Conference Talks
This section lists all the talks at the conference together with the speakers’
abstracts.
Dirac Cohomology and unipotent representations
Dan Barbasch
In this talk we study the problem of classifying unitary representations with
Dirac cohomology. We will focus on the case when the group G is a complex reduc-
tive group viewed as a real group. It will easily follow that a necessary condition
for having nonzero Dirac cohomology is that twice the infinitesimal character is
regular and integral. The main conjecture is the following.
Conjecture: Let G be a complex reductive Lie group viewed as a real group,
and π be an irreducible unitary representation such that twice the infinitesimal
character of π is regular and integral. Then π has nonzero Dirac cohomology if and
only if π is cohomologically induced from an essentially unipotent representation
with nonzero Dirac cohomology. Here by an essentially unipotent representation
we mean a unipotent representation tensored with a unitary character. This work
is joint with Pavle Pandzic.
Equivariant K-homology
Paul Frank Baum
K-homology is the dual theory to K-theory. There are two points of view on K-
homology: BD (Baum-Douglas) and Atiyah-Kasparov. The BD approach defines
K-homology via geometric cycles. The resulting theory in a certain sense is simpler
and more direct than classical homology. For example, K-homology and K-theory
are made into equivariant theories in an utterly immediate and canonical way. For
classical (co)homology, there is an ambiguity about what is the “correct” definition
of equivariant (co)homology. In the case of twisted K-homology, the cycles of the
BD theory are the D-branes of string theory. This talk will give the definition of
equivariant BD theory and its extension to a bivariant theory. An application to
the BC (Baum-Connes) conjecture will be explained. The above is joint work with
N. Higson, H. Oyono-Oyono and T. Schick.
Moduli spaces of vector bundles on non-K¨ ahler Calabi-Yau type 3-folds
Vasile Brinzanescu
We compute the relative Jacobian of a principal elliptic bundle as a coarse
moduli space and find out that it is the product of the fiber with the basis. Using
the relative Jacobian we adapt the construction of Caldararu to our case obtaining
a twisted Fourier-Mukai transform. Using this transform and the spectral cover
xi
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