Date and Time: Friday 4th September 2020, 5:30 pm IST - 6:30 pm IST
(joining time : 5:15 pm IST - 5:30 pm IST)
Google Meet link:
https://meet.google.com/yqu-mvvy-jrs
Speaker: Mandira Mondal, Chennai Mathematical Institute.
Title: Density functions for the coefficients of the Hilbert-Kunz function
of polytopal monoid algebra
Abstract: We shall discuss Hilbert-Kunz density function of a Noetherian
standard graded ring over a perfect field of characteristic $p \geq 0$. We
will also talk about the second coefficient of the Hilbert-Kunz function
and the possibility of existence of a $\beta$-density function for this
coefficient.
Watanabe and Eto have shown that Hilbert-Kunz multiplicity of affine
monoid rings with respect to a monomial ideal of finite colength can be
expressed as relative volume of certain nice set arising from the convex
geometry associated to the ring. In this talk, we shall discuss similar
expression for the density functions of polytopal monoid algebra with
respect to the homogeneous maximal ideal in terms of the associated convex
geometric structure. This is a joint work with Prof. V. Trivedi. We shall
also discuss the existence of $\beta$-density function for monomial prime
ideals of height one of these rings in this context.