HIROTAKA TAMANOI Professor of Mathematics B.S., University of Toyko M.S., University of Tokyo Ph.D., The Johns Hopkins University My Page

Phone: 831-459-5174 Office: McHenry 4180 Office Hours: W: 2-3:30pm, Th: 4-5pm & By Appt. Email: tamanoi@ucsc.edu

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.

SELECTED PUBLICATIONS  (complete list)

-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nite product decomposition of orbifold mapping spaces. Algebraic & Geometric Topology 9 (2009) 569-592.

-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.

-H. Tamanoi: Generalized orbifold Euler characteristics of symmetric orbifolds and covering spaces. Algebraic and Geometric Topology, Volume 3 (2003) 791-856.

-H. Tamanoi: Genera defined by hyperelliptic integrals and Siegel modular functions. J. Pure and Applied Algebra, Vol 172(2002), no.2-3, 305-323.

-R. Molzon and H. Tamanoi: Generalized Schwarzians in several variables and Mobius invariant differential operators. Forum Mathematicum, vol.14, no.2(2002), 165-188.

-H. Tamanoi: Generalized orbifold Euler characteristics of symmetric products and equivariant Morava K-theory.Algebraic and Geometric Topology, Vol.1(2001), 115-141.

-A. Baker and H. Tamanoi: Invariants for finite dimensional groups in vertex operator algebras associated to basic representations. CRM Proceedings and Lecture Notes, Vol.30(2001), 1-13.

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