- 10/27/2020: Special Kähler and related geometries`
- 1/9/2020: On the blow up set for the Seiberg-Witten equations with two spinors
- 9/9/2018: Special Kaehler structures with isolated singularities in real dimension two
- 1/10/2018: Seiberg-Witten monopoles and flat PSL(2,R)-connections
- 9/14/2017: G₂-instantons and the Seiberg-Witten monopoles
- 9/8/2016: On degenerations of the Seiberg–Witten monopoles and G₂-instantons

### October 27, 2020

TITLE: Special Kähler and related geometries`

ABSTRACT:

Slides of Lecture

### 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.

### 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 -instantons.