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DTSTART:20260308T070000
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DTSTART;TZID=America/Toronto:20260730T143000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-seminar-maryam-yekta
SUMMARY:Algebraic and Enumerative combinatorics seminar -Maryam Yekta-New\n
 bounds for integer flows and Verma modules via denormalized Lorentzian\nLa
 urent series
CLASS:PUBLIC
DESCRIPTION:SPEAKER:\n Maryam Yekta\n\nAFFILIATION:\n University of Waterlo
 o\n\nLOCATION:\n MC 5479\n\nABSTRACT: The theory of log concave polynomia
 ls has recently been\ndeveloped to study objects and problems in combinato
 rics and other\nsubfields in mathematics. Particular classes of log concav
 e\npolynomials called Lorentzian polynomials and denormalized and dually\n
 Lorentzian polynomials have been used to prove log concavity\nstatements f
 or various combinatorial sequences. This includes the\nstrongest form of M
 ason's log concavity conjecture on the independent\nsets of matroids and t
 he log concavity of sequences of Kostka numbers.\nIn this talk\, we develo
 p an analogous class of power series called\ndenormalized Lorentzian (DL) 
 Laurent series. This class is the natural\ngeneralization of DL polynomial
 s to homogeneous power series with the\nbenefit of capturing a number of c
 ombinatorial generating series\nincluding the Kostant partition function f
 or integer flows of directed\ngraphs. We then analyze specific DL Laurent 
 series to obtain new\nbounds for integral flows on general directed acycli
 c graphs and new\nbounds for the dimensions of weight spaces of parabolic\
 n𝔰𝔩ₙ₊₁(ℂ) Verma modules.\n\nTHERE WILL BE A PRE-SEMINAR PRES
 ENTING RELEVANT BACKGROUND AT\nBEGINNING GRADUATE LEVEL STARTING AT 1:30PM
  IN MC 5417.
DTSTAMP:20260723T171012Z
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