Time Table

8:45-9:00
9:00-10:00
10:00-10:30
10:30-12:00
12:00-13:30
13:30-14:30
14:30-14:45
14:45-15:45
15:45-16:15
16:15-17:15
17:15-18:30
18:30-21:00
1/12(Mon)
Registration
& Opening
W. Yan
(chair: Bourgine)
Discussion Break
M. Yamazaki
(chair: Bourgine)
Lunch
J. Bao
(chair: Nosaka)
Short Break
F. Del Monte*
(chair: Nosaka)
Discussion Break
C. Hwang
(chair: Nosaka)
Poster Session
+ Reception
1/13(Tue)
C. Young
(chair: Gui)
Discussion Break
E. Vasserot
(chair: Gui)
Lunch
A. Minets
(chair: Bojko)
Short Break
R. Fujita
(chair: Bojko)
Discussion Break
A. Latyntsev
(chair: Bojko)
Conference
Dinner
1/14(Wed)
M. Aganagic*
(chair: Dedushenko)
Short Break
(10:00-10:15)
H. Awata
(10:15-11:15)(chair: Dedushenko)
Short Break
(11:15-11:30)
J. Shiraishi
(11:30-12:30)(chair: Dedushenko)
Lunch
(12:30-13:30)
Free Afternoon
1/15(Thu)
J. Yagi
(chair: Zhou)
Discussion Break
A. Okounkov
(chair: Zhou)
Lunch
G. Noshita
(chair: Zou)
Short Break
T. Nishinaka
(chair: Zou)
Discussion Break
S. Jeong
(chair: Zou)
1/16(Fri)
K. Zeng
(chair: Sopin)
Discussion Break
T. Arakawa
(chair: Sopin)
Lunch
N. Haouzi
(chair: Ishtiaque)
Short Break
Y. Zenkevich
(chair: Ishtiaque)
Discussion Break
N. Lee
(chair: Ishtiaque)
*: online talk

Talk titles and abstracts

• Mina Aganagic* (UC, Berkeley): Quantum Groups from Fukaya Categories
There is a family of Fukaya categories, or categories of A-branes, labeled by a choice of a Lie algebra, which categorify Chern-Simons invariants of links. The categories admit a gluing operation, by which they emerge from simpler ones. This solves a long standing open problem which is to provide a monoidal structure for the categorified representations of the quantum group. As a byproduct, this illuminates how quantum group symmetry emerges in Chern-Simons theory.


• Tomoyuki Arakawa (RIMS): Chiral differential operators on classical invariant rings via BRST reduction
We present a uniform geometric framework that connects the representation theory of vertex algebras with symplectic geometry and invariant theory. More precisely, we construct chiral analogues of differential operators acting on classical invariant rings as global sections of sheaves of chiral differential operators associated with vector bundles on smooth open subvarieties of affine GIT quotients, using BRST reduction. Within this framework, we develop a localization theory for modules over these global sections, following Borisov’s approach, and establish several fundamental properties of the resulting vertex algebras. As an application, we construct new infinite families of simple conformal quasi-lisse vertex algebras, which we expect to arise from 3D N=4 gauge theories. This is joint work with Xuanzhong Dai and Bailin Song.


• Hidetoshi Awata (Nagoya U.): Non-stationary difference equation and affine Laumon space: quantum Knizhnik-Zamolodchikov equation
We discuss on the non-stationary difference equation which was discovered for the \(q\)-Virasoro conformal block by S. Shakirov (2021). This equation is equivalent to the quantized discrete Painleve IV equation. With the truncation by mass parameters, this equation is regarded as a quantum Knizhnik-Zamolodchikov equation for the quantum affine algebra \(U_q(\hat{sl_2})\). Ref. arXiv:2211.16772, arXiv:2309.15364, arXiv:2510.27142.


• Jiakang Bao (Tokyo U.): Alphabet Stories of the Quiver (BPS) Algebras
I will review the constructions of the quiver algebras arised from counting BPS states for generic quivers with two or four supercharges. I will also mention some properties of the quiver BPS algebras for the affine Dynkin type quivers. Then I will focus on the non-generic quivers, such as the DE-type ones, where they do not satisfy the conditions in the constructions of the quiver algebras. In particular, the usual constructions of the combinatorial modules (i.e., crystal representations) would have some issues. I will discuss the extensions of such combinatorial modules to these cases. Besides the theories with unitary groups, it would be natural to consider theories with orientifolds where the gauge groups are of BCD types. It is not clear how the combinatorial structures for the BPS counting and the BPS algebras would be. Nevertheless, some twisted versions of the quiver algebras are expected. I will talk about some possible definitions of these algebras.


• Fabrizio Del Monte* (Birmingham U.): BPS Quivers on Orbifolds: From BPS Spectra to New 5d SCFTs
In this talk I will report new results that sharpen our understanding of five-dimensional SQFTs and their geometric engineering via M-theory on local Calabi–Yau threefolds, using their BPS quivers as the main tool. First, I will present a theorem explaining how to induce stability conditions on (resolved) orbifolds of local CY3s. This provides a new approach to constructing Bridgeland stability conditions for local Calabi–Yau threefolds with compact divisors (i.e. interacting physical theories), and it allows to describe the BPS spectrum of these substantially more complicated geometries in terms of the simpler space being orbifolded. As an application, I will give a closed formula for the spectrum of stable BPS states and for the Kontsevich–Soibelman wall-crossing invariant for the local Calabi–Yau threefolds \(Y^{(N,0)}\) for any \(N\). This reproduces, for \(N=2\), the case of local \(\mathbb{P}^1 \times \mathbb{P}^1\), which we previously derived with P. Longhi by different methods. While much of the existing understanding of five-dimensional QFTs has relied on toric Calabi–Yau threefolds, the techniques presented here do not rely on toric constructions. I will show that they can be used to generate infinitely many new five-dimensional theories from non-toric orbifolds, including a surprising infinite family of rank-1 theories that evades all known classifications.


• Ryo Fujita (RIMS): On the Hernandez conjecture
In 2004, Nakajima established a unified algorithm to compute the q-characters (in the sense of E. Frenkel and Reshetikhin) of finite-dimensional simple representations of the quantum affine algebras of simply-laced type (an analog of the Kazhdan--Lusztig algorithm) based on the geometric theory of his quiver varieties. Hernandez showed that the similar algorithm can be formulated for non-simply-laced type as well and conjectured that it actually computes the simple q-characters. In this talk, I will report some recent progress toward the Hernandez conjecture, including its proof for classical type, based on joint works with Hernandez, Oh, Oya, and with Qin.


• Nathan Haouzi (Perimeter Institute): An update on the AGT conjectures
The Alday-Gaiotto-Tachikawa correspondence predicts that the count of instantons in (suitably twisted) supersymmetric gauge theories in 4 dimensions should coincide with the conformal block of a W-algebra on a punctured Riemann surface C. While the correspondence is by now well-understood for gauge and W-algebras of Lie type A, very little is known outside of this case. Whenever C has genus 0, we will formulate a q-deformation of the correspondence which applies to any simple Lie algebra, and elucidate aspects of the underlying geometric representation theory; a key role will be played by certain modules introduced a decade ago by Hernandez and Leclerc. We will also explain the meaning of the limit q ->1 for the original AGT correspondence.


• Chiung Hwang (USTC, Hefei): Indices of the ADHM Quiver and Black Holes
As an exact count of protected states, the superconformal index offers a powerful window into holography and the quantum structure of gravity, reproducing the Bekenstein–Hawking entropy of supersymmetric AdS black holes in the large-N limit. As a step toward understanding quantum black hole microstates and the growth of their degeneracies, we investigate the finite-N index of the three-dimensional ADHM quiver gauge theory, which provides a UV description of the three-dimensional N=8 superconformal field theory dual to M-theory on AdS4 times S7. In this work, we examine both microcanonical and canonical aspects of the index. By computing it to sufficiently high orders using the factorized index formula, we identify signatures of quantum black hole states within the finite-N spectrum of the ADHM quiver, and these signals align with the leading large-N contribution associated with the holographic black hole entropy. We also introduce the complex-beta phase diagram of the index, which shows distinct peaks that may correspond to different gravitational saddles.


• Saebyeok Jeong (IBS, Pohang): Miura operators as R-matrices from M-brane Intersections
Abstract: In this talk, I will discuss how M2-M5 intersections in a twisted M-theory background yield the R-matrices of the quantum toroidal algebra of gl(1). These R-matrices are identified with the Miura operators for the q-deformed W- and Y-algebras. Additionally, I will show how the M2-M5 intersection (or equivalently, the Miura operator) generates the qq-characters of the 5d N=1 gauge theory, offering new insight into the algebraic meaning of the latter.


• Alexei Latyntsev (BIMSA): (Vertex) quantum groups from Calabi-Yau three categories: coproducts
We show how to make (critical*) CY3 CoHAs into vertex quantum groups, how this gives a universal way to extend/bosonise and double, and how these constructions recover Drinfeld/Davison/Yang-Zhao/...'s (meromorphic) coproducts.
In detail: we review what is the COHA of a CY3 (due recently to Kinjo-Park-Safronov/Descombes), and translate its physics definition--via line operators--into a precise expectation about associated categories of modules. We then define a vertex coproduct on the critical* CoHA and show it forms a vertex quantum group internal to a suitable meromorphic braided category: H-Mod for H the tautological cohomology classs/Cartan RTT construction. We then prove vertex Majid-Radford bosonisation, allowing us to extend CoHAs by H, and compute these extended vertex coproducts.
We explain conjectural relations to the critical stable envelope construction, double deformed current algebras of Gaiotto-Rapcak-Zhou, ...
Joint with Šarūnas Kaubrys and Shivang Jindal for critical CY3s
*Joint work in progress with Pierre Descombes and Šarūnas Kaubrys in general


• Norton Lee (IBS, Pohang): Cluster algebra in 5d N=1 supersymmetric gauge theories and quantization
Integrable systems provide a tool studying the 4d N=2 supersymmetric gauge theories. The picture can be uplifted to 5d compactified on a circle. The integrabile system describing the Coulomb moduli space of the 5d theory has a X cluster structure deeply linked to the BPS quiver of point-like particles of the 5d theory. The integrable systems are known as the dimer model, with the Casimirs and Hamiltonians represented as geometric objects on a bipartite graph. In this talk I will give some example how the cluster algebra arise from the 5d N=1 theory in both the classical and quantum level.


• Alexandre Minets (Max Planck Institute): Equivariant multiplicities and mirror symmetry for Hilbert schemes
Hausel--Hitchin recently introduced the notion of very stable components of the global nilpotent cone, and computed scheme-theoretic multiplicities of such components. More interestingly, they showed that these numbers admit a natural quantization, called equivariant multiplicity. I will explain how this result can be extended beyond very stable components, and in fact to the greater generality of proper integrable systems. I will then zero in on Hilbert schemes of points on elliptic surfaces, compute multiplicities of all core components, and gesture at the meaning of these numbers from the point of view of mirror symmetry/Dolbeault Langlands. Based on a joint work with F. Zivanovic.


• Takahiro Nishinaka (Osaka Metropolitan U.): Chern-Simons matter theories from Argyres-Douglas theories of \((A_m, A_n)\) type
It was recently proposed by D. Gaiotto and H. Kim that the IR formula for the Schur index of Argyres-Douglas (AD) theories tells us about 3d Chern-Simons (CS) matter theories describing the R-twisted circle reduction of these AD theories. Using this proposal, we study 3d Chern-Simons (CS) matter theories corresponding to the AD theories of \((A_m, A_n)\) type. In particular, we identified a series of 3d N=2 CS matter theories for the R-twisted 3d reduction of \((A_2, A_n)\) and \((A_3, A_n)\) theories that have no flavor symmetry. This talk is based on my joint work with Yutaka Yoshida.


• Go Noshita (Tokyo U.): Quiver W-algebras and DT/PT qq-characters
Quiver W-algebras are deformed W-algebras associated with a quiver with weighted arrows, generalizing the definition of the q-Virasoro , q-\(W_N\)-algebra, and Frenkel-Reshetikhin’s q-character. Gauge theoretically, they are operator versions of Nekrasov’s qq-character and could be understood within the gauge origami framework. In this talk, I will first review the construction of the qq-characters for the gauge origami system of C^4 and discuss generalizations to toric Calabi-Yau 4-folds. In particular, I will discuss the qq-characters associated with the DT and PT vertices. This talk is based on recent works with T. Kimura.


• Andrei Okounkov (Columbia U.): Quantum critical cohomology
This will be a report on joint work with Yalong Cao, Yehao Zhou, and Zijun Zhou. As a part of our recent work on critical stable envelope, we are able to determine the quantum critical cohomology for symmetric quiver with potential. Moreover, a certain asymmetry of the framing of the quiver is allowed, making geometries like the Hilbert scheme of points in the affine 3-space an example of our general theory.


• Jun’ichi Shiraishi (Tokyo U.): Non-stationary \(q\)-difference equations and Affine Laumon space
Braverman and Finkerberg constructed the Whittaker vector associated with the quantum affine algebra \(U_q(\widehat{sl}_N)\) using the \(K\)-theory of the affine Lumon space (2005). The Whittaker function is defined to be a Shapovalov pairing of two Whittaker vectors. However, no equation was found in their work. I show that an insertion of the Drinfeld Casimir gives rise a non-stationary \(q\)-difference equation, thereby proving my conjecture found some years ago (2019). Note that the Whittaker function is regarded as a pure gauge Nekrasov partition function on the affine Laumon space. Then introducing a set of fundamental matters, we have affine Laumon function with matters, and the associated mass deformed non-stationary equations. I present a system of compatible equations which determines the mass deformed Whittaker vector, and the deformed non-stationary equation.


• Eric Vasserot (Sorbonne U.): COHA’s and χ-independence for K3 surfaces
BPS invariants naturally appear in the enumerative geometry of sheaves with one-dimensional support on a Calabi-Yau threefold. Toda conjectured that these invariants are independent of the Euler characteristic χ of the sheaves. I will explain a proof of this conjecture in a joint work in progress with Davison-Hennecart-Kinjo-Schiffmann for the case of K3 surfaces. This proof is based on Cohomological Hall algebras. To do this I will first recall the general theory of COHA’s and BPS sheaves.


• Jun’ya Yagi (YMSC): Quantized six-vertex model on a torus
The six-vertex model is arguably the most famous 2D integrable lattice model. Less known is the fact that the model has a 3D origin. In this talk I will discuss the quantization of the six-vertex model, introduced by Kuniba, Matsuike and Yoneyama in 2022 generalizing earlier work of Bazhanov, Mangazeev and Sergeev. The quantized six-vertex model is a 3D integrable lattice model, which has a remarkable property that commuting layer transfer matrices can be defined not only for square lattices but also on more general "admissible" graphs on a torus. Time permitting, I will also explain how the model is related to dimer models, supersymmetric gauge theories and string theory. This talk is based on my joint work with Rei Inoue, Atsuo Kuniba and Yuji Terashima.


• Masahito Yamazaki (IPMU): Quivers, Crystals, and Quiver Yangians
In this lecture, I will review the decades-old interplay between gauge theory, geometry, and combinatorics, which has led to the development of quiver Yangians and their representation theory.


• Wenbin Yan (YMSC): Chiral algebra, Wilson lines, and mixed Hodge structure of Coulomb branch
In the talk we will discuss an intriguing relation between the chiral algebra and the mixed Hodge structure of the Coulomb branch of four dimensional N = 2 superconformal field theories. Using Wilson line operators and modularity, one can compute characters of modules of VOAs corresponding to class-S theories. One can then check that the representation information is also encoded into the pure part of the mixed Hodge structure of the Coulomb branch of the same theory. This provides more relation between the Higgs and Coulomb branch of 4d N=2 theories, expanding the scope of 4d mirror symmetry.


• Charles Young (Hertfordshire U.): Higher current algebras and chiral algebras
Vertex algebras capture physicists' notion of OPEs in chiral CFTs, in complex dimension one. For various motivations, one would like to have analogs of vertex algebras in higher dimensions. Chiral algebras, in the sense of Beilinson-Drinfeld and Francis-Gaitsgory, provide a promising framework here, because they re-express the vertex algebra axioms (which are rather sui generis, and therefore hard to generalize) as something more recognizable (a chiral algebra is a Lie algebra, of a sort). I will review this, and then go on to introduce a certain concrete model of the unit chiral algebra in higher complex dimensions. We shall see that in going to higher dimensions, one naturally moves from Lie algebras to their homotopy analogs, L-infinity algebras, and from chiral algebras to homotopy chiral algebras in a sense recently introduced by Malikov-Schechtman. The main tool in the talk will be a new model -- the polysimplicial model -- of derived sections of the sheaf of functions on higher configuration spaces. The hope is that this model will prove well-adapted to doing concrete calculations. This is joint work with Zhengping Gui and Laura Felder and is based on the preprint 2506.09728


• Keyou Zeng (Harvard U.): Quantum algebra from generlized Poisson sigma model
We introduce a family of holomorphic–topological field theories, which we call generalized Poisson sigma models. They naturally generalize the well-known 2d Poisson sigma model and are closely related to the deformation quantization of holomorphic–topological factorization algebras. They also provide various constructions of quantum groups via Koszul duality. Using these techniques, we construct new, and revisit old, examples of quantum field theories in various dimensions, related to the quantization of Lie bialgebras, \(\mathcal{W}\)-algebras, Yangian and more.


• Yegor Zenkevich (Edinburgh U.): Wall-crossing in N=4 super Yang-Mills and quantum toroidal algebra
Line operators in 4d N=2 gauge theories can be expressed in terms of line operators in the low-energy effective abelian theory living at a generic point on the vacuum moduli space. These "abelianized" expressions determine framed BPS invariants which undergo nontrivial wall-crossing transitions between different chambers in the vacuum moduli space. I argue that for N=4 U(M) gauge theories the algebra of line operators given by spherical double affine Hecke algebra can be naturally understood as a certain quotient of the quantum toroidal algebra of type gl(1). Different abelianizations coincide with the tensor product of M vector representations of the quantum toroidal algebra with the action given by different coproducts. Wall-crossing transformations are identified with Drinfeld twists transforming coproducts into each other. S-duality of the N=4 theory is built into the construction as an automorphism group of the quantum toroidal algebra acting transitively on the space of coproducts. This description is uniform in M and fits into the interpretation of the quantum toroidal algebra as the universal algebra of (p,q) strings in Type IIB string theory.

Poster presentations

• Nikita Belousov (BIMSA): Hallnäs–Ruijsenaars functions
In the 1980s, Ruijsenaars discovered a family of quantum integrable systems, which come in several types: rational, trigonometric, hyperbolic, and elliptic. Around the same time, solutions for the first two types appeared independently in the works of Heckman and Opdam (rational case) and Macdonald (trigonometric). The solution to the hyperbolic model was found more recently by Hallnäs and Ruijsenaars (2012). The properties of Hallnäs–Ruijsenaars functions are similar to those of Macdonald polynomials, but their non-polynomial character requires different analytical techniques. Furthermore, in a certain limit, the Hallnäs–Ruijsenaars functions reduce to a multivariable generalization of hypergeometric functions over the complex field, introduced by Gelfand, Graev, and Retakh. This poster is based on joint works with S. Derkachov, S. Khoroshkin, G. Sarkissian, and V. Spiridonov.


• Hank Chen (BIMSA): Aspects of derived Chern-Simons theory in 4-dimensions
Chern-Simons theory is one of the most important gauge theories in 3-dimensions. I will present a higher-derived generalization of Chern-Simons theory to 4d, based on the structure of an internal “Lie 2-group”. I will discuss its higher-gauge symmetry, its higher-dimensional holonomies, as well as a novel 3d integrable boundary it hosts. I will also briefly mention my recent works towards its combinatorial quantization framework, from the perspective of categorified quantum topology.


• Ban Lin (KIAS): Categorical Symmetry in CY3
The monodromy action on the brane charge lattice \(H^{ev}(X,Q)\) of a CY3 \(X\) in its “stringy Kahler moduli space” \(M(X)\) gives various symplectic dualities that generate \(\pi_1(M(X))\). The mysterious \(M(X)\) can be desribed by the FI-theta parameter space of a UV gauge linear sigma model (GLSM) that realize \(X\) NLSM in its IR phase, especially for those \(X\) as Green-Hubsch CY: “complete intersection Calabi-Yau” (CICY) in projective spaces. By investigating its quantum critical loci from the Witten-Morrison-Plesser (Hori-Tong) GLSM effective twisted potential, the fundamental group structure in CICY hypersurfaces is tested using monodromy matrices. Furthermore, using Herbst-Hori-Pages results for abelian GLSMs, we conjecture a conifold transition formula for the categorical symmetries in the small resolutions of singular \(X\).


• Qinjian Lou (Peking U.): Vacuum Tunneling from Conifold Transitions in IIB
We investigate the quantum tunneling process through a topology transition near a conifold singularity, in the setup of IIB CY3 orientifold compactification. We propose a novel method to do moduli stabilization in an extended moduli space, parametrized by both the geometric moduli and the light D3-brane wrapping modes arisen from the brane quantization. Assuming the absence of flux through the vanishing exceptional 3-cycle, we find two types of vacuum solutions, one corresponds to the resolved conifold and the other one is interpreted as a novel non-geometric phase. We compute the quantum tunneling rate between these two solutions and find that it is difficult to achieve a significantly large tunneling rate in the controllable regime.


• Veronica Pasquarella (SIMIS): Primitive invariants from laminations
Combining geometric group theory techniques with geometric topology tools, we showed in arXiv:2507.17973 [math.GT] how primitive cohomologies provide useful insights towards unifying the mathematical formulation of Gromov-Witten invariants. In particular, we emphasised the role played by geodesic laminations in analysing such invariants for the case of complete intersections in projective space. We now translate that analysis in the language of Seiberg-Witten invariants and the study of Coulomb branches of supersymmetric theories arising in string theory settings.


• Lu-Yao Wang (BIMSA): Geometric realization of W-operators
Motivated by the Gaussian Hermitian \(\beta\)-ensemble, we construct a bridge from symmetric-group class algebras to the bosonic Fock space and its geometric realization. We realize the raising operator \(E_1=[W_{[2]},p_1]\) as the Hecke correspondence on \(\mathrm{Hilb}_n(\mathbb C^2)\). Finally, we outline a colored extension to Nakajima quiver varieties where the commutator towers are expected to realize quiver \(W\)-algebras.


• Kilar Zhang (Shanghai U.): Charge functions for high dimensional partitions
To construct a BPS algebra with representations furnished by n-dimensional partitions, the first step is to construct the eigenvalue of the Cartan operators acting on them. The generating function of the eigenvalues is called the charge function. It has an important property that for each partition, the poles of the function correspond to the projection of the boxes which can be added to or removed from the partition legally. The charge functions of lower dimensional partitions, i.e., Young diagrams for 2D, plane partitions for 3D and solid partitions for 4D, are already given in the literature. We propose an expression of the charge function for arbitrary odd dimensional partitions and have it proved for 5D case. Some explicit numerical tests for 7D and 9D case are also conducted to confirm our formula.


• Xianghang Zhang (Nagoya U.): Open N=2 superstring field theory with homotopy algebraic structure
We formulate a string field theory for open N=2 strings, whose spacetime field theory is equivalent to anti-self-dual Yang-Mills, with an homotopy algebra structure. Starting from the BRST cohomology relative to the U(1) anti-ghost zero-mode, we constructed all interacting vertices recursively and without singularity.


• Dongao Zhou (Tokyo U.): Elliptic Genera of 2d N=(0,1) Gauge Theories
Two-dimensional SQFTs with minimal supersymmetry induced some interests these days. Recently, we derived a residue-type formula for the equivariant elliptic genera of 2d (0,1) gauged linear sigma models (GLSMs) with certain conditions. This result generalizes the earlier work on (0,2) and (2,2) cases by Benini, Eager, Hori, and Tachikawa [1308.4896]. As a validity check, we applied our formula to the family of (0,1) GLSMs proposed by Gukov, Pei, and Putrov in [1910.13455] and verify the triality relationship. This presentation is based on the work [2508.06865] in collaboration with Bao and Yamazaki.