This Week at ICERM
February 21, 2021
There are no events currently scheduled for February 21st.
February 22, 2021
11:00 - 12:00 pm ESTGrad Student/ PostDoc Professional Development: Ethics 1Professional Development - Virtual
February 23, 2021
There are no events currently scheduled for February 23rd.
February 24, 2021
3:30 - 4:30 pm ESTLog-Concavity of Littlewood-Richardson CoefficientsVirtual
- Avery St. Dizier, Univeristy of Illinois at Urbana-Champaign
We describe a log-concavity property of the Littlewood--Richardson numbers and explain its connection to the theory of Lorentzian polynomials.
February 25, 2021
10:00 - 11:00 am ESTLearning Seminar - Differential forms on tropical moduli spacesSeminar - Virtual
- Melody Chan, Brown University
- Sam Payne, University of Texas at Austin
The goal is to understand Francis Brown's recent arXiv preprint Invariant differential forms on complexes of graphs and Feynman integrals. A sub-goal, which we hope takes shape over the course of the seminar, is to draw out the connection between Brown's article and tropical moduli spaces of curves and abelian varieties.
This is not an introductory seminar per se in that the choice of topic is of specialized interest and of particular interest to us vis-a-vis our current work. On the other hand, we will try to develop the machinery without relying on background from tropical geometry, much as Brown's article is able to do.
Resources to get started:
1. Sam's lectures from the introductory Workshop, available from the webpage
2. Draft of a survey articleon classical/tropical moduli spaces by Melody, which outlines the appearance of graph complexes in the study of tropical moduli.
11:00 - 12:00 pm ESTSemistable Reduction SeminarSeminar - Virtual
- Dan Abramovich, Brown University
February 26, 2021
10:00 - 10:30 am ESTGraduate Student/ PostDoc pre-seminar break in GatherCoffee Break - Virtual
10:30 - 11:30 am ESTCM-regularityPost Doc/Graduate Student Seminar - Virtual
- Matthew Larson, Stanford University
- Mahrud Sayrafi, University of Minnesota
The geometry of Castelnuovo-Mumford regularity - Matt Larson, Stanford University
Castelnuovo-Mumford regularity is a tool for proving effective versions of Serre vanishing. I will explain why this is frequently necessary throughout algebraic geometry. I will also define Castelnuovo-Mumford regularity, state its basic properties, and explain its relationship to syzygies of graded module.
Computing the Multigraded Castelnuovo-Mumford Regularity - Mahrud Sayrafi, University of Minnesota
Motivated by toric geometry, Maclagan-Smith defined the multigraded Castelnuovo- Mumford regularity. While this definition reduces to the usual regularity for saturated modules in P^n, some properties of the classical regularity are not yet proven to be true in the multigraded case, while others hold true with subtle differences that illuminate the differences in geometry. In this talk I will focus on the case of a product of projective spaces and describe an algorithm for computing the multigraded regularity for saturated modules implemented in Macaulay2.
11:30 - 12:00 pm ESTGraduate Student/ PostDoc post-seminar break in GatherCoffee Break - Virtual
February 27, 2021
There are no events currently scheduled for February 27th.
Connect with ICERM
July 13, 2020 - ICERM received the largest National Science Foundation grant in Brown University's history. The $23.7M grant will support the institute's continuing mission to broaden the relationship between mathematics and computation for the next five years and enable the expansion of cutting-edge programming. Read more
June 9, 2020 - ICERM joins Brown University in its message about confronting racial injustice.