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DESCRIPTION: 14:15-14:35 Uhr Lehrprobe zum Thema  The Theorem of Carathéodo
 ry  (auf Englisch)   ca. 14:45-15:25 Uhr Fachvortrag:   Constructing Koszul
  Gorenstein algebras from Cohen-Macaulay simplicial complexes   My main are
 a of interest is combinatorial commutative algebra\, a topic that sits at t
 he crossroads between algebra\, combinatorics and topology. The main aim of
  this talk is to discuss a joint project with Lorenzo Venturello (KTH Stock
 holm) relating Koszul Gorenstein algebras and Cohen-Macaulay simplicial com
 plexes.  Koszul algebras are quadratic algebras satisfying desirable homolo
 gical properties and arising naturally in many geometric and combinatorial 
 contexts: for instance\, the coordinate rings of Veronese\, Segre and Grass
 mannian varieties (in their natural embeddings) are all Koszul\, and so is 
 the Stanley-Reisner ring of any flag simplicial complex. However\, the Kosz
 ul property is hard to control and to check in general\, and many conjectur
 es about the general behaviour of Koszul algebras are currently open. Start
 ing from a flag pure simplicial complex Δ\, we propose a construction of a 
 (non-monomial) Gorenstein ring R_Δ which is Koszul if and only if Δ is Cohe
 n-Macaulay\, thus providing a bridge between these two worlds. On a more co
 mbinatorial level\, the very same correspondence also yields that R_Δ has a
  Gröbner basis of quadrics if and only if Δ is shellable. As an application
 \, we provide counterexamples to an algebraic generalization of a conjectur
 e by Charney and Davis about flag homology spheres. 
DTEND:20210824T153500
DTSTAMP:20210820T101900
DTSTART:20210824T141500
CLASS:PUBLIC
LOCATION:Die Veranstaltung wird virtuell via Webex-Meetings stattfinden. \n
  https://fu-berlin.webex.com/fu-berlin/j.php?MTID=m5497d01eaea770dee34bfc7e
 2751dddb\n Meeting-Kennnummer (Zugriffscode): 188 591 7254\n Meeting Passwo
 rt: Villa\n 
SEQUENCE:0
SUMMARY:Alessio D’Alì (Osnabrück): Constructing Koszul Gorenstein algebras
  from Cohen-Macaulay simplicial complexes
UID:118446535@/www.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/math/dates/colloquium/2021/2021-08-24-1415-
 DAli.html
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