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Dobrushin Mathematics Laboratory Seminar
February 28, 2012 16:00, room 307, IITP RAS (Bolshoy Karetniy per., 19), Moscow
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Cluster expansions and topology
W. G. Faris
University of Arizona, Department of Mathematics
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Abstract:
A fundamental problem in mathematical physics is to
perform a sum of terms indexed by connected graphs.
Penrose showed that this sum may be rewritten as a sum
indexed by tree graphs. This exhibits remarkable
cancellations that lead to a proof of convergence.
What makes this work? The set of connected graphs
defines a simplicial complex. For a simplicial complex
such resummation is possible when the topology of the
complex is exclusively in top dimension. Penrose
had the good fortune to encounter this case.
Dedicated to Robert A. Minlos on his 81st birthday.
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