# Faculty

**Title**- Professor

**Division**Physical & Biological Sciences Division**Department**- Mathematics Department

**Phone**831-459-5174**Email****Fax**831-459-4511**Website****Office Location**- McHenry Library, McHenry 4180

**Mail Stop**Mathematics Department**Mailing Address**- 1156 High Street
- Santa Cruz CA 95064

**Faculty Areas of Expertise**Mathematics

### Research Interests

Hirotaka Tamanoi primarily works in (algebraic) topology. His latest interest is in string topology, studying topological aspects of strings moving in space. This theory uses topological quantum field theory and homological/topological conformal field theory. Part of the theory is motivated by string theory in physics. He has also worked in topics including elliptic cohomology theory which is closely related to geometry and representation theory of loop groups and loop spaces. He is also interested in generalized Schwarzian derivatives in several variables and Moebius invariant differential operators. Professor Tamanoi's interests also include generalized hypergeometric functions in several variables which arise in conformal field theory. These functions correspond to certain graphs which describe sewing of basic hypergeometric functions.

### Biography, Education and Training

B.S., University of Toyko

M.S., University of Tokyo

Ph.D., The Johns Hopkins University

### Selected Publications

- H. Tamanoi : Loop coproducts in string topology and triviality of higher genus TQFT operations. In press, Journal of Pure and Applied Algebra, 2009. 15 pages. Available online on August 5, 2009.
- H. Tamanoi : Stable string operations are trivial. International Mathematics Research Notices, Article ID: rnp104, 44 pages. Advance Access published July 13, 2009.
- H. Tamanoi: Cap products in string topology. Algebraic & Geometric Topology 9 (2009) 1201-1224.
- H. Tamanoi: In
- H. Tamanoi: Batalin-Vilkovisky Lie algebra structure on the loop homology of complex Stiefel manifolds. International Mathematics Research Notices, Volume 2006, Article ID 97193, pages 1-23.