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2008 - 2009
announces
seminar
on
Recent Trends in Invariant Theory
by
Prof. Roger Howe
Mathematics Department, Yale University
on
February 10, 2009
at
4PM,
L H – 1, Department of Mathematics
Indian Institute of Science, Bangalore
Abstract
Since the early days of invariant theory, an important goal has been to
describe the ring of all invariant polynomial functions for a given group
action on a vector space. However, progress has been limited by the fact
that aside from a restricted number of favorable examples, these rings
tend to have rather complicated structure. In recent years, the value of
using the idea of toric deformation has emerged as a promising tool in
invariant theory. Toric deformation allows one to replace a complicated
ring by a simpler one that still carries most or all of the numerical and
combinatorial information that one wants from the ring of invariants. The
simpler rings can be described in terms of {\it lattice cones}:the
collection of integral points in a convex polyhedral cone in Euclidean
space. This gives rise to a theory with a geometric flavor in which
numbers of interest, such as dimensions of eigenspaces, are described the
the collection of integral points in a convex polyhedron. Toric
deformations promise to provide a systematic understanding of topics that
have been the submect of intense and continuing study since the early 20th
century. The goal of this talk is to provide an overview of this new
approach to invariant theory.
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