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Aleksander Doan: Lectures

January 09, 2018
TITLE: Multiple covers of associatives and ADHM monopoles

ABSTRACT: Continuing Thomas Walpuski’s talk, I will explain how to extend the definition of the putative enumerative invariant of G_2 manifolds to include contributions from multiple covers of associative submanifolds. The main idea, which is a special instance of the Haydys-Walpuski proposal, is to incorporate into the invariant solutions of the ADHM Seiberg-Witten equations on associatives.

September 12, 2017
TITLE: Fueter sections and wall-crossing in Seiberg-Witten theory

ABSTRACT: Fueter sections are solutions to a non-linear generalization of the Dirac equation on a Riemannian spin three-manifold. The goal of this talk, based on joint work in progress with Thomas Walpuski, is to explore the relationship between Fueter sections taking values in instanton moduli spaces and wall-crossing for solutions to the Seiberg-Witten equation with multiple spinors. Time permitting, I will explain how this discussion fits into the Donaldson-Segal program of counting G2-instantons.