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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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