UNIST International Workshop on Calabi-Yau Crystals and BPS Counting 2025
Talks
Talk 1
Torus Knots and Virasoro Minimal Models
Dongmin Gang (Seoul National University)
Thursday, October 30, 2025
108-320, 10:00 - 10:45
Talk 2
Gauge Origami and BPS qq-characters
Go Noshita (University of Tokyo)
Thursday, October 30, 2025
108-320, 11:00 - 11:45
Talk 3
Refined open BPS invariants, quantum curves, and codimension-two defects in 5d gauge theory
Saebyeok Jeong (IBS-CGP, Pohang)
Thursday, October 30, 2025
108-320, 13:30 - 14:15
Talk 4
Nekrasov’s gauge origami via DT4 theory
Woonam Lim (Yonsei University)
Thursday, October 30, 2025
108-320, 14:30 - 15:15
The study of classical instantons on spacetime has led to many interesting developments in mathematics. In a series of papers, Nekrasov introduced the generalized ADHM equations, whose solutions are instantons on the “origami spacetime.” In this talk, I will explain how to interpret gauge origami via DT4 theory. The main result shows that Nekrasov’s origami partition function, defined by local contributions, coincides with a global definition via Oh–Thomas classes in DT4 theory. This global definition is crucial for deriving the Dyson–Schwinger equation, which was one of Nekrasov’s main motivations for introducing gauge origami theory. I will also briefly discuss a conjectural sheaf-theoretic description of gauge origami. This is joint work in progress with N. Arbesfeld and M. Kool.
Colloquium
A Dual Tale of Physics and Geometry
Sebastian Franco (City College, City University of New York)
Thursday, October 30, 2025
108-320, 16:00 - 17:00
Talk 5
4d Crystals for Toric Calabi-Yau 4-Folds: the Exploration Continues
Sebastian Franco (City College, City University of New York)
Friday, October 31, 2025
108-320, 10:00 - 10:45
Talk 6
Quiver Algebras from Crystals
Jiakang Bao (University of Tokyo)
Friday, October 31, 2025
108-320, 11:00 - 11:45
Quiver Yangians are BPS algebras arised from Type IIA string theory on toric Calabi-Yau threefolds. The crystals in the BPS counting form representations of the quiver Yangians. In this talk, I will discuss some recent progress on constructing the crystals and certain quiver algebras encoding the information of the BPS states for generic quivers (not necessarily toric) satisfying the so-called no-overlap condition and also for theories with fewer supercharges (such as those arised from Calabi-Yau fourfolds). If time permits, I will mention the work in progress with Duncan Laurie on the cases of affine DE-types, where we do not have the no-overlap condition.
Talk 7
Symplectic pushforwards and DT theory
Hyeonjun Park (KIAS, Seoul)
Friday, October 31, 2025
108-320, 13:30 - 14:15
Talk 8
Aspects of dualities in supersymmetric quantum mechanics and DT4 invariants from quivers
Cyril Closset (University of Birmingham)
Friday, October 31, 2025
108-320, 14:30 - 15:15
Talk 9
Calabi Yau Lattice Paths and BPS Counting
Piotr Sulkowski (University of Warsaw)
Friday, October 31, 2025
108-320, 16:00 - 16:45
Talk 10
Non-perturbative quantum geometry of topological strings and BPS invariants
Murad Alim (Technical University Munich)
Friday, October 31, 2025
108-320, 17:00 - 17:45
The partition function of topological string theory on any family of Calabi-Yau threefolds is defined perturbatively as an asymptotic series in the topological string coupling and encodes, in a holomorphic limit, higher genus Gromov-Witten as well as Gopakumar-Vafa invariants. I will prove that the partition function of topological strings of any CY in this limit can be written as a product, where each factor is given by the partition function of the resolved conifold with shifted arguments, raised to the power of certain sheaf invariants. I will use this result to study the Borel summation of topological string theory.
Talk 11
A pullback between sheaves on log Calabi-Yau 4-folds
Jeongseok Oh (Seoul National University)
Saturday, November 1, 2025
108-320, 10:00 - 10:45
Talk 12
Stable envelope for critical loci
Yehao Zhou (SIMIS, Shanghai)
Saturday, November 1, 2025
108-320, 11:00 - 11:45
In this talk we will introduce a generalization of Maulik-Okounkov’s stable envelopes to equivariant critical cohomology. In the case of a tripled quiver variety with standard cubic potential, this reduces to MO’s stable envelope for the Nakajima variety of the corresponding doubled quiver along the dimensional reduction. We define non-abelian stable envelopes for quivers with potentials following a similar construction of Aganagic-Okounkov, and use them to relate critical COHAs to the abelian stable envelopes. RTT formalism leads to natural (shifted) (super) Yangian action on the critical cohomology of quiver varieties with potentials. This talk is based on joint work with Yalong Cao, Andrei Okounkov, and Zijun Zhou.