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Andriy Haydys: Lectures

January 9, 2020
TITLE: On the blow up set for the Seiberg-Witten equations with two spinors

ABSTRACT: Unlike in the case of the classical Seiberg-Witten equations, the energy density of a solution to the Seiberg-Witten equations with two spinors can concentrate along one-dimensional sets, which are called blow up sets. I will discuss some properties of blow up sets including bounds on its total length and the structure of an integer multiplicity rectifiable current.

September 9, 2018
TITLE: Special Kaehler structures with isolated singularities in real dimension two.

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.