Act globally, compute locally: group actions, fixed points, and
localization -- Tara Holm

<p>

Localization is a technique that allows us to make global
equivariant computations in terms of local data at the fixed points.  We
may compute a global integral by summing the integrals at all the fixed
points.  Or, if we know that the global integral is zero, we conclude that
the sum of the local integrals is zero.  This often turns topological
questions into combinatorial ones and vice versa.

<p>

This lecture will feature several instances of localization that occur at
the crossroads of algebraic geometry and combinatorics. First I will
describe briefly the background of localization. Then as time permits, I
will focus on:
<br>
-- Equivariant cohomology in terms of graphs, and combinatorial
localization;
<br>
-- Virtual localization and the computation of Gromov-Witten invariants;
and
<br>
-- Lattice polytopes, toric varieties and the Euler-MacLaurin formula.