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SUMMARY:Mandira Mondal (Chennai Mathematical Institute)
DTSTART:20200904T120000Z
DTEND:20200904T130000Z
DTSTAMP:20260423T021105Z
UID:VCAS/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/18/">De
 nsity functions for the coefficients of the Hilbert-Kunz function of polyt
 opal monoid algebra</a>\nby Mandira Mondal (Chennai Mathematical Institute
 ) as part of IIT Bombay Virtual Commutative Algebra Seminar\n\n\nAbstract\
 nWe shall discuss Hilbert-Kunz density function of a\nNoetherian standard 
 graded ring over a perfect field of characteristic $p>0$.  We will \nalso 
 talk about the second coeffcient of the Hilbert-Kunz function and the poss
 ibility of existence\nof a $\\beta$-density function for this coefficient.
 \n\nWatanabe and Eto have shown that Hilbert-Kunz multiplicity  of affine 
 monoid rings with respect to a monomial ideal of finite colength can be ex
 pressed as relative\nvolume of certain nice set arising from the convex ge
 ometry associated to the ring. In this talk\, we shall discuss similar exp
 ression for the density functions of polytopal monoid algebra with respect
  to the homogeneous maximal ideal in terms of the associated convex geomet
 ric structure. This is a joint work with Prof. V. Trivedi. We shall also d
 iscuss the existence of $\\beta$-density function for monomial prime ideal
 s of hight one of these rings in this context.\n
LOCATION:https://researchseminars.org/talk/VCAS/18/
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