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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240926T140000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240926T150000
URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-seminar-jonathan
SUMMARY:Algebraic and enumerative combinatorics seminar-Jonathan Leake
CLASS:PUBLIC
DESCRIPTION:Approximately Counting Flows via Generating Function Optimizati
 on\n\nSpeaker\n Jonathan Leake\n\nAffiliation\n University of Waterloo\n\n
 Location\n MC 5479\n\nAbstract: In this talk\, we will present recent new 
 lower bounds on the\nnumber of non-negative integer flows on a directed ac
 yclic graph with\nspecified total vertex flows (or equivalently\, the numb
 er of lattice\npoints of a given flow polytope\, or the coefficients of th
 e A-type\nKostant partition function). We will also give a sketch of the p
 roof\,\nwhich involves three main parts: (1) prove a certain log-concavity
 \nproperty of the associated multivariate generating function\, (2) prove\
 nbounds on the coefficients in terms of an associated optimization\nproble
 m\, and (3) dualize the optimization problem to obtain the\ndesired lower 
 bounds. If time permits\, we will also briefly discuss\nother applications
  of this technique\, including to approximating\nKostka numbers and to the
  traveling salesperson problem. Joint work\nwith Alejandro Morales\, and w
 ith Petter Brändén and Igor Pak.\n\nTHERE WILL BE A PRE-SEMINAR PRESENTI
 NG RELEVANT BACKGROUND AT THE\nBEGINNING GRADUATE LEVEL STARTING AT 1PM\,
DTSTAMP:20260403T083103Z
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