Saturday, September 26, 2009
Ottawa-Carleton Institute of Mathematics and Statistics
Title: Words and polynomial invariants of finite groups in
non-commutative variables
Speaker: Christophe Hohlweg (UQAM)
Abstract: TBA
Title: Distinguished representations of reductive p-adic groups
Speaker: Fiona Murnaghan (Toronto)
Abstract: Let H be a subgroup of a group G. We say that a
representation
of G on a vector space V is H-distinguished if the dual space V*
contains
a nonzero H-invariant element. We will consider the situation where H is
the fixed points of an involution of G and G is a reductive p-adic
group.
In that case, G/H is called a p-adic symmetric space and the
H-distinguished irreducible smooth representations of G play a central
role in harmonic analysis on the space G/H. We will discuss some
examples, questions, and results related to distingushed representations
and p-adic symmetric spaces.
Title: Algebras of chiral differential operators and
representation theory
Speaker: Fyodor Malikov (USC)
Abstract: Attached to any smooth algebraic variety is an algebra
of differential
operators or, more generally its twisted version. Perhaps the best known
application of such algebras in the context of algebra and algebraic
geometry
is the Beilinson-Bernstein equivalence of appropriate module categories
over a
simple Lie algebra and an algebra of twisted differential operators. A
particular
case of this theory is the classic Borel-Weil-Bott theorem that
computes the
cohomology of equivariant line bundles over flag manifolds.
Algebras of differential operators have a vertex algebra analogue,
algebras of
chiral differential operators that were introduced some 10 years ago
(Gorbounov, Schechtmam, Vaintrob, FM.) These have found applications in
topology (they pick the Pontrjagin class as an obstruction and allow to
compute
the elliptic genus) and string theory (rigorous definition of
Witten's half-twisted
model). Algebras of twisted chiral differential operators is a more
recent
invention (joint with Arakawa and Chebotarov.) We shall show how the
latter
allow to formulate and prove a chiral version of the Borel-Weil-Bott
theorem,
where the cohomology of a certain sheaf, a chiral version of an
equivariant line
bundle, is a direct sum of irreducible modules over the corresponding
affine
Lie algebra at the critical level. This is joint work with Arakawa.
Title: What is the Congruence Subgroup Property?
Speaker: David Witte Morris (Lethbridge)
Abstract: We will present a few different characterizations of the
Congruence Subgroup Property, and describe some of its connections
with other important topics in the field of arithmetic groups,
including superrigidity, subgroup growth, bounded generation, and
Algebraic K-Theory.
