Seminars are listed in reverse chronological order. The
top of the list is subject to change, since more seminars
are still being planned. All seminars are held at 3:10p.m.
in 1431 Stevenson Center unless otherwise noted. For further
information on events in the department, you may also
consult the
colloquia schedule, the
weekly
calendar and past
calendars.
Wednesday, November 6th, 2002.
Erik Boczko, of the
Department of Biomedical Informatics,
Vanderbilt University.
Polygonal Approximaton for Flows
The work presented emphasizes a new direction in the
numerical analysis of dynamical systems. The ideas are
based on those of the Conley Index theory. Given flow
a polygonal complex is introduced to discretizes the flow,
and the flow induces a map on the cells of the complex.
Under very general conditions we prove that the induced map
recurrent sets form isolating blocks, thus Conley Index
information
can be extracted from them. We also prove the result that if
each cell of the complex is sufficiently "oriented"
then the induced map recurrent sets approximate
the chain recurrent set of the flow as closely as you like. This
says that if one is willing to pay for the computational gas
one can as detailed an approximation of a complete Lyapunov
function on the maximal invariant set under consideration.
Wednesday, October 2nd, 2002.
Rainer Nagel, of the
University of Tübingen,
Germany.
Semigroups Everywhere.
The goal of this talk is to convince the audience that
"semigroups are everywhere" (E. Hille, 1948).
This is done by discussing population equations at various
levels of complexity: scalar-valued, with delay in the
birth term, with diffusion, with nonautonomous past.
Previous semesters:
