KONNO, Hokuto

Title
Assistant Professor
Field
Geometry and Topology
Research interests
Gauge theory and its applications to geometry and topology
Current research

I am mainly working on 4-dimensional gauge theory and its applications to geometry and topology. A major part of my research activity focuses on finding new problems in dimension four inspired from other dimensions, and solving the problems using gauge-theoretical techniques. Recently, I studied a foundation of gauge theory for families of 4-manifolds, and applied it to extract differences between homotopy groups of the homeomorphism and diffeomorphism groups of 4-manifolds.

Selected publications
  1. Bounds on genus and configurations of embedded surfaces in 4-manifolds, J. Topol. 9 (2016), no. 4, 1130-1152.
  2. Positive scalar curvature and higher-dimensional families of Seiberg-Witten equations, J. Topol. 12 (2019), no. 4, 1246-1265.
  3. (with D. Baraglia) A gluing formula for families Seiberg-Witten invariants, Geom. Topol. 24 (2020), no. 3, 1381-1456.
  4. Characteristic classes via 4-dimensional gauge theory, Geom. Topol. (to appear)
  5. (with M. Taniguchi) Positive scalar curvature and 10/8-type inequalities on 4-manifolds with periodic ends , Invent. Math. (to appear) 

Memberships, activities and

Awards

The Mathematical Society of Japan