Seminars/Conferences | Institute for the Physics and Mathematics of the Universe (IPMU)

IPMU Komaba Lectures

Date:	April 8, 2008, 10:30 - 12:00 April 15, 2008, 10:30 - 12:00 April 22, 2008, 10:30 - 12:00 May 13, 2008, 10:30 - 12:00
Place:	Room 002, Mathematical Sciences Building, Komaba Campus, The University of Tokyo. (Second Lecture can be attended in room 031, basement floor, Research Centers Building, Kashiwa Campus using TV conference.)
Speaker:	Akihiro Tsuchiya (IPMU)
Title:	Homotopy Theory (before 1970)
Abstract:	Recently the notion of homotopy theory has been widely used in many areas of contemporary mathematics including mathematical physics. The purpose of the lectures is to present an overview of the developments of homotopy theory mainly from 1940's through 1960's, partly in view of more recent progress in other areas. (1) Prehistory of homotopy theory -- Hurewicz theorem, Hopf theorem, Freudentahl suspension theorem (2) Eilenberg-MacLane space and Postnikov system (3) Steenrod algebras (4) Serre's theorem on the homotopy groups of spheres (5) Rational homotopy theory (6) Stable homotopy category and Adams spectral sequence (7) Vector bundles and characteristic classes (8) Complex cobordism and Quillen's theorem (9) Miscellaneous topics Rereferences: (1) J.P.May, A Concise Course in Algebraic Topology, The University of Chicago Press http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf (2) Douglas Ravenel, Complex cobordism and stable homotopy groups of spheres The second edition, AMS Chelsea Series http://www.math.rochester.edu/u/faculty/doug/mu.html (3) Mark Hovey, Model Category, AMS (4) Gelfand and Manin, Homology Algebra
IPMU Komaba Seminar Web Page:	http://faculty.ms.u-tokyo.ac.jp/~topology/IPMU/index.html