Program

Time	Dec 8 (Mon)	Dec 9 (Tue)	Dec 10 (Wed)	Dec 11 (Thu)	Dec 12 (Fri)
09:30 – 10:00	Welcome and Registration / Breakfast
10:00 – 11:00	Cheol-Hyun Cho	Philip Boalch	Myungho Kim	Adam Gyenge	Sergey Cherkis
11:00 – 11:10	Break / Teatime
11:10 – 12:10	Masahito Yamazaki	Ben Davison	Amihay Hanany	Harold Williams	Hyun Kyu Kim
12:10 – 14:00	Lunch
14:00 – 15:00	Dongwook Ghim	Saebyeok Jeong	Excursion	Albrecht Klemm	Free Discussion & Closing
15:00 – 15:10	Break / Teatime			Break / Teatime
15:10 – 16:10	Free Discussion			Xiaomeng Xu
16:10 – 16:40				Photo Session & Discussions
16:40 – 17:30
17:30 – 19:30				Banquet

Abstract

Monday, December 8

Time	Speaker	Title & Abstract
10:00 – 11:00	Cheol-Hyun Cho (Pohang University of Science and Technology)	Geometric models of simple Lie algebras via singularity theory It is well-known that ADE Dynkin diagrams classify both the simply-laced simple Lie algebras and simple singularities. We introduce a polygonal wheel in a plane for each case of ADE, called the Coxeter wheel. We show that equivalence classes of edges and spokes of a Coxeter wheel form a geometric root system isomorphic to the classical root system of the corresponding type. This wheel is in fact derived from the Milnor fiber of corresponding simple singularities of two variables, and the bilinear form on the geometric root system is the negative of its symmetrized Seifert form. Furthermore, we give a completely geometric definition of simple Lie algebras using arcs, Seifert form and variation operator of the singularity theory.
11:10 – 12:10	Masahito Yamazaki (University of Tokyo)	Quiver Algebras and Their Representations I will give an overview of recent developments in the representation theory of quiver algebras—including quiver Yangians and their relatives—from both physical and mathematical perspectives.
14:00 – 15:00	Dongwook Ghim (IBS Center for Theoretical Physics of the Universe)	Birational Transformations and Deformations in 2d Quiver Gauge Theories In this talk, we explore the interplay between birational transformations of toric Calabi-Yau 4-folds and relevant deformations of (1+1)d quiver gauge theories through their string-theoretic realization, called brane brick models. Taking T-duality, we can understand the latter as Type IIA brane configuration which describes the worldvolume theories of probe D1-branes at the toric Calabi-Yau 4-folds in Type IIB string theory. We begin by reviewing how brane brick models combinatorially encode the geometric data of toric Calabi-Yau 4-folds and translate it into the physical elements of (1+1)d (0,2) supersymmetric gauge theories. We then introduce birational transformations, a mathematical notion that transforms one Calabi-Yau geometry into another, and discuss one of its physics interpretations in terms of brane brick models—relevant deformations in the corresponding gauge theories. In particular, we show that the mesonic moduli spaces of brane brick models related by such deformations have the same number of algebraic generators and share the same Hilbert series under a specific refinement by R-symmetry, though their mesonic global symmetries may differ. Extending this perspective, we examine how birational transformations can classify toric Calabi-Yau 4-folds and their associated gauge theories into non-trivial equivalence classes.

Tuesday, December 9

Time	Speaker	Title & Abstract
10:00 – 11:00	Philip Boalch (Paris Rive Gauche, CNRS)	Quivers at the boundary and global Cartan matrices I’ll start by recalling the quiver modularity theorem showing how the Nakajima quiver varieties for all the supernova quivers appear in 2d gauge theory as additive DeRham moduli spaces [CB, B08, HY]. In turn I will explain how the same quivers appear in terms of the Stokes arrows and wild monodromy relations [BY20], on the multiplicative/Betti side of the Stokes–Birkhoff–Riemann–Hilbert map, leading to a much more general story: the notion of graph (= doubled quiver) may be generalized to a diagram, and Douçot has defined a diagram (and thus a global Cartan matrix) for any meromorphic connection on the Riemann sphere [D21], generalising [BY20] (for connections that are tame at finite distance). Crucial use is made of work of Laumon and Malgrange on the local Fourier transform, and Martinet-Ramis on the wild fundamental group. If time permits the recent work [B25, D25] will be discussed, aiming to classify the non-abelian Hodge graphs, i.e. the special “modular” quivers that appear in relation to the wild nonabelian Hodge moduli spaces. B08 Irregular connections and Kac-Moody root systems, arxiv:0806.1050 (published as part of Simply-laced isomonodromy systems, Pub. Math. IHES 2012) . BY20 P.B. & D. Yamakawa, Diagrams for nonabelian Hodge spaces on the affine line, Comptes Rendus Mathématique 358 (2020) no. 1, 59–65. B25 Counting the fission trees and nonabelian Hodge graphs (untwisted case), J. Geom. Phys. 214 (2025) . CB W. Crawley-Boevey, On matrices in prescribed conjugacy classes, Duke 118(2) 2003. . D21 J. Douçot, Diagrams and irregular connections on the Riemann sphere, arXiv:2107.02516, 2021. D25 J. Douçot, New nonabelian Hodge graphs from twisted irregular connections,arxiv:2509.24861, 2025. HY K. Hiroe and D. Yamakawa, Moduli spaces of meromorphic connections and quiver varieties, Adv. Math 266, 2014
11:10 – 12:10	Ben Davison (University of Edinburgh)	Okounkov's conjecture via BPS Lie algebras Given an arbitrary finite quiver Q, Maulik and Okounkov defined a new Yangian-style quantum group. It is built via the FRT formalism and their construction of R matrices on the cohomology of Nakajima quiver varieties, via the stable envelopes that Maulik and Okounkov also defined. Just as in the case of ordinary Yangians, there is a Lie algebra $g_Q$ inside their new algebra, and the Yangian is a deformation of the current algebra of this Lie algebra. Outside of extended ADE type, numerous basic features of $g_Q$ have remained mysterious since the outset of the subject, for example, the dimensions of its graded pieces. A conjecture of Okounkov predicts that these dimensions are given by the coefficients of Kac's polynomials, which count isomorphism classes of absolutely indecomposable Q-representations over finite fields. I will explain a recent result, with Botta, stating that the Maulik-Okounkov Lie algebra associated to a quiver Q is isomorphic to the BPS Lie algebra associated to the tripled quiver of Q, along with its canonical cubic potential. Thanks to joint work of myself with Hennecart and Schlegel Mejia, this result implies Okounkov's conjecture, as well as determining the generators and relations of $g_Q$ in terms of intersection cohomology of singular quiver varieties.
14:00 – 15:00	Saebyeok Jeong (IBS Center for Geometry and Physics)	Quantum curves and refined BPS invariants from defects in gauge theory In this talk, I will discuss codimension-two defects in five-dimensional N=1 gauge theories placed in the $\Omega$-background. The partition functions of these defects can be interpreted as generating functions for refined open BPS invariants. In the Nekrasov–Shatashvili limit, these partition functions satisfy specific q-difference equations that provide an unambiguous quantization of the classical Seiberg–Witten curves. Remarkably, these equations coincide with Baxter’s TQ relations for integrable systems naturally associated with the underlying 5d gauge theories.

Wednesday, December 10

Time	Speaker	Title & Abstract
10:00 – 11:00	Myungho Kim (Kyunghee University)	Monoidal categorification of the cluster algebra A(b) associated with a positive braid (This is a joint work with Masaki Kashiwara, Se-jin Oh, and Euiyong Park.) In this talk, I will describe a recent approach to understanding the cluster algebra structure of the algebra A(b), which arises from a positive braid b and is a special subalgebra inside the so-called bosonic extension A. The bosonic extension is an extension of the positive half U_q(n) of a quantum group, and A(b) is constructed by selecting the PBW-type elements determined by the braid b. Our construction takes place inside the category of finite-dimensional representations of a quantum affine algebra. Starting from basic modules determined by the braid, we apply braid symmetries to obtain fundamental building blocks that generate a monoidal subcategory denoted C^D(b), within which suitable heads of tensor products serve as cluster variables. We show that these modules give rise to a monoidal seed in the sense of cluster algebra theory, yielding a cluster algebra structure on A(b). Moreover, the Grothendieck ring of C^D(b) recovers the algebra A(b), and in fact every cluster monomial corresponds to a real simple module in the category.
11:10 – 12:10	Amihay Hanany (Imperial College London)	TBA TBA

Thursday, December 11

Time	Speaker	Title & Abstract
10:00 – 11:00	Adam Gyenge (Budapest University of Technology and Economics)	On the topology of affine bow varieties Cherkis bow varieties were introduced as an ADHM type description of moduli spaces of $U(n)$-instantons on the Taub-NUT space equivariant under a cyclic group Z/mZ-action. An algebro-geometric description using quivers was constructed by Nakajima-Takayama, who have also shown that they generalise Nakajima quiver varieties, in particular Hilbert schemes of points on the affine plane. We compute the equivariant K-theory of their torus fixed points and give formulas for the generating series of their Euler numbers/motives. These series generalise the results of Ellingsrud-Stromme-Göttsche. Joint work with Richárd Rimányi.
11:10 – 12:10	Harold Williams (University of Southern California)	Dimer Models and Tropical Lagrangian Coamoebae Dimer models are of interest from many perspectives across geometry, combinatorics, and mathematical physics. In this talk, we explain how one throughline among these perspectives --- the spectral relationship between dimer models in $T^2$ and line bundles on curves in $(\mathbb{C}^*)^2$ --- may be understood as part of a more general mirror relationship between simplicial complexes in $T^n$ and coherent sheaves on $(\mathbb{C}^*)^n$. We refer to the complexes arising this way as tropical Lagrangian coamoebae, as from a symplectic point of view they are in a sense dual objects to tropical varieties. This is joint work with Chris Kuo.
14:00 – 15:00	Albrecht Klemm (University of Sheffield)	Symplectic Invariants on Calabi-Yau 3 folds, Modularity and Stability TWe discuss techniques to calculate symplectic invariants on CY 3-folds $M$, namely Gromov-Witten (GW) invariants, Pandharipande-Thomas (PT) invariants, and Donaldson-Thomas (DT) invariants. Physically the latter are closely related to BPS brane bound states in type IIA string compactifications on $M$. We focus on the rank $r_{\bar 6}=1$ DT invariants that count $\bar D6-D2-D0$ brane bound states related to PT- and high genus GW invariants, which are calculable by mirror symmetry and topological string B-model methods modulo certain boundary conditions, and the rank zero DT invariants that count rank $r_4=1$ $D4-D2-D0$ brane bound states. It has been conjectured by Madacena, Strominger, Witten and Yin that the latter are governed by an index that has modularity properties to due $S-$ duality in string theory and extends to a mock modularity index of higher depth for $r_4>1$. Again the modularity allows to fix the at least the $r_4=1$ index up to boundary conditions fixing their polar terms. Using Wall crossing formulas obtained by Feyzbakhsh certain PT invariants close to the Castelnouvo bound can be related to the $r_4=1,2$ $D4-D2-D0$ invariants. This provides further boundary conditions for topological string B-model approach as well as for the $D4-D2-D0$ brane indices. The approach allows to prove the Castenouvo bound and calculate the $r_{\bar 6}=1$ DT- invariants or the GW invariants to higher genus than hitherto possible.
15:10 – 16:10	Xiaomeng Xu (Beijing International Center for Mathematical Research)	Quantum Riemann-Hilbert-Birkhoff maps and WKB approximation This talk first gives an introduction to the Stokes phenomenon and the Riemann-Hilbert-Birkhoff (RHB) map of meromorphic connections at a k-th order pole, as a local analytic Poisson isomorphism between the de Rham and Betti moduli spaces. It then introduces the quantum Stokes matrices at a k-th order pole, and explains how they give rise to a quantization of the RHB map. In the case of second order pole, it shows that the WKB approximation of the quantum Stokes matrices can be described by the crystal structures of quantum group $U_q(\mathfrak{gl}_n)$.

Friday, December 12

Time	Speaker	Title & Abstract
10:00 – 11:00	Sergey Cherkis (University of Arizona)	Exponentially Accurate Metric for Far-separated Monopole Moduli Spaces Segal and Selby’s proof of (the relatively prime case of) Sen’s conjecture presupposes that a moduli space of k monopoles possesses a certain finite cover by spaces labeled by partitions $(k_1, k_2,…,k_r)$ of k. Each of these spaces with the metric sufficiently close to the monopole metric and possessing a $U(1)^r$ isometry. We present such spaces and prove that their metrics are hyperkaehler, exponentially close to the monopole metric, and have the required symmetry. Our construction and proof are essentially twistorial. It leads to a new generalization of bows and the corresponding Nahm data. This work is in collaboration with Jacques Hurtubise and Roger Bielawski.
11:10 – 12:10	Hyun Kyu Kim (Korea Institute for Advanced Study)	Skein algebras of genus zero surfaces and quantized K-theoretic Coulomb branches The Kauffman bracket skein algebra of an oriented surface S is a quantization of the SL2 character variety of S, and is generated by isotopy classes of framed links living in S times an interval, modulo skein relations. We show that the skein algebra of a punctured surface of genus zero is isomorphic to the Braverman-Finkelberg-Nakajima quantized K-theoretic Coulomb branch, associated to a certain group G and representation N, built from a specific quiver. This gives a monoidal categorification of the genus zero skein algebra, which in particular yields a positive basis through the work of Cautis and Williams, partially answering a question posed by D. Thurston. Based on the joint work with Dylan Allegretti and Peng Shan, arXiv:2505.13332.

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Room Type	POSCO Int'l Center	Hotel Yeongildae	Apple Tree Hotel	Tour de Pohang (Woman's Safety Sohotel)
Double Room	90,200 KRW	110,000 KRW	45,000 KRW	43,000 ~ 48,000 KRW (1 person)
Twin Room	90,200 KRW	132,000 KRW	-	58,000 ~ 63,000 KRW (2 persons)
Breakfast (1 person)	13,200 KRW	Free	Free	Free
Distance from Venue	5 min. drive	10 min. drive	15 min. drive	15 min. drive
Contact	+82-54-279-8500	+82-54-280-8900	+82-54-241-1234	+82-0507-1397-1234

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