OSU Mathematics Seminars and Colloquia
Calendar
Wed, Apr 20, 2022
Combinatorial and Commutative Algebra Seminar
4:30 PM
MSCS 114
Multiplicities and Volumes: An interplay among Algebra, Combinatorics, and Geometry
Jonathan MontaƱo, New Mexico State University
https://zoom.us/j/95233859929?pwd=UGdpSE9EUmlFaVJHc0pJb09TVllLdz09
[Abstract] [PDF]
Abstract: The notion of multiplicity in algebra traces back to the work of Samuel in 1951 in connections with intersection theory of algebraic varieties. Multiplicities are closely related to the theory of convex bodies, and this relation is an active research topic lying in the interaction of Commutative Algebra, Combinatorics, and Algebraic Geometry. In this talk we will discuss some of the history of this topic and its applications. We also report on recent results in joint work with Federico Castillo, Yairon Cid-Ruiz, Binglin Li, Fatemeh Mohammadi, and Naizhen Zhang. In one of these results, we show that mixed volumes of arbitrary convex bodies can be interpreted algebraically as mixed multiplicities of graded families of monomial ideals. In another result, we present a complete characterization of the positivity of multidegrees of multiprojective algebraic varieties and establish a combinatorial description using convex geometry. We also use our methods to prove that double Schubert polynomials have Saturated Newton Polytopes, which settles a conjecture by Monical, Tokcan and Yong.
Automatically add seminars to your own calendar (e.g., Google Calendar) via an ical link.

List of links (urls) directly to a seminar series.

Return to Math Department Login Page

To add/edit talks, please log in on the department web page, then return to Announce.
Alternatively if you know the Announce username/password, click the link below:

Announce Seminar Calendar Login