# Seminar by Dr. Prangama Sarkar

Speaker: Dr. Prangama Sarkar.

Title: Mixed multiplicities, Minkowski inequalities and Rees' theorem for
filtrations.

Date: 12th March, 2019 (Tuesday);
Time: 12 Noon.
Venue: Committee Room, Department of Mathematics.

Abstract: We define mixed multiplicities of (not necessarily Noetherian) filtrations of \$\mathfrak m\$-primary ideals in a Noetherian local ring \$(R,\mathfrak m)\$, generalizing the classical theory for \$\mathfrak m\$-primary ideals. We construct a real polynomial whose coefficients give the mixed multiplicities. Many of the classical theorems for mixed multiplicities of \$\mathfrak m\$-primary ideals hold for filtrations (not necessarily Noetherian). In this talk we mainly focus on the famous Minkowski inequalities of Teissier and Rees' Theorem on multiplicity.