Fri, February 5, 2021
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5:00pm [5:30pm] Vijaylaxmi Trivedi, TIFR, Mumbai, India
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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.
6:00pm