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SUMMARY:Isabelle Shankar (UC Berkeley)
DTSTART:20200413T191000Z
DTEND:20200413T200000Z
DTSTAMP:20260422T225658Z
UID:BerkeleyCombinatorics/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BerkeleyComb
 inatorics/1/">An SOS counterexample to an inequality of symmetric function
 s</a>\nby Isabelle Shankar (UC Berkeley) as part of The UC Berkeley combin
 atorics seminar\n\nLecture held in 939 Evans Hall.\n\nAbstract\nIt is know
 n that differences of symmetric functions corresponding to various bases a
 re nonnegative on the nonnegative orthant exactly when the partitions defi
 ning them are comparable in dominance order. The only exception is the cas
 e of homogeneous symmetric functions where it is only known that dominance
  of the partitions implies nonnegativity of the corresponding difference o
 f symmetric functions. It was conjectured by Cuttler\, Greene\, and Skande
 ra in 2011 that the converse also holds\, as in the cases of the monomial\
 , elementary\, power-sum\, and Schur bases. I will derive a counterexample
  using the theory of sum of squares relaxations and thus show that homogen
 eous symmetric functions break the pattern.\n
LOCATION:https://researchseminars.org/talk/BerkeleyCombinatorics/1/
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BEGIN:VEVENT
SUMMARY:Robert Scherer (UC Davis)
DTSTART:20200420T191000Z
DTEND:20200420T200000Z
DTSTAMP:20260422T225658Z
UID:BerkeleyCombinatorics/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BerkeleyComb
 inatorics/2/">A criterion for asymptotic sharpness in the enumeration of s
 imply generated trees</a>\nby Robert Scherer (UC Davis) as part of The UC 
 Berkeley combinatorics seminar\n\nLecture held in 939 Evans Hall.\n\nAbstr
 act\nWe study the identity y(x) = xA(y(x))\, from the theory of rooted tre
 es\, for appropriate generating functions y(x) and A(x) with non-negative 
 integer coefficients. A problem that has been studied extensively is to de
 termine the asymptotics of the coefficients of y(x) from analytic properti
 es of the complex function z 􏰀→ A(z)\, assumed to have a positive rad
 ius of convergence R. It is well-known that the vanishing of A(x) − xA
 ′(x) on (0\, R) is sufficient to ensure that y(r) < R\, where r is the r
 adius of convergence of y(x). This result has been generalized in the lite
 rature to account for more general functional equations than the one above
 \, and used to determine asymptotics for the Taylor coefficients of y(x). 
 What has not been shown is whether that sufficient condition is also neces
 sary. We show here that it is\, thus establishing a criterion for sharpnes
 s of the inequality y(r) ≤ R. As an application\, we prove a 1996 conjec
 ture of Kuperberg regarding the asymptotic growth rate of an integer seque
 nce arising in the study of Lie algebra representations.\n
LOCATION:https://researchseminars.org/talk/BerkeleyCombinatorics/2/
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BEGIN:VEVENT
SUMMARY:Jesus de Loera (UC Davis)
DTSTART:20200427T191000Z
DTEND:20200427T200000Z
DTSTAMP:20260422T225658Z
UID:BerkeleyCombinatorics/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BerkeleyComb
 inatorics/3/">Combinatorics on the space of monotone paths of a polytope</
 a>\nby Jesus de Loera (UC Davis) as part of The UC Berkeley combinatorics 
 seminar\n\nLecture held in 939 Evans Hall.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerkeleyCombinatorics/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brendan Pawlowski (USC)
DTSTART:20200406T191000Z
DTEND:20200406T200000Z
DTSTAMP:20260422T225658Z
UID:BerkeleyCombinatorics/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BerkeleyComb
 inatorics/5/">The fraction of an Sn-orbit on a hyperplane</a>\nby Brendan 
 Pawlowski (USC) as part of The UC Berkeley combinatorics seminar\n\nLectur
 e held in 939 Evans Hall.\n\nAbstract\nHuang\, McKinnon\, and Satriano con
 jectured that if a real vector $(v_1\,...\,v_n)$ has distinct coordinates 
 and $n\\ge3$\, then a hyperplane through the origin other than $x_1+...+x_
 n=0$ contains at most $2(n−2)!\\lfloor n/2\\rfloor$ of the vectors obtai
 ned by permuting the coordinates of $v$. I will discuss a proof of this co
 njecture.\n
LOCATION:https://researchseminars.org/talk/BerkeleyCombinatorics/5/
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