Recorded June 2020
TITLE: Twistor spaces and hyperkahler metrics

ABSTRACT: I discuss several questions about twistor spaces of hyperkaehler manifolds:
multiple components of the Kodaira moduli space of sections; differential
geometry of spaces of sections which include sections with “wrong” normal
bundle; and (pseudo-)hyperkaehler metrics arising on Hilbert schemes of higher
degrees curves in a twistor space.
On this last topic, in addition to older results, I discuss the current project
with Lorenzo Foscolo, where we construct (presumably QALF) hyperkaehler manifolds
from W-invariant hypertoric varieties. We suggest that a subclass of these
corresponds precisely to the Coulomb branches of 3-dimensional N=4 SUSY gauge theories.
Slides of Lecture