Workshop on Quantum Geometry

Liste des Contributions

2. Gromov-Witten Theory of Complete Intersections I

Hülya Argüz (IST Austria)

25/04/2022 14:00

I will describe an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. This uses a monodromy analysis, as well as new degeneration and splitting formulas for nodal Gromov--Witten invariants. This is joint work with Pierrick Bousseau, Rahul Pandharipande, and Dimitri Zvonkine. This will be the...

3. Quantizations of Complex Lagrangian Fibrations, Normal Forms, and Spectra

Alexander Soibelman (IHES)

25/04/2022 15:30

Under certain conditions, it is possible to compute the spectrum of a polynomial differential operator via its Birkhoff normal form. In this talk, I will explain a geometric approach for obtaining the Birkhoff normal form of a quantized Hamiltonian using the variation of Hodge structure for a formal deformation of a complex Lagrangian fibration. This is joint work in progress with Maxim Kontsevich.

7. Length Partition of Random Multi-geodesics on Large Genus Hyperbolic Surfaces

Mingkun Liu (IMJ-PRG)

25/04/2022 16:45

On a hyperbolic surface, a closed geodesic is said to be simple if it has no self-intersection. A multi-geodesic is a multiset of disjoint simple closed geodesics. A multi-geodesic can be decomposed into connected components, and therefore induces a partition of its total length. In this talk, I will present an attempt to answer the following question: what is the shape of the length partition...

4. Gromov-Witten Invariants of Complete Intersections II

Pierrick Bousseau (ETH Zurich)

26/04/2022 14:00

I will describe an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. This uses a monodromy analysis, as well as new degeneration and splitting formulas for nodal Gromov--Witten invariants. This is joint work with Hülya Argüz, Rahul Pandharipande, and Dimitri Zvonkine. This will be the...

5. Riemann-Hilbert Problems from Refined Donaldson-Thomas Theory

Anna Barbieri (University of Milano Statale)

26/04/2022 15:30

The notion of BPS structure (or symmetric stability structure) describes the output of Donaldson-Thomas's theory on a 3-Calabi-Yau category and can be realized also from a quadratic differential on a Riemann surface. A BPS structure can be associated with a Riemann-Hilbert problem, which allows us to understand the Kontsevich-Soibelman wall-crossing formula as an iso-Stokes property when the...

6. Moduli Spaces of Irregular Singular Connections: Quantization and Braiding

Gabriele Rembado (Hausdorff Centre for Mathematics, Bonn)

26/04/2022 16:45

Holomorphic connections on Riemann surfaces have been widely studied, as well as their monodromy representations. Their moduli spaces have natural Poisson/symplectic structures, and they can be both deformed and quantized: varying the Riemann surface structure leads to the action of mapping class groups on character varieties (the "symplectic nature" of the fundamental group of surfaces),...

8. Gromov-Witten Invariants of Complete Intersections III

Pierrick Bousseau (ETH Zurich)

27/04/2022 14:00

I will describe an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. This uses a monodromy analysis, as well as new degeneration and splitting formulas for nodal Gromov--Witten invariants. This is joint work with Hülya Argüz, Rahul Pandharipande, and Dimitri Zvonkine. This will be the...

9. Argyres-Douglas Theories, Isomonodromy and Topological Recursion

Joshua Lam (IHES)

27/04/2022 15:00

Argyres-Douglas theories are certain supersymmetric physical theories in four dimensions, many of which belong to "Class S" and are in some sense the simplest examples of such. On the other hand, isomonodromy is the analogue of the Gauss-Manin connection in non-abelian Hodge theory. I will explain how physical dualities between different Argyres-Douglas theories lead to remarkable...

10. Donaldson-Thomas Invariants of Toric Quivers

Pierre Descombes (Sorbonne Université UPMC)

27/04/2022 16:30

Donaldson-Thomas theory aims at counting sheaves on Calabi-Yau threefolds. The category of sheaves on a toric threefold is derived equivalent to the category of representation of a quiver with potential obtained from a tiling of the torus. On this class of example, the virtual Euler number of the moduli space of quiver representations can be computed by toric localization with respect to an...

11. Jeffrey-Kirwan Localization for Quiver Varieties

Riccardo Ontani (SISSA)

27/04/2022 17:30

In this talk, I will present an ongoing project on Jeffrey-Kirwan localization in the theory of quiver moduli spaces. In order to motivate the interest in this topic, in the first part of the talk I will recall the content of a previous joint work with Jacopo Stoppa (SISSA). Given a complete bipartite quiver, there is a natural way to construct a log Calabi-Yau surface. We show how the...

12. Integrable Systems on (Multiplicative) Quiver Varieties

Maxime Fairon (University of Glasgow)

28/04/2022 14:00

Following the pioneering work of Wilson who realized the phase space of the (classical complex) Calogero-Moser system as a quiver variety, Chalykh and Silantyev observed in 2017 that various generalizations of this integrable system can be constructed on quiver varieties associated with cyclic quivers. Building on these results, I will explain how such systems can be visualized at the level of...

16. The Invariant Part of the Center of the Small Quantum Group

Oscar Kivinen (EPFL)

28/04/2022 15:30

The Hitchin fibration has already found many beautiful applications to representation theory, such as Cherednik algebras and automorphic representations. Using the recent work of Bezrukavnikov-Boixeda Alvarez-Shan-Vasserot relating the invariant part of the center of the small quantum group to the geometry of a specific singular Hitchin fiber, we prove a conjecture of Igor Frenkel describing...

14. Quantisation of Spectral Curves of Arbitrary Rank and Genus via Topological Recursion

Elba Garcia-Failde (IMJ-PRG)

28/04/2022 16:45

The topological recursion is a ubiquitous procedure that associates to some initial data called spectral curve, consisting of a Riemann surface and some extra data, a doubly indexed family of differentials on the curve, which often encode some enumerative geometric information, such as volumes of moduli spaces, intersection numbers and knot invariants. The quantum curve conjecture claims that...

15. Combinatorial Quantisation of Supergroup Chern-Simons Theory

Nezhla Aghaei (SDU/QM Center)

29/04/2022 14:00

Chern-Simons Theories with gauge super-groups appear naturally in string theory and they possess interesting applications in mathematics, e.g. for the construction of knot and link invariants. In my talk, I will review the framework of combinatorial quantization of Chern Simons theory and explain how this framework can be adapted for applications to superalgebras. This will give rise to...

13. The Negative Side of Witten’s Conjecture

Alessandro Giacchetto (IPhT)

29/04/2022 15:15

In 2017, Norbury introduced a collection of cohomology classes on the moduli space of curves, and predicted that their intersection with psi classes solves the KdV hierarchy. In a joint work in progress with N. Chidambaram and E. Garcia-Failde, we consider a deformation of Norbury’s class and, via the Givental–Teleman reconstruction theorem, we express such deformation in terms of kappa...