Department/College/UnitPhysical & Biological Sciences Division

TitleProfessor

AffiliationFaculty

Web SiteCV

Primary Office LocationMcHenry Library
McHenry 4180

Mail StopMathematics Department

Biography, Education and Training

B.S., University of Toyko
M.S., University of Tokyo
Ph.D., The Johns Hopkins University

Summary of Expertise

Hirotaka Tamanoi has worked in homotopy theory, in particular, generalized cohomology theories known as cobordism theories. He is fascinated by mathematical ideas and methods inspired by string theory and conformal field theory in mathematical physics. His work has been centered around algebraic topological aspects of loop spaces such as elliptic genus (which was given a quantum field theoretical interpretation by Witten’s work on string theory), and Sullivan’s string topology and its relation to symplectic topology. He has written a book on vertex operator algebras and elliptic genera. More recently, he is interested in topological quantum field theories and their applications.

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

• 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.