KONNO, Hokuto

Title
Associate 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. On four-dimensional Dehn twists and Milnor fibrations (with Jianfeng Lin, Anubhav Mukherjee, and Juan Muñoz-Echániz), to appear in Duke Math. J.
  2. Irreducible 4-manifolds can admit exotic diffeomorphisms (with David Baraglia), to appear in Duke Math. J.
  3. Involutions, knots, and Floer K-theory (with Jin Miyazawa and Masaki Taniguchi), Compos. Math. 161 (2025), no. 11, 2852-2910.
  4. The homology of moduli spaces of 4-manifolds may be infinitely generated, Forum Math. Pi 12 (2024), Paper No. e25.
  5. The groups of diffeomorphisms and homeomorphisms of 4-manifolds with boundary (with Masaki Taniguchi), Adv. Math. 409 (2022), Paper No. 108627, 58 pp.
  6. Rigidity of the mod 2 families Seiberg-Witten invariants and topology of families of spin 4-manifolds (with Tsuyoshi Kato and Nobuhiro Nakamura), Compos. Math. 157 (2021), no. 4, 770-808.
  7. Characteristic classes via 4-dimensional gauge theory, Geom. Topol. 25 (2021), no. 2, 711-773.
  8. A gluing formula for families Seiberg-Witten invariants (with David Baraglia), Geom. Topol. 24 (2020), no. 3, 1381-1456.
  9. Positive scalar curvature and 10/8-type inequalities on 4-manifolds with periodic ends (with Masaki Taniguchi), Invent. Math. 222 (2020), no. 3, 833-880.

Memberships, activities and

Awards

The Mathematical Society of Japan

JSPS Prize of Japan Society of Promotion of Science (2025)

Spring Prize of the Mathematical Society of Japan (2025)

Geometry Prize of the Mathematical Society of Japan (2024)