Tulane Home Tulane Shield logo linking to site home page

Research Seminars: Algebra and Combinatorics

Fall 2021

Time & Location: All talks are on Wednesday in Zoom Meeting at 3:00 PM unless otherwise noted.
Organizer: Kalina Mincheva

Archives

 

September 22

Title: Group Algebras of Compact Groups and Enveloping Algebras of Profinite-Dimensional Lie Algebras

Karl H. Hofmann | Tulane University

Abstract: 

October 6

Title: Modular forms and divisibility properties of partition numbers

Olivia Beckwith | Tulane University

Abstract: My research focuses on elliptic modular forms and their connections to different areas of number theory. Two of my favorite areas are the study of integer partitions and quadratic number fields. For Part 1 of this series, I will start with a brief crash course defining modular forms. Then I will describe some of my work studying the divisibility properties of numbers which count integer partitions. This includes joint work with Scott Ahlgren and Martin Raum, and may briefly mention ongoing work with Jack Chen, Maddie Diluia, Oscar Gonzales, and Jamie Su.

Location: GI-310

Time: 3:00

 

October 13

Title: Real analytic modular forms and quadratic number fields

Olivia Beckwith | Tulane University

Abstract: For Part 2 of my introduction to my research, I will focus on my other favorite area: quadratic number fields. First I will define a class of real-analytic modular forms. Then I will show how they can be used in the study of class numbers of imaginary quadratic number fields, as well as Hecke series for real quadratic number fields. This includes joint ongoing work with Gene Kopp.

Location: GI-310

Time: 3:00

 

October 20

Title: Toric ideals from statistics

Daniel Bernstein | Tulane University

Abstract: Toric ideals are prime polynomial ideals that are generated by monomial differences. They have a rich theory with connections to polyhedral combinatorics, optimization, and statistics, which I will discuss in this talk.

Location: GI-310

Time: 3:00

 

October 27

Title: Algebraic matroids in rigidity theory and matrix completion

Daniel Bernstein | Tulane University

Abstract: A set of quantities is algebraically independent over a field F if they satisfy no polynomial equations with coefficients in F. Matroids are a combinatorial generalization of (algebraic) independence. In this talk, I will give an introduction to matroids from an algebraic perspective, and explain how they arise in rigidity theory and matrix completion. Time permitting, I will intr

Location: GI-310

Time: 3:00

 

November 3

Title: Saturation bounds for smooth varieties.

Tài Huy Hà | Tulane University

Abstract: Let X be a smooth variety which is ideal-theoretically defined by an ideal J. We discuss linear bounds for the saturation degrees of powers of J in terms of its generating degrees. Our work extends a classical result of Macaulay, and fills the gap between studies on algebraic and geometric notions of the Castelnuovo-Mumford regularities of smooth varieties. This is a joint work with L. Ein and R. Lazarsfeld.

Location: GI-310

Time: 3:00