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SUMMARY:Lorenzo Venturello (KTH Stockholm)
DTSTART:20220331T141500Z
DTEND:20220331T160000Z
DTSTAMP:20260422T065841Z
UID:CJCS/59
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CJCS/59/">Go
 renstein algebras from simplicial complexes</a>\nby Lorenzo Venturello (KT
 H Stockholm) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAb
 stract\nGorenstein algebras form an intriguing class of objects which ofte
 n show up in combinatorics and geometry. In this talk I will present a con
 struction which associates to every pure simplicial complex a standard gra
 ded Gorenstein algebra. We describe a presentation of this algebra as a po
 lynomial ring modulo an ideal generated by monomials and pure binomials. W
 hen the simplicial complex is flag\, i.e.\, it is the clique complex of it
 s graph\, our main results establish equivalences between well studied pro
 perties of the complex (being S_2\, Cohen-Macaulay\, Shellable) with those
  of the algebra (being quadratic\, Koszul\, having a quadratic GB). Finall
 y\, we study the h-vector of the Gorenstein algebras in our construction a
 nd answer a question of Peeva and Stillman by showing that it is very ofte
 n not gamma-positive. This is joint work with Alessio D'Alì.\n
LOCATION:https://researchseminars.org/talk/CJCS/59/
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