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

Phone: 831-459-5174 Office: Baskin 369 Office Hours: By Appt. Email: tamanoi_at_ucsc_dot_edu

RESEARCH INTERESTS

Hirotaka Tamanoi is primarily interested in (algebraic) topology, particularly elliptic cohomology theory which is closely related to geometry and representation theory of loop groups and loop spaces, quantum field theory, and conformal field theory. Part of the theory is motivated by physics. 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: Elliptic Genera and Vertex Operator Super Algebras. Lecture Notes in Mathematics (Book) Vol. 1705, 390 pp (1999).

H. Tamanoi: Hyperelliptic genera. Preprint.

R. Molzon and H. Tamanoi: Generalized Schwarzians in several variables and Moebius invariant differential operators. Preprint.

H. Tamanoi: Q-subalgebras, Milnor basis and cohomology of Eilenberg-MaLane spaces. Jour. of Pure and Applied Algebra (1999) 132, 153-198.

H. Tamanoi: Spectra of BP-linear relations, Vn-series, and BP-cohomology of Eilenberg-MacLane spaces. To appear in Trans. Amer. Math. Soc., (1999).

H. Tamanoi: Invariant symmetric pairings in vertex operator super algebras and Gramians. To appear in J. Pure Appl. Algebra (1999).

H. Tamanoi: The image of BP-Thom maps for Eilenberg-MacLane spaces. Trans. Amer. Math. Soc. vol 349 (1997) 1209-1237.

H. Tamanoi: Higher Schwarzian operators and combinatorics of the Schwarzian derivative. Math. Ann. 305, 127-151 (1996).

H. Tamanoi: Elliptic genera and vertex operator super algebras. Proc. Japan Acad., 71, Ser.A 177-181 (1995).

PUBLISHED BOOKS AND ARTICLES

Published Research Monograph

H. Tamanoi: Elliptic Genera and Vertex Operator Super Algebras. 390pp. (Springer Lecture Notes in Mathematics, Volume 1705, 1999.)
Chapter I : Elliptic Genera.
Chapter II : Vertex operator super algebras.
Chapter III : G-invariant vertex operator super algebras.
Chapter IV : Geometric structures in vector spaces and reductions of structure groups on manifolds.
Chapter V : Infinite dimensional symmetries in elliptic genera for Kþhler manifolds.

Published Articles

(1) J. Morava and H. Tamanoi: A vanishing theorem for the conformal anomaly. Proceedings of the AMS, vol.100, 767-774, (1987).

(2) H. Tamanoi: Elliptic genera and vertex operator super algebras. Proc. Japan Acad., 71, Ser.A 177-181 (1995).

(3) H. Tamanoi: Higher Schwarzian operators and combinatorics of Schwarzian derivative. Math. Ann. 305(1996), pp. 127-151.

(4) H. Tamanoi: The image of BP-Thom maps for Eilenberg-MacLane spaces. Transactions of AMS, vol 349 (1997) 1209-1237.

(5) H. Tamanoi: Multiplicative indecomposable splittings of MSp[2] . Mathematische Zeitschrift, 225(1997), pp. 577 610.

(6) H. Tamanoi: Q-subalgebras, Milnor basis, and cohomology of Eilenberg-Mac Lane spaces. Journal of Pure and Applied Algebra, 132(1999), pp. 153-198.

(7) H. Tamanoi: Invariant symmetric pairings in vertex operator super algebras and Gramians. J. Pure and Applied Algebra 140(1999), pp. 149-189.

(8) H. Tamanoi: Spectra of BP-linear relations, vn-series, and BP-cohomology of Eilenberg-Mac Lane spaces. Trans. Amer. Math. Soc., 352(2000), no.11, 5139-5178.

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

Articles Accepted for Publication

(10) R. Molzon and H. Tamanoi: Generalized Schwarzians in several variables and Mšbius invariant differential operators. Accepted for publication in Forum Mathematicum.

(11) A. Baker and H. Tamanoi: Invariants for infinite dimensional groups in vertex operator algebras associated to basic representations. Accepted for publication in Proceedings of Moonshine Conference held at CRM, Montreal.

(12) H. Tamanoi: Genera defined by hyperelliptic integrals and Siegel modular functions. Accepted for publication in Journal of Pure and Applied Algebra.

WORKS IN PROGRESS

Research Monograph

H. Tamanoi: Conformal Generalized Hypergeometric Differential Forms. In preparation at 248 pages.
Chapter I : Holomorphic (semi-group) representations of (semi)-groups PSU(1, 1) and PSL2 (C).
Chapter II : Highest weight, lowest weight, and intermediate series representations.
Chapter III : 2-disc operators and 3-disc operators.
Chapter IV : Holonomicity of generalized hypergeometric D-modules.
Chapter V : Invariant hypergeometric local systems on configuration spaces.
Chapter VI : Refined sewing diagrams and associated cross ratios.
Chapter VII : Hypergeometric differential forms associated to refined sewing diagrams.
Chapter VIII : Solutions to hypergeometric D-modules and Combinatorial identities.
Chapter IX : Commuting linear partial differential operators for hypergeometric D-modules.

Articles

(i) H. Tamanoi: Conformal generalized hypergeometric differential forms on P1. Preprint, 9 pages.

(ii) H. Tamanoi: Geometric Schwarzians and projective structures on complex manifolds. Preprint, 43 pages.

(iii) H. Tamanoi: A note on the Hopf algebra MU* (BU), MU-Chern characters, and Bell Polynomials. Preprint, 10 pages.

(iv) H. Tamanoi: Generalized orbifold Euler characteristics of symmetric orbifolds and covering spaces. Preprint, 46 pages

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