Junsheng Zhang: Lectures
September 11, 2023 TITLE: On complete Calabi-Yau manifolds asymptotic to cones ABSTRACT: We proved a “no semistability at infinity” result for complete Calabi-Yau metrics asymptotic to cones, by eliminating the possible appearance of an intermediate K-semistable cone in the 2-step degeneration theory developed by Donaldson-Sun. As a consequence, a classification result for complete Calabi-Yau manifolds […]
Valentino Tosatti: Lectures
September 12, 2023 TITLE: Holomorphic Lagrangian fibrations and special Kähler geometry ABSTRACT: Consider a compact hyperkähler manifold (aka irreducible holomorphic symplectic) with a nontrivial fiber space structure onto a lower-dimensional space. Classical work of Matsushita shows that the base must be half-dimensional, and the smooth fibers are holomorphic Lagrangian tori. A basic conjecture is that […]
Langte Ma: Lectures
September 13, 2023 TITLE: Instantons on Joyce’s G2-manifolds ABSTRACT: As 7-manifolds with special holonomy, examples of compact G2-manifolds were first constructed by Joyce as resolutions of flat G2-orbifolds. Later, Walpuski constructed non-trivial G2-instantons over Joyce’s manifolds via gluing techniques. In this talk, I will first explain how to define a deformation invariant of G2-orbifolds by […]
Mingyang Li: Lectures
September 10, 2023 TITLE: Classification results for Hermitian non-Kahler gravitational instantons ABSTRACT: We will discuss some classification results for Hermitian non-Kähler gravitational instantons. There are three main results: (1) Non-existence of certain Hermitian non-Kähler ALE gravitational instantons. (2) Complete classification for Hermitian non-Kähler ALF/AF gravitational instantons. (3) Non-existence of Hermitian non-Kähler gravitational instantons under suitable […]
Jin Li: Lectures
September 12, 2023 TITLE: On the geometry of resolutions of G-2-manifolds with ICS ABSTRACT: Given a compact G_2 manifold with isolated conical singularities (ICS), the process of resolutions of these singularities gives us a one-parameter family of torsion-free G_2 structures, which can be viewed as a curve in some moduli space. This talk reports the […]
Jonas Lente: Lectures
September 12, 2023 TITLE: Modular Mathai-Quillen currents ABSTRACT: The Mathai-Quillen current is a correction term that appears in the Poincaré-Hopf theorem for manifolds with boundary, similar to the eta invariant in the Atiyah-Patodi-Singer theorem. In this talk, I will explain how to extract a modular Mathai-Quillen current from modular cobordism invariants, such as the Witten […]
Julius Grimminger: Lectures
September 10, 2023 TITLE: Stratified hyper-Kähler moduli spaces and physics ABSTRACT: Singular hyper-Kähler varieties are stratified into smooth subsets called symplectic leaves. In recent years the 3d Coulomb branch construction of hyper-Kähler varieties has been a powerful tool to study this stratification, going under the name of quiver subtraction. This algorithm is derived from intuition […]
Charles Cifarelli: Lectures
September 11, 2023 TITLE: Steady gradient Kähler-Ricci solitons and Calabi-Yau metrics on Cn ABSTRACT: I will present a new construction of complete steady gradient Kähler-Ricci solitons on C^n, using the theory of hamiltonian 2 forms, introduced by Apostolov-Calderbank-Gauduchon-Tønnesen-Friedman, as an Ansatz. The metrics come in families of two types with distinct geometric behavior, which we […]
Olivier Biquard: Lectures
September 12, 2023 TITLE: Limits of Kähler-Einstein metrics with cone singularities, and Calabi-Yau metrics ABSTRACT: There exist various constructions of open Calabi-Yau metrics (Kähler Ricci flat metrics on quasiprojective varieties). There are general questions about obtaining them as limits of Kähler-Einstein metrics with cone singularities on compactifications. I will discuss several cases, in particular the […]
Mina Aganagic: Lectures
September 11, 2023 TITLE: Homological link invariants from Floer theory ABSTRACT: A new relation between homological mirror symmetry and representation theory solves the knot categorification problem. The symplectic geometry side of mirror symmetry is a theory which generalizes Heegard-Floer theory from gl(1|1) to arbitrary simple Lie (super) algebras. The corresponding category of A-branes has many […]
