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Семинар Добрушинской лаборатории Высшей школы современной математики МФТИ
28 февраля 2012 г. 16:00, комн. 307 ИППИ РАН (Большой Каретный пер., 19), Москва
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Cluster expansions and topology
W. G. Faris
University of Arizona, Department of Mathematics
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| Эта страница: | 143 |
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Аннотация:
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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