.May.11, Tsukasa Ishibashi (Mathematical Institute, Tohoku University, Japan): Moduli space of decorated G-local systems and skein algebras
2023.Jan.12, Shunsuke Kano (Research Alliance Center for Mathematical Sciences, Tohoku University, Japan): Unbounded sl(3)-laminations and their shear coordinates
2022.Dec.22, Hironori Oya (Tokyo Institute of Technology, Japan): Wilson lines on the moduli space of $G$-local systems on a marked surface
2022.Dec.8, Kyoung-Seog Lee (IMSA, Univ. of Miami, US): Parabolic bundles on curves and their applications
2022.Oct.24, Daniel Douglas (Yale University, US): Dimers, webs, and local systems
2022.Oct.17, Dylan Allegretti (Yau Mathematical Sciences Center at Tsinghua University, China): Teichmüller spaces, quadratic differentials, and cluster coordinates
links
(workshop held on Jan.29-31, 2024) Physical Mathematics and Beyond: the 1st workshop
(workshop held on Jun.17-19, 2024) Physical Mathematics and Beyond: the 2nd workshop
(workshop held on Jul.8-12, 2024) Summer School in Geometry And Physics
(conference on Jan.5-9, 2026) Geometry, Algebra and Physics at KIAS
(conference scheduled at SNU on Jun.15-19, 2026) Physical Mathematics 2026 in Korea
last updated: Jul. 5, 2026