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URL:/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-seminar-michael
SUMMARY:Algebraic and enumerative combinatorics seminar-Michael Borinsky
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE: Asymptotic count of edge-bicolored graphs\n
 \nSpeaker\n Michael Borinsky\n\nAffiliation\n Perimeter Institute and C&O 
 \n\nLocation\n MC 5479\n\n ABSTRACT: I will talk about recent joint work 
 with Chiara Meroni and\nMax Wiesmann\, where we showed that specific expon
 ential bivariate\nintegrals serve as generating functions of labeled edge-
 bicolored\ngraphs. Based on this\, we prove an asymptotic formula for the 
 number\nof regular edge-bicolored graphs with arbitrary weights assigned t
 o\ndifferent vertex structures. \n\nThe asymptotic behavior is governed by
  the critical points of a\npolynomial. An interesting application of this 
 purely combinatorial\nwork to mathematical physics is the Ising model on a
  random graph. I\nwill explain how its phase transitions arise from our fo
 rmula.\n\nTHERE WILL BE A PRE-SEMINAR PRESENTING RELEVANT BACKGROUND AT TH
 E\nBEGINNING GRADUATE LEVEL STARTING AT 1PM\,\n 
DTSTAMP:20250711T115750Z
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