Saman Habini Esfahani, Stony Brook University

Title: Gauge theory, Floer homology and manifolds with special holonomy

Abstract: Gauge theory and Floer homology have proven to be useful in the study of low-dimensional manifolds. Donaldson and Thomas put forward the idea of extending these techniques to higher dimensions, especially to study manifolds with special holonomy groups. In this talk, after a brief introduction to the Donaldson-Thomas program --- and Doan-Walpuski's approach --- we focus on the differential-geometric aspects and study some of the fundamental questions in this direction, including the singularities, compactness and gluing problems, and give solutions to some of them. Parts of this work is based on an on-going project, joint with Daniel Fadel, Àkos Nagy and Gonçalo Oliveira.