Speaker: Eric Sharpe (Virginia Tech)
Date: 11 February 2020, at 14:00
Venue: SISSA Room 137
Title: A proposal for nonabelian mirrors in two-dimensional theories
Abstract: In this talk we will describe a proposal for nonabelian mirrors to two-dimensional (2,2) supersymmetric gauge theories, generalizing the Hori-Vafa construction for abelian gauge theories. By applying this to spaces realized as symplectic quotients, one can derive B-twisted Landau-Ginzburg orbifolds whose classical physics encodes quantum cohomology rings of those spaces. The proposal has been checked in a variety of cases, but for sake of time the talk will focus on exploring the proposal in the special case of Grassmannians.
Speaker: Yegor Zenkevich (ITEP and Milano Bicocca University)
Date: 21-23-28 January 2020, at 14:30
Venue: SISSA Room 126
Title: Macdonald polynomials technology
Abstract: In this minicourse we will study the basics of Macdonald polynomials and quantum Ruijsenaars-Schneider integrable system associated with them. We will start with Schur symmetric functions and then try to understand how they are deformed into Macdonald polynomials. We will also consider some generalizations of the Ruijsenaars-Schneider system and its relations to supersymmetric gauge theories, representation theory and algebraic geometry.
Speaker: Veronica Fantini (SISSA)
Date: Thursday 12 December 2019, at 14:30
Venue: IGAP (Institute for Geometry and Physics, the old SISSA building)
Title: Kahler Meeting
Speaker: Mauricio Romo (Tsinghua University)
Date: Tuesday 27 August 2019, at 14:30
Venue: IGAP (Institute for Geometry and Physics, the old SISSA building)
Title: B-branes and Anomalous Gauged Linear Sigma Models
Abstract: B-branes on Calabi-Yau (CY) X manifolds are in 1-1 correspondence with objects in the derived category of coherent sheaves. B-branes on Gauged Linear Sigma Models (GLSM) can be roughly interpreted as objects of the derived category of a CY stack. This interpretation can be used to generate equivalences between various categories associated to geometric and nongeometric phases of a CY. I will introduce these concepts and present some results for the case when the stack is not CY (physically, this means the GLSM is anomalous), that can be derived from physics. In particular I will explain how the equivalences between categories associated to phases are modified and comment on some consequence on K-theory using as a guide the example of Hirzebruch-Jung resolutions of cyclic surface singularities.
Speaker: Nadir Fasola (SISSA)
Date: Friday 28 June 2019, at 10:00
Venue: IGAP (Institute for Geometry and Physics, the old SISSA building)
Title: Nested instantons and punctual nested Hilbert schemes
Abstract: Nested Hilbert schemes of points and curves on smooth projective surfaces carry interesting quantities for both geometry and physics. Their virtual fundamental classes have been shown to recover both the virtual classes of SW and reduced stable pair theories, while their obstruction theories can be used to obtain information about VW and reduced DT invariants. We show that the effective SUSY theory of a certain surface defect gives rise to a quiver GLSM which, in a particular case, models punctual nested Hilbert schemes on the complex plane. We will show how the partition function of such a theory naturally computes certain virtual invariants of these moduli spaces and how these results relate to a conjecture of Hausel, Letellier and Rodriguez-Villegas about the cohomology of character varieties.
Speaker: Du Pei (QGM-Caltech)
Date: Tuesday, 28 May 2019, at 14:30.
Venue: IGAP (Institute for Geometry and Physics, the old SISSA building)
Title: Brane Quantization and Representations of DAHA
Abstract: Double affine Hecke algebra (DAHA) is closely related to the algebra of line operators in 4d N=2* theory. In this talk, I will show how to use the A-model to the Coulomb branch of this theory to gain insight into the representation category of DAHA.
Speaker: Andrea Ricolfi (SISSA)
Date: Thursday, 11 April 2019 at 11:30.
Venue: IGAP (Institute for Geometry and Physics, the old SISSA building)
Title: Enumerative Geometry of Quot schemes on 3-folds
Abstract: We discuss the existence of a virtual fundamental class on Quot schemes of locally free sheaves on complex 3-folds. We compute Behrend’s virtual Euler characteristic of these Quot schemes, which in some cases gives rise to new examples of (higher rank) Donaldson-Thomas invariants. If time permits, we will sketch the parallel theory of motivic invariants.
Speaker: Fabrizio Del Monte (SISSA)
Date: Tuesday, 26 March 2019 at 14.30.
Venue: IGAP (Institute for Geometry and Physics, the old SISSA building)
Title: Class S Theories, Free Fermions and Isomonodromic Deformations Beyond Genus Zero
Abstract: Using arguments from Conformal Field Theory, Gamayun Iorgov and Lisovyy provided in 2012 an explicit expression for the tau function of the sixth Painlevé equation as a Fourier transform of Virasoro conformal blocks. This “Kiev formula” has been later generalized to more general isomonodromic problems on the sphere, with both regular and irregular punctures. Further, by using the AGT correspondence, one can see that the isomonodromic tau function is the dual partition function of an appropriate class S theory, for which the Painlevé equations (and generalizations thereof) can be thought of as renormalization group or, for the conformal case, conformal manifold deformation equations. In this talk we will first recap the role of Hitchin systems in the context of class S theories, and what the isomonodromy deformations mean from this perspective. Then, we will show how one can generalize the connection between gauge theory and isomonodromic deformations to the genus one case, by using an approach based on free fermions. This will provide a formula connecting the tau function to the dual partition function of a circular quiver gauge theory with both bifundamental and adjoint hypermultiplets, which has new features absent in the genus zero case.
Speaker: Lothar Göttsche (ICTP)
Date: Tuesday, 12 March 2019 at 14:30.
Venue: IGAP (Institute for Geometry and Physics, the old SISSA building)
Title: Virtual topological invariants of moduli spaces of sheaves on surfaces II
Abstract: Using arguments from theoretical physics, Vafa and Witten gave a generating function for the Euler numbers of moduli spaces of rank 2 coherent sheaves on algebraic surfaces. These moduli spaces are in general very singular, but they carry a perfect obstruction theory (they are virtually smooth). This gives virtual versions of many invariants of smooth projective varieties. Such virtual invariants occur everywhere in modern enumerative geometry, like Gromov-Witten invariants and Donaldson Thomas invariants, when attempting to make sense of the predictions from physics. We conjecture that the Vafa-Witten formula is true for the virtual Euler numbers. We confirm this conjecture in many examples. Then we give refinements of the conjecture. Our approach is based on Mochizuki’s formula which reduces virtual intersection numbers on moduli spaces of sheaves to intersection numbers on Hilbert schemes of points.
Speaker: Lothar Göttsche (ICTP)
Date: Tuesday, 26 February 2019 at 14:30.
Venue: IGAP (Institute for Geometry and Physics, the old SISSA building)
Title: Virtual topological invariants of moduli spaces of sheaves on surfaces
Abstract: Using arguments from theoretical physics, Vafa and Witten gave a generating function for the Euler numbers of moduli spaces of rank 2 coherent sheaves on algebraic surfaces. These moduli spaces are in general very singular, but they carry a perfect obstruction theory (they are virtually smooth). This gives virtual versions of many invariants of smooth projective varieties. Such virtual invariants occur everywhere in modern enumerative geometry, like Gromov-Witten invariants and Donaldson Thomas invariants, when attempting to make sense of the predictions from physics. We conjecture that the Vafa-Witten formula is true for the virtual Euler numbers. We confirm this conjecture in many examples. Then we give refinements of the conjecture. Our approach is based on Mochizuki’s formula which reduces virtual intersection numbers on moduli spaces of sheaves to intersection numbers on Hilbert schemes of points.
Speaker: Pavlo Gavrylenko (Skolkovo Institute of Science and Technology Moscow)
Date: Tuesday, 5 February 2019 at 14:30.
Venue: SISSA Room 136
Title: Introduction to Fredholm determinant representation of isomonodromic tau functions, II
Abstract: In these two lectures I will try to give an elementary explanation of how one can get the representation of the general isomonodromic tau function on sphere with punctures as the Fredholm determinant of certain operator with matrix-valued integral kernel. I’m going to show the free-fermionic construction of the isomonodromic tau function, introduce generalized Wick theorem, and explain how to get the Fredholm determinant of our interest from the free-fermionic formulas. The second part will be devoted to the study of such obtained Fredholm determinant. It will be rewritten in terms of some projection operators, as matrix Toeplitz determinant, and after all differentiated explicitly in order to reproduce the definition of the Jimbo-Miwa-Ueno tau function.
Speaker: Pavlo Gavrylenko (Skolkovo Institute of Science and Technology Moscow)
Date: Tuesday, 29 January 2019 at 14:30.
Venue: SISSA Room 136
Title: Introduction to Fredholm determinant representation of isomonodromic tau functions, I
Abstract: In these two lectures I will try to give an elementary explanation of how one can get the representation of the general isomonodromic tau function on sphere with punctures as the Fredholm determinant of certain operator with matrix-valued integral kernel. I’m going to show the free-fermionic construction of the isomonodromic tau function, introduce generalized Wick theorem, and explain how to get the Fredholm determinant of our interest from the free-fermionic formulas. The second part will be devoted to the study of such obtained Fredholm determinant. It will be rewritten in terms of some projection operators, as matrix Toeplitz determinant, and after all differentiated explicitly in order to reproduce the definition of the Jimbo-Miwa-Ueno tau function.
Speaker: Andrew Kels (SISSA)
Date: Tuesday, 22 January 2019 at 16:00.
Venue: SISSA Room 136
Title: On elliptic functions and tau-functions for the discrete Painleve equation of type E8, part II
Abstract: In this talk I will introduce the concept of (Ohta-Ramani-Grammaticos) tau-functions on the E8 lattice. I will introduce an elliptic hypergeometric integral, and show how the latter can be used to construct hypergeometric solutions for these tau-functions. This talk is based on the speakers recent work (with Yamazaki), arXiv:1810.12103, which is in turn based on a work of Noumi, arXiv:1604.06869.
Speaker: Andrew Kels (SISSA)
Date: Tuesday, 15 January 2019 at 14:30.
Venue: SISSA Room 136
Title: On elliptic functions and tau-functions for the discrete Painleve equation of type E8, part I
Abstract: In this talk I will introduce the concept of (Ohta-Ramani-Grammaticos) tau-functions on the E8 lattice. I will introduce an elliptic hypergeometric integral, and show how the latter can be used to construct hypergeometric solutions for these tau-functions. This talk is based on the speakers recent work (with Yamazaki), arXiv:1810.12103, which is in turn based on a work of Noumi, arXiv:1604.06869.