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.