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DTSTAMP:20210217T200000Z
UID:1613487499069@events.msu.edu
CATEGORIES:Conferences / Seminars / Lectures
DTSTART:20210217T200000Z
DTEND:20210217T205000Z
SUMMARY:Math Seminar Series
DESCRIPTION:
Combinatorics and Graph Theory\n
\n
Tom Roby, University
of Connecticut, will be speaking.\n
\n
The
presentation is titled "An action-packed
introduction to homomesy."\n
\n
Contact Bruce
E Sagan (bsagan@msu.edu) for more information.\n
\n
Dynamical
Algebraic Combinatorics explores
maps on sets of discrete combinatorial objects
with particular attention to their orbit
structure. Interesting counting questions immediately
arise: How many orbits are there? What
are their sizes? What is the period of the
map if it's invertible? Are there any interesting
statistics on the objects that are well-behaved
under the map? One particular phenomenon
of interest is homomesy'', where a statistic
on the set of objects has the same average
for each orbit of an action. Along with its
intrinsic interest as a kind of hidden invariant'',
homomesy can be used to help understand
certain properties of the action. Proofs
of homomesy often lead one to develop tools
that further our understanding of the underlying
dynamics, e.g., by finding an equivariant
bijection. These notions can be lifted to higher
(piecewise-linear and birational) realms,
of which the combinatorial situation is a discrete
shadow, and the resulting identities
are somewhat surprising. Maps that can be decomposed
as products of toggling'' involutions
are particularly amenable to this line of analysis.
This talk will be a introduction to these
ideas, giving a number of examples.\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
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