Special Workshop in Gauge Theory

January 9 - January 12, 2024
Room 110, Science Building No.3 (Department of Mathematics), North campus, Kyoto university
Registration is required from the following links:


Jan 9, JST 10:00-11:00, Francesco Lin (Columbia University) -> KTGU SPECIAL WEEKS

Jan 10, JST 10:00-11:00, Nobuhiro Nakamura (Fukushima Medical University)

Title: Conjectures on inequalities of 10/8-type

Abstract: We will explain several conjectures proposed by Tsuyoshi Kato which state that inequalities of 10/8-type on $L^2$-Betti numbers, Euler characteristics and signatures hold for compact spin 4-manifolds with infinite fundamental groups. There are three versions of conjectures: covering version, aspherical version and non-negative Ricci version, which are verified to be true for some special cases. We hope that we can also mention the extensions of these conjectures to the case of spin 4-manifolds with boundary.

Jan 11, JST 10:00-11:00, Francesco Lin (Columbia University) -> KTGU SPECIAL WEEKS

Jan 12, JST 10:00-11:00, Masaki Taniguchi (Kyoto University)

Title: Monopoles and Transverse Knots

Abstract: We develop a framework to study transverse knots and symplectic surfaces using the Seiberg-Witten monopole equation. Our primary approach involves an examination of an equivariant Seiberg-Witten theory introduced by Baraglia-Hekmati on branched covers, incorporating invariant contact/symplectic structures. Within this framework, we introduce a new slice torus invariant, derived from the equivariant Seiberg-Witten theory. Leveraging the properties of the invariant, we establish an adjunction equality for immersed symplectic surfaces in certain symplectic fillings. As an application of this kind of discussion, we give some constrains of homology classes of symplectic surfaces. This is joint work with Nobuo Iida.

Tsuyoshi Kato (Kyoto University)
Nobuhiro Nakamura (Fukushima Medical University, nnaka[at]fmu.ac.jp ([at]->@))