Algebra and Quantum Geometry of BPS Quivers

Contribution List

1. Non-toric brane webs, Calabi-Yau 3-folds, and 5d SCFTs

Pierrick Bousseau

20/01/2025, 09:30

One of the most remarkable predictions of string/M-theory is the existence of 5-dimensional superconformal field theories (5d SCFTs). There are two main approaches for constructing these 5d SCFTs, using either M-theory on canonical 3-fold singularities, or intersecting branes in Type IIB string theory. A natural question is to compare these two approaches. The answer is well-known for webs of...

2. Mock modularity of Calabi-Yau threefolds

Sergey Alexandrov

20/01/2025, 11:00

I'll explain the modular properties, and their physical origin, of the generating functions of rank 0 DT invariants of Calabi-Yau threefolds counting D4-D2-D0 bound states in type II compactifications of string theory. These properties can be used to find generating functions up to a finite number of coefficients, the so-called polar terms, which in turn can be fixed using wall-crossing. I'll...

3. Nekrasov’s gauge origami and Oh-Thomas’s virtual cycles

Martijn Kool

20/01/2025, 16:30

Nekrasov's 4D ADHM quiver is a generalisation of the 2D and 3D ADHM quivers. I will give a mathematical definition of the corresponding "gauge origami" partition function in terms of certain torus localized Oh-Thomas virtual cycles. I will relate the orientation problem of gauge origami to the one of Hilbert schemes of points on affine 4-space, which was previously analysed in physics by...

4. Towards relative Donaldson-Thomas theory in dimension 4

Gufang Zhao

20/01/2025, 18:00

The goal of this talk is to explore definitions of numerical invariants from moduli spaces originated from relative Donaldson-Thomas theory in dimension 4. The definition of invariants is formulated as functoriality of the cohomology or K-theory of these moduli spaces. Existence in examples will be given. Partially based on joint works with Cao, Toda, and Zhou.

5. Riemann-Hilbert correspondence and wall-crossing structures

Yan Soibelman

21/01/2025, 09:30

Generalized Riemann-Hilbert correspondence proposed by Maxim Kontsevich and myself in 2015 relates two areas of mathematics: deformation quantization and Floer theory. The aim of my talk is to revisit various aspects of the generalized RH-correspondence. In particular I am going to explain how wall-crossing structures relate local and global versions of the RH-correspondence.

6. Universal Virasoro constraints for additive theories

Arkadij Bojko

21/01/2025, 11:00

Recently, Virasoro constraints were formulated for sheaf-counting theories which was motivated by their original appearance on the Gromov-Witten side. The main difference lies in the ability to take direct sums of sheaves which allowed us (B.-Lim-Moreira) to connect these constraints to the geometric vertex algebra of Joyce. The upshot, that moduli spaces satisfying Virasoro constraints...

7. Scattering diagram for noncommutative resolutions

Pierre Descombes

21/01/2025, 16:30

Scattering diagrams techniques allows to compute the BPS invariants of quiver with potential in terms of some initial data, which are expected to be simple in physically sensible examples (eg, they have been determined for class S theory).

We are interested in quiver with potential giving noncommutative resolution of CY3 singularities: in this case, the space of stability conditions of the...

8. BPS categories for quivers and Higgs bundles

Tudor Padurariu

21/01/2025, 17:30

I will report on joint work with Yukinobu Toda about a refinements of BPS invariants using derived categories of coherent sheaves.

We propose two conjectural dualities between BPS categories for Higgs bundles, which can be interpreted as a version of SYZ mirror symmetry and of the Dolbeault Langlands equivalence. I will also discuss some results about BPS categories for quivers, with a...

9. Topological correlators of massive N = 2 SQCD and 5d N = 1 SYM on S1

Jan Manschot

22/01/2025, 18:00

TBA

10. Overview of DT invariants from Exponential Networks

Mauricio Romo

23/01/2025, 09:30

I will give an overview on how to compute DT invariants of toric CYs, using exponential networks. I will present an proposal on the interpretation of these networks from the perspective of special Lagrangians on the mirror. As time allows, I will also present some new results involving DT invariants with the inclusion of noncompact divisors.

11. Skein valued topological vertex

Tobias Ekholm

23/01/2025, 11:00

12. Membranes and Maps

Yannik Schueler

23/01/2025, 16:30

In joint work with Andrea Brini, we proposed a definition of the refined topological string on a Calabi-Yau threefold X with a torus action in terms of the equivariant Gromov-Witten theory of the fivefold X x C^2. In my talk, I will outline the construction, mention some of its features, and especially discuss an anticipated equivariant generalisation of Gopakumar-Vafa invariants. This...

13. Cohomological Hall Algebra and Categories of Line Defects

Davide Gaiotto

23/01/2025, 17:30

14. Skein-valued abelianization via skein-valued curve counting

Vivek Shende

24/01/2025, 09:30

15. Algebraic aspects of linking and unlinking for symmetric quivers

Vladimir Dotsenko

24/01/2025, 11:00

Several years ago, Ekholm, Kucharski and Longhi introduced operations of linking and unlinking for symmetric quivers; under these operations, the motivic generating series associated to symmetric quivers transform in a controllable way. I shall discuss two recent categorifications of these operations: the one via quadratic algebras associated to symmetric quivers (this is my joint work with...