Apr 26 Simon Norton, Cambridge
Titles and Abstracts
Thursday January 11
Speaker : Sam Evens, University of Arizona
Title : Characteristic cycles for nilpotent orbits and loop Grassmanian
Abstract: We explain how to compute characteristic cycles of D-modules in
several settings relevant to representation theory, in particular for the
loop Grassmannian and for many nilpotent orbits. In the case of the
subregular nilpotent orbit, elliptic curves appear in a natural way. This
talk is based on joint work with Ivan Mirkovic
Monday January 22
Speaker : Bob Griess UofM
Title : Vertex Operator Algebras, I
Monday January 29
Speaker : Arvind Nair UofM
Title : Weighted cohomology of arithmetic groups
Abstract : Let G be a semisimple Lie group, K a maximal compact subgroup
and Gamma an arithmetic group in G. The geometric and
cohomological properties of the group Gamma are reflected
in the geometry of the locally symmetric space X=Gamma\G/K.
Among the invariants of Gamma one can define this way are
L_2 cohomology and weighted L_2 cohomology. It is now known
that these actually have a topological interpretation (when
X is Hermitian) using geometric cohomology theories on certain
compactifications of X (intersection cohomology, and in
general using recently defined weighted cohomology). The
importance of the space X to automorphic forms means that
many of the results have interesting applications to
arithmetic problems (e.g. computing the trace of Hecke
operators etc.) The first half will be mostly an introductory
survey of some of the past results due to many people.
In the second half I will present some results in greater
detail with indications of proofs.
Monday February 05
Speaker : Gopal Prasad UofM
Title : Computation of the metaplectic kernel
Abstract : Computation of the metaplectic kernel is required for the
congruence subgroup problem and also in the theory of automorphic
forms of fractional weights. a good upper bound for it was
obtained earlier for all simply connected semi-simple isotropic
groups. Jointly with A.S. Rapinchuk, we have now been able to
give a good bound for the metaplectic kernel for all simply
connected semi-simple group. Using a recent result of P. Deligne,
we are able to compute the absolute metaplectic kernel precisely.
Monday February 12
Speaker : Roger Howe, Yale
Title : Multiplicity-free actions in invariant theory
Abstract : In recent years, multiplicity-free actions have become a focus of
research in invariant theory. This is in part because they provide
a unified viewpoint on many of the successful computations in the
subject. This talk will give an overview of the basic aspects of
the theory of multiplicity free actions, with some examples of
important classical computations which rely essentially on
multiplicity-freeness.
Monday February 19
Speaker : Bob Griess UofM
Title : Vertex Operator Algebras, II
Abstract : In VOA, I, we discussed axioms and some consequences then
quickly toured examples. This time, we take a more careful look at the
differential operators required to describe the basic module for an affine
Kac Moody algebra (this goes back to old work of Frenkel-Kac, inspored by
older work of physicists) and show how operators like them make this basic
module a VOA (Frenkel-Zhu, 1992). In some order (in VOA II and III) I
will cover topics (1) the Zhu algebra A(V), a "small" associative algebra
whose representation theory smartly captures that of the VOA V; (2) fusion
rules; (3) discrete series; (4) low degree products; (5) idempotents and
VOAs.
Monday February 26 No Seminar
Monday March 4 Break
Monday March 11
Speaker : Curt Bennett, Bowling Green
Title : Exponentiation of bounded elements in infinite dimensional Lie algebras over fields of characteristic zero.
Abstract : In the usual technique of exponentiating representations
of infinite dimensional Lie Algebras, only locally nilpotent elements can be
exponentiated. By embedding a representation on V into a representation on
the dual of V, we define an exponential map which can be applied to
elements of the Lie algebra satisfying a less stringent condition. We then
apply this technique to affine Kac-Moody Lie Algebras and certain of the
Kac-Moody Lie algebras of indefinite type. In the latter case, we define
extensions of the Kac-Moody Lie Group over R[[t]].
Monday March 18
Speaker : Pavel Etingof, Harvard
Title : Quantization of Lie bialgebras
Abstract : In this talk I will give an account of my recent
work with David Kazhdan, where Drinfeld's program of quantization of
Poisson-Lie groups was implemented. In particular, I will explain how to
quantize any classical r-matrix and any Poisson-Lie group.
Monday March 25 No Seminar
Monday April 1 No Seminar
Monday April 8 No Seminar
Monday April 15 No Seminar
Monday Friday 26
Speaker : Simon Norton, Cambridge
Title : Group Sex and the Monster
Introduction to Abstract : To begin to satisfy your curiosity, I may as well say that when reading a
certain science fiction book I was struck by an analogy between the mode of
reproduction of the aliens in that book and how Baby Monsters can generate
Monsters via football theory. There is absolutely nothing about human sex --
well, almost nothing ...
Abstract :
Inside the Monster, consider three copies of the Baby Monster. Their
intersection is the centralizer of the group generated by their centres
(sorry centers). It can be shown that if the intersection is trivial, then
the three Babies give birth to the Monster in the sense that their centers
generate it. Study of the various configurations of Babies yields a number
of interesting phenomena, including a hint of links with moonshine.
Further information: