# Marston Morse Lectures

**Topic: **Exceptional holonomy and related geometric structures: Dimension reduction and boundary value problems

**Speaker: **Simon Donaldson

**Affiliation: **Stonybrook University

**Date & Time: **Friday April 6th, 2018, 2:00pm - 3:00pm

**Location: **Simonyi Hall 101

**Video:** https://video.ias.edu/MarstonMorse/2018/0406-SimonDonaldson

By imposing symmetry on manifolds of exceptional holonomy we get a variety of differential geometric questions in lower dimensions. Related to that, one can consider “adiabatic limits”, where the manifold has a fibration and the fibre size is scaled to zero. In another direction, one can study natural boundary value problems. In this lecture we will explain some theory and discuss a number (as time allows) of questions in geometric analysis that arise in this way, in particular the Plateau problem for maximal submanifolds in spaces of indefinite signature, and problems involving Monge-Ampere equations.