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DESCRIPTION: About 5 years ago\, the Heron-Rota-Welsh conjecture (log-conca
 vity of the coefficients of the characteristic polynomial of a matroid) was
  proven by Adiprasito\, Huh\, and Katz via the exciting development of a ne
 w combinatorial Hodge theory for matroids. In very recent work with Petter 
 Brändén\, we have given a new short "polynomial proof" of the Heron-Rota-We
 lsh conjecture. Our proof uses an extension of the theory of Lorentzian pol
 ynomials to convex cones. In this talk\, I will briefly discuss the basics 
 of Lorentzian (aka completely log-concave) polynomials\, and then I will gi
 ve an overview of our new proof of the Heron-Rota-Welsh conjecture. 
DTSTAMP:20211117T132000
DTSTART:20211122T160000
CLASS:PUBLIC
LOCATION:Technische Universität Berlin\n Institut für Mathematik\n Straße d
 es 17. Juni 136\n 10623 Berlin\n Room MA 041 (Ground Floor)
SEQUENCE:0
SUMMARY:Jonathan Leake (Technische Universität Berlin): Lorentzian polynomi
 als on cones and the Heron-Rota-Welsh conjecture
UID:107919503@/www.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/en/facetsofcomplexity/monday/20211122-C-Lea
 ke.html
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