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DTSTAMP:20260407T051541Z
UID:648ae9a96382d659660509@ist.ac.at
DTSTART:20240508T140000
DTEND:20240508T160000
DESCRIPTION:Speaker: Leonid Monin\nhosted by Tamas Hausel\nAbstract: A clas
 sical construction associates a Poincar duality algebra to a homogeneous p
 olynomial on a vector space. This construction was used to give a presenta
 tion for cohomology rings of complete smooth toric varieties by Khovanskii
  and Pukhlikov and of some spherical varieties (including full flag variet
 ies) by Kaveh. More recently\, motivated by this construction\, Brndn and 
 Huh defined Lorenzian polynomials.In my talk\, I will recall the above res
 ults and will give two recent generalizations of the construction of duali
 ty algebras. The first one replaces the homogeneous polynomial by weighted
  homogeneous polynomial (and more general functions). In contrast to the c
 lassical construction\, this allows us to construct Poincar duality algebr
 as which are not necessarily generated in degree 1. The second extension i
 s the discrete analogue of the classical construction\, which associates a
 n algebra with Gorenstein duality to a polynomial on a lattice (free abeli
 an group). As a corollary\, this provides a presentation of K-ring of smoo
 th complete toric varieties as well as full flag varieties.
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
 )\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Leonid Monin: Discrete and continues duality algebras
URL:https://talks-calendar.ista.ac.at/events/4945
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