Abstract: Dehn twists on surfaces form a basic class of diffeomorphisms.
On 4-manifolds, an analogue of Dehn twist can be defined by considering twists along Seifert fibered 3-manifolds.
In this talk, I will explain how this type of diffeomorphism exhibits interesting properties from the perspective of differential topology,
and occasionally from the viewpoint of symplectic geometry as well.
The proof involves gauge theory for families.
This talk includes joint work with Abhishek Mallick and Masaki Taniguchi,
as well as joint work with Jianfeng Lin, Anubhav Mukherjee, and Juan Muñoz-Echániz.
Abstract: Slope inequalities of fibered surfaces are important in relation to the classification of algebraic surfaces and the complex structure of Lefschetz fibrations in four-dimensional topology.
It is also known that many slope inequalities for semi-stable fibered surfaces can be derived from the intersection theory on the moduli space of stable curves.
In this talk, after outlining the background of these studies,
I will explain how various slope inequalities can be obtained for fibered surfaces that are not necessarily semi-stable by extending the discussion of the moduli space.
10月22日 -- オンライン開催, 17:00 -- 18:00
桑垣 樹 (京都大学)
On the generic existence of WKB spectral networks/Stokes graphs
