Paul F. Baum (Penn State) ATIYAH-SINGER INDEX THEOREM AND GROUP ACTIONS

Oddział: 
Oddział Warszawski
czw, 2010-02-18 16:30

Polskie Towarzystwo Matematyczne, Oddzial Warszawski; Instytut Matematyczny PAN
oraz Centrum Banacha

zapraszaja na

Wyklad-Kolokwium we czwartek, 18 lutego 2010 o godz. 16:30
w sali 403 Instytutu Matematycznego PAN, ul. Sniadeckich 8, pod tytulem:

ATIYAH-SINGER INDEX THEOREM AND GROUP ACTIONS

ktory wyglosi Paul F. Baum (Pennsylvania State University/IMPAN).

Wyklad jest przeznaczony dla szerokiej publicznosci matematycznej.
Przed wykladem, od godz. 16, zapraszamy na kawe, herbate i ciasteczka.

Streszczenie wykladu:
Let G be a (countable) discrete group acting by diffeomorphisms on a smooth manifold M. Assume that the action is smooth, proper, and co-compact. Let D be a G-invariant elliptic differrential (or perhaps pseudo-differential) operator on M. What should we mean by the equivariant index of D? This talk will take up this issue. The underlying idea is that the equivariant index is the basic topological invariant of the operator. The talk will explain how this is used in the Atiyah-Singer index theorem and in the Baum-Connes conjecture. From this point of view, Atiyah-Singer is the special case of Baum-Connes when the group G is the trivial one-element group.

The example when G = Z, and M is the real line R, and D = d/dx, and Z acts on R by the usual translation action will be considered in detail.

This talk is intended for non-specialists. The relevant definitions will be carefully stated.