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Boris Pioline: Lectures
January 11, 2023 TITLE: Modularity of BPS indices on Calabi-Yau threefolds ABSTRACT: Unlike in cases with maximal or half-maximal supersymmetry, the spectrum of BPS states in type II string theory compactified on a Calabi-Yau threefold with generic SU(3) holonomy remains partially understood. Mathematically, the BPS indices coincide with the generalized Donaldson-Thomas invariants associated to the […]
Miguel Moreira: Lectures
January 11, 2023 TITLE: Virasoro constraints: vertex algebras and wall-crossing ABSTRACT: This talk will be the second one concerning the Virasoro constraints in moduli spaces of sheaves (see Woonam’s abstract), based on joint work with A. Bojko and W. Lim. In this talk, I will focus on the connection between Virasoro constraints and the vertex […]
Woonam Lim: Lectures
January 11, 2023 TITLE: Virasoro constraints; history and moduli of sheaves ABSTRACT: Virasoro constraints were first conjectured for the moduli of stable curves (the Witten conjecture) and stable maps. These conjectures provide a set of universal relations among descendent invariants described by a representation of half of the Virasoro algebra. Recently, the analogous constraints were […]
Thibault Langlais: Lectures
January 12, 2023 TITLE: An introduction to some aspects of the swampland distance conjectures ABSTRACT: The swampland program aims at distinguishing the quantum field theories which can be consistently coupled to quantum gravity at high energies from those which cannot. It leads to the formulation of many interesting problems at the intersection of geometry and […]
Thomas Grimm: Lectures
January 12, 2023 TITLE: Quantum gravity conjectures and asymptotic Hodge theory ABSTRACT: In this talk I will explain how asymptotic Hodge theory can be used to provide general evidence for some of the quantum gravity conjectures. In particular, I will describe how the orbit theorems of Hodge theory can be used in addressing the so-called […]
Arkadij Bojko: Lectures
January 11, 2023 TITLE: Wall-crossing for Calabi-Yau fourfolds and applications ABSTRACT: To count SU(4)-instantons on Calabi-Yau fourfolds, Borisov-Joyce and later on Oh-Thomas formulated a theory which counts Gieseker stable sheaves. An interesting question is what happens when one changes the stability condition and crosses walls where sheaves get destabilized. Relying on the ideas introduced by […]
Luis Alvarez Consul: Lectures
January 10, 2023 TITLE: Embedding superconformal vertex algebras from Killing spinors and (0,2) mirror symmetry ABSTRACT: I will construct embeddings of the N=2 superconformal vertex algebra under appropriate conditions inspired by the Killing spinor equations in supergravity. Firstly, when these equations are formulated on a quadratic Lie algebra, they become purely algebraic conditions that induce […]
Yuri Tschinkel: Lectures
September 8, 2022 TITLE: Equivariant Birational Geometry Slides of Lecture
Camillo De Lellis: Lectures
09/08/2023: Area-minimizing integral currents: singularities and structure September 8, 2023 TITLE: Area-minimizing integral currents: singularities and structure ABSTRACT: Let T be an area-minimizing integral current of dimension m in a smooth closed Riemannian manifold of dimension m + n. It is known since the work of De Giorgi, Fleming, Almgren, Simons, and Federer in the […]
Jiahua Tian: Lectures
September 14, 2022 TITLE: 5D SCFTs from C3 Orbifolds ABSTRACT: In this talk, we will consider the orbifold singularities X = C3/Γ where Γ is a finite subgroup of SU(3). M-theory on X gives rise to a rich class of 5D SCFTs. We will study these SCFTs via 3D McKay correspondence which relates the group […]
