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Albert Wood: Lectures
May 15, 2024 TITLE: Infinite-Time Singularities of Lagrangian Mean Curvature Flow ABSTRACT: Lagrangian mean curvature flow is the name given to the phenomenon that, in a Calabi-Yau manifold, the class of Lagrangian submanifolds is preserved under mean curvature flow. An influential conjecture of Thomas and Yau, refined since by Joyce, proposes to utilise the Lagrangian […]
Thorsten Hertl: Lectures
May 13, 2024 TITLE: On the Moduli Space of G2 Manifolds ABSTRACT: In his two seminal articles, Dominic Joyce not only constructed the first examples of closed manifolds with G2-holonomy metrics, but also proved that the moduli space of all G2-metrics on a closed manifold is itself a finite-dimensional manifold. The statement is, however, only […]
Dominik Gutwein: Lectures
May 14, 2024 TITLE: G2-instantons over generalised Kummer constructions via finite group actions ABSTRACT: This talk explanes a method for producing new examples of G2-instantons over generalised Kummer constructions. This method is based on an extension of Walpuski’s original gluing theorem for G2-instantons over generalised Kummer constructions and deforms a connection that is (in a […]
Emily Windes: Lectures
May 17, 2024 TITLE: The Moduli Space of Graphical Associative Submanifolds ABSTRACT: In this talk, I discuss an infinite-dimensional Lagrange-multipliers problem that first appeared in Donaldson and Segal’s paper “Gauge Theory in Higher Dimensions II”. The longterm goal is to apply Floer theory to a functional whose critical points are generalizations of three (real) dimensional, […]
Shubham Dwivedi: Lectures
May 17, 2024 TITLE: Geometric flows of G_2 and Spin(7)-structures ABSTRACT: We will discuss a family of flows of G_2-structures on seven dimensional Riemannian manifolds. These flows are negative gradient flows of natural energy functionals involving various torsion components of G_2-structures. We will prove short-time existence and uniqueness of solutions to the flows and a […]
Gilles Englebert: Lectures
May 16, 2024 TITLE: Stability of Cayley fibrations ABSTRACT: Motivated by the SYZ conjecture, it is expected that G_2 and Spin(7)-manifolds admit calibrated fibrations as well. One potential way to construct examples is via gluing of complex fibrations, as in the program of Kovalev. For this to succeed we need the fibration property to be […]
Viktor Majewski: Lectures
May 15, 2024 TITLE: Resolutions of Spin(7)-Orbifolds ABSTRACT: In Joyce’s seminal work, he constructed the first examples of compact manifolds with exceptional holonomy by resolving flat orbifolds. Recently, Joyce and Karigiannis generalised these ideas in the G2 setting to orbifolds with Z2-singular strata. In this talk I will present a generalisation of these ideas to […]
Yuanqi Wang: Lectures
May 14, 2024 TITLE: Spectral theory of singular G2-instantons ABSTRACT: G2-instantons on 7-dimensional manifolds generalize both flat connections in dimension 3, and anti self-dual connections in dimension 4. Donaldson-Segal program expects a certain count of G2-instantons and other objects could yield a topological invariant for 7–manifolds, called the prospective G2–Casson invariant. Related to the compactification/boundary […]
Evyatar Sabag: Lectures
September 10, 2023 TITLE: G2 Manifolds from 4d N=1 Theories ABSTRACT: We propose new G2-holonomy manifolds, which geometrize the Gaiotto-Kim 4d N = 1 duality domain walls of 5d N = 1 theories. These domain walls interpolate between different extended Coulomb branch phases of a given 5d superconformal field theory. Our starting point is the […]
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 […]
