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Andriy Haydys: Lectures

January 10, 2018
TITLE: Seiberg-Witten monopoles and flat PSL(2,R)-connections

ABSTRACT: I will talk about a relation between the Seiberg-Witten monopoles with two spinors and flat PSL(2,R)-connections. This relation can be used to obtain some explicit examples of moduli spaces of the Seiberg-Witten monopoles with two spinors as well as to get some insight into degenerate solutions, which, in this case, are the so called Z/2 harmonic 1-forms.

September 14, 2017
TITLE: G₂-instantons and the Seiberg-Witten monopoles

ABSTRACT: I will talk about gauge theory on G₂ manifolds and its relation to the (generalized) Seiberg-Witten equations on three-manifolds. In particular, I will focus on the compactness properties for the corresponding moduli spaces and related problems.

Slides of lecture

September 8, 2016
TITLE: On degenerations of the Seiberg–Witten monopoles and G₂-instantons

ABSTRACT: A sequence of the Seiberg-Witten monopoles with multiple spinors on a three-manifold can converge after a suitable rescaling to a Fueter section, say I, only on the complement of a subset Z. I will discuss the following question: Which pairs (I,Z) can (or can not) appear as the limit of a sequence of the Seiberg–Witten monopoles? I will also address an analogous question for the sequences of G_2-instantons.