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Current research
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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.
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Selected publications
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- Bounds on genus and configurations of embedded surfaces in 4-manifolds, J. Topol. 9 (2016), no. 4, 1130-1152.
- Positive scalar curvature and higher-dimensional families of Seiberg-Witten equations, J. Topol. 12 (2019), no. 4, 1246-1265.
- A gluing formula for families Seiberg-Witten invariants (with David Baraglia), Geom. Topol. 24 (2020), no. 3, 1381-1456.
- 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.
- Characteristic classes via 4-dimensional gauge theory, Geom. Topol. 25 (2021), no. 2, 711-773.
- 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.
- A cohomological Seiberg-Witten invariant emerging from the adjunction inequality, J. Topol. 15 (2022), no. 1, 108-167.
- On the Bauer-Furuta and Seiberg-Witten invariants of families of 4-manifolds (with David Baraglia), J. Topol. 15 (2022), no. 2, 505-586.
- The groups of diffeomorphisms and homeomorphisms of 4-manifolds with boundary (with Masaki Taniguchi), Adv. Math. 409 (2022), Paper No. 108627, 58 pp.
- A note on the Nielsen realization problem for K3 surfaces (with David Baraglia), Proc. Amer. Math. Soc. 151 (2023), no. 9, 4079-4087.
- Positive scalar curvature and homology cobordism invariants (with Masaki Taniguchi), J. Topol. 16 (2023), no. 2, 679-719.
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