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DTSTART;TZID=America/Toronto:20260127T100000
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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-158
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:ERICA LIU\, UNIVERSITY OF WATERLOO\n\n_Toric Compactifications 
 and Critical Points at Infinity in Analytic\nCombinatorics_\n\nThe field o
 f Analytic Combinatorics in Several Variables (ACSV)\nprovides powerful to
 ols for deriving asymptotic information from\nmultivariate generating func
 tions. A key challenge arises when\nstandard saddle-point techniques fail 
 due to the presence of critical\npoints at infinity (CPAI)\, obstructing l
 ocal analyses near\nsingularities. Recent work has shown that Morse-theore
 tic\ndecompositions remain valid under the absence of CPAI\, traditionally
 \nverified using projective compactifications. In this talk\, I will\npres
 ent a toric approach to compactification that leverages the Newton\npolyto
 pe of a generating function to construct a toric variety\ntailored to the 
 function’s combinatorial structure. This refinement\nnot only tightens c
 lassification of CPAI but also enhances\ncomputational efficiency. Through
  concrete examples and an\nintroduction to tropical and toric techniques\,
  I will demonstrate how\nthese methods clarify the asymptotic landscape of
  ACSV problems\,\nespecially in combinatorially meaningful settings. This 
 talk draws on\njoint work studying toric compactifications as a bridge bet
 ween\nalgebraic geometry and analytic combinatorics.\n\nMC 5479
DTSTAMP:20260408T022806Z
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