BEGIN:VCALENDAR
VERSION:2.0
METHOD:PUBLISH
PRODID:-//Virginia Tech//VT Calendar//EN
BEGIN:VEVENT
DTSTAMP:20201028T200000Z
UID:1603718348637@events.msu.edu
CATEGORIES:Conferences / Seminars / Lectures
DTSTART:20201028T200000Z
DTEND:20201028T210000Z
SUMMARY:Math Seminar Series
DESCRIPTION:
Keshav Sutrave from Michigan State University
will be speaking.\n
\n
The seminar is titled "The
Principle of Symmetric Criticality."\n
\n
This
is a virtual meeting.\n
\n
Contact Danika Vanniel
(vannield@msu.edu) for more information.\n
\n
(Palais,
1979) Many problems are set up
as variational problems. That is, on a (possibly
infinite-dimensional) manifold M with a group
of symmetries G, we look for critical points
of a G-invariant functional f. In order
to do this, we might first restrict ourselves
to looking at the set S of G-symmetric points
of M (points p such that gp=p for all g). The
principle asserts that if p is a critical
point of f restricted to S, then p is in fact
a critical point in M. In other words: "Critical
symmetric points are symmetric critical
points". For example, harmonic functions on a
space X are critical points of an energy functional
on a space of functions M = {X to R}.
To find a harmonic map on X, we might start
by considering only maps which are rotationally
symmetric. The principle states that it suffices
to consider only rotationally symmetric
variations as well. This reduces the problem
from a PDE to an ODE, how nice! Anyway, the
Principle does not always hold, but in some
very general situations it does. Let's find out
about them.\n\n
Price: free\n
Sponsor: Department of Mathematics\n
Sponsor's Homepage: https://www.math.msu.edu/\n
Contact name: Department of Mathematics\n
Contact phone: (517) 353-0844\n
for more info visit the web at:\n
https://www.math.msu.edu/Seminars/CalendarView.aspx?month-of=September2016\n
LOCATION:Online via Zoom
END:VEVENT
END:VCALENDAR