- Index theory
- Noncommutative geometry
- KK-theory
- Representation theory
Introduction to my Research Areas
- My research interests involve interplays between topology and geometry. Index theory, established in the foundational papers of index theory of elliptic operators by Atiyah and Singer in the 1960s, is a bridge between several most important fields in mathematics. I work on index theory in the context of noncommutative geometry, especially for geometric objects carrying symmetries.
- Here are some notes and slides about my research area.
- T. Kato, H. Sasahira, H. Wang: Twisted Donaldson invariants. Submitted.
- H. Guo, V. Mathai, H. Wang: Spin^c, K-homology and proper actions. Submitted.
- P. Hochs, H. Wang: A fixed point theorem on noncompact manifolds. Submitted.
- P. Hochs, H. Wang: A fixed point formula and Harish-Chandra’s character formula. Proceedings of the London Mathematical Society (3) 00 (2017) 1-32.
- K.F. Chao, H. Wang: Langlands functoriality in K-theory for C*-algebras. I. Base change. Journal of Noncommutative Geometry (to appear).
- V.G. Bardakov, S. Jablan, H. Wang: Monoid and group of pseudo braids. Journal of Knot Theory and its Ramifications Vol. 25 Issue 9, 164002 (2016) [13 pages].
- B.-L. Wang, H. Wang : Localized index and L^2-Lefschetz fixed point formula for orbifolds. Journal of Differential Geometry Vol. 102, No. 2 (2016) 285-349.
- R. Ponge, H. Wang: Noncommutative geometry and conformal geometry III. Vafa-Witten inequality and Poincare duality. Advances in Mathematics Vol. 272 (2015) 761-819.
- R. Ponge, H. Wang: Noncommutative Geometry and Conformal Geometry. II. Connes-Chern character and the local equivariant index theorem. Journal of Noncommutative Geometry 10. no. 1 (2016), 303-374 .
- R. Ponge, H. Wang: Noncommutative geometry and conformal geometry I. Local index formula and conformal invariants. Journal of Noncommutative Geometry (to appear).
- R. Ponge, H. Wang: Index map, sigma-connections, and Connes-Chern character in the setting of twisted spectral triples. Kyoto Journal of Mathematics 56, no. 2 (2016), 347-399.
- V. O. Manturov, H. Wang: Markov theorem for free links. Journal of Knot Theory and its Ramifications 21, (2012) [23 pages].
- H. Wang: L^2-index formula for proper cocompact group actions. Journal of Noncommutative Geometry 8 (2014), 393-432.