Interests

My research interests range over 3- and 4-dimensional topology and gauge theory.

Keywords

Yang-Mills gauge theory, Donaldson invariant, Donaldson's diagonalization theorem, Instanton Floer homology, h-invariant, Floer homotopy type, spaces of Morse trajectories, gauge theory on 4-manifolds with periodic ends,  Seiberg-Witten theory, 10/8-inequality, positive scalar curvature,  surgery obstruction, the 3-dimensional homology cobordism group, Seifert hypersurface of 2-knots, Chern-Simons functional for 2-knots, knot group, codimension-1 embedding of 3-manifolds, groups of diffeomorphisms and homeomorphisms of 4-manifolds, Seiberg-Witten  Floer homotopy contact invariant,  contact topology, symplectic filling, K-theoretic contact invariant,  Bauer-Furuta type invariant of Kronheimer-Mworka's invariant for 4-manifold with boundary, adjunction inequality, symplectic cap, H-sliceness in general 4-manifolds, exotic pairs of 4-manifolds with boundary, branched covering spaces of knots and surfaces, involutions on 3- and 4-manifolds, Floer homotopy type for knots and involutions, Floer K-theory for knots and involutions, 10/8-inequality for knots and involutions, relative genus bounds, extension problems of involutions, real Seiberg-Witten theory,  stabilizing numbers for knots, exotic diffeomorphisms of 4-manifolds, exotic surfaces in 4-manifolds, exotic codimension-1 embeddings in 4-manifolds, generalized Thurston-Bennequin type inequality, singular instanton knot theory, local equivalence theory with Chern-Simons filtration, satellite operations on the knot concordance group, stabilization of exotic embeddings of 3-manifolds into 4-manifolds, small exotic 4-manifolds, strong cork detections, genus bounds from alpha, beta and gamma, non-smoothable diffeomorphisms on 4-manifolds, exotic Dehn twits along Seifert 3-manifolds, exotic diffeomorphisms which survive after a stabilization, exotic diffeomorphism on a contractible 4-manifold, involutive (S^1-family ver) instanton Floer homology, strong corks which survive after definite stabilization, linear independence of surgeries of slice knots in the homology bordism group of diffeomorphisms, transverse knot invariants from Floer homotopy, symplectic surfaces, quasi-positivity of Montesinos knots, slice torus invariant from equivariant Seiberg-Witten theory

Schedule of talks (overseas): 

Travel schedule  (overseas):