Final Report: Geometry and Elementary Particle Physics

Singer, Isadore M.

Massachusetts Institute of Technology

关键词: Geometry;    Symmetry Geometry;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;    Mirrors;    Geometry;   

DOI  :  10.2172/925850
RP-ID  :  DOE/ER/25066-FINAL
RP-ID  :  FG02-88ER25066
RP-ID  :  925850

美国|英语

来源: UNT Digital Library

【 摘 要 】

The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists’ quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.