# University of Toronto's Symplectic Geometry Seminar

** WEDS *** November 24, 2004, (Note different day) 14:10--15:00

*** SS 2130 *** (Note different room)

## Tara Holm

###
UC Berkeley

##
Surjectivity techniques in symplectic geometry

** Abstract: **
Toric varieties provide an interesting class of examples in algebraic and
symplectic geometry. From the symplectic point of view, toric varieties
are symplectic reductions of a complex vector space by a linear torus
action. In this talk, I will discuss the topology of symplectic (and
other) quotients. I will briefly review Kirwan's techniques for proving
that the restriction map from the equivariant cohomology of the originial
space to the ordinary cohomology of the symplectic reduction is a
surjection. I will show how this result can be used to understand various
aspects of the topology of quotients, touching on such themes as real
loci, orbifolds and orbifold cohomology. Throughout, I will illustrate
the main results with examples of toric varieties.