Speaker:* Vijaylaxmi Trivedi, TIFR, Mumbai, India*.
Date/Time: *5 February 2021, 5:30pm IST/ 12:00pm GMT/ 7:00am EST* (joining
time: 5:15 pm IST - 5:30 pm IST).
Google meet link:
https://meet.google.com/vnc-vhqp-axj.
Title: *Hilbert-Kunz density function and its applications*.
Abstract: In this talk, we recall the notion of Hilbert-Kunz density
function for graded rings. This function was introduced to understand the
Hilbert-Kunz multiplicity which is a difficult characteristic $p$
invariant
to compute and to make speculation about its properties. It turns out the
HK density function is also related to another characteristic
$p$-invariant
namely $F$-threshold. Here we describe its properties and give its
applications to HK multiplicity, $F$-thershold and to a conjecture of
Watanabe-Yoshida. The talk is partly based on a joint work with K.I.
Watanabe.
For more information and links to previous seminars, visit the website of
VCAS:
https://sites.google.com/view/virtual-comm-algebra-seminar.