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# Algebra

## Spring 2021

Seminars will be held in Parker 236 on Tuesdays from 3:00 to 3:50. We will also live-stream the seminar on Zoom via the following link:

**https://auburn.zoom.us/j/83583246175**.

**DMS Algebra Seminar**

Sep 21, 2021 03:00 PM

250 Parker Hall

Speaker: **Frédéric Holweck** (Université de Technologie de Belfort-Montbéliard/Laboratoire Interdisciplinaire Carnot de Bourgogne)

Title: Graph states and the variety of principal minor

Abstract: In quantum information graph states are quantum states that can be encoded by a graph. They are used in many applications in quantum information like error correcting codes, measured based quantum computation, etc. The variety of binary symmetric principal minors is a well-known object in algebraic geometry with application to matrix theory, probability, and computer vision. I'll present in this talk some recent work with Vincenzo Galgano where we established a bijection between the orbits of graph states under Local Clifford operations and the natural orbits of the variety of binary symmetric principal minors.

**DMS Algebra Seminar**

Sep 28, 2021 03:00 PM

250 Parker Hall

Speaker: **Justin Chen** (Georgia Tech University)

**DMS Algebra Seminar**

Sep 14, 2021 03:00 PM

250 Parker Hall

Speaker: **Frank Moore** (Wake Forest University)

Title: Color DG Algebra Techniques over Skew-Commutative Rings

Abstract: Differential graded (DG) algebra techniques in commutative algebra were introduced by Cartan, Eilenberg, and MacLane to compute the homology of Eilenberg-MacLane spaces. Since then, they have been used to great effect by Avramov, Gulliksen, Quillen, Roos, and many others to provide algebraic characterizations of rings with extremal homological behavior. We show that much of the foundations of this theory may be extended to quotients of skew-polynomial rings by normal elements, provided one works with so-called color DG algebras. We will discuss features of several joint works, coauthored with Luigi Ferraro, Desiree Martin, and Josh Pollitz.

**DMS Algebra Seminar**

Sep 07, 2021 03:00 PM

250 Parker Hall

Speaker: **Luke Oeding**

Title: Restrictions of Projective Duals (Part 2)

Abstract: The determinant of a matrix factors when one restricts to even-sized skew-symmetric matrices, but remains irreducible for symmetric matrices. Why is this? I’ll explain this in the context of projective duality and its restriction. I’ll focus on several examples that served as inspiration for recent work with F. Holweck.

**DMS Algebra Seminar**

Aug 31, 2021 03:00 PM

250 Parker Hall

Speaker: **Luke Oeding**

Title: Restrictions of Projective Duals

Abstract: The determinant of a matrix factors when one restricts to even-sized skew-symmetric matrices, but remains irreducible for symmetric matrices. Why is this? I’ll explain this in the context of projective duality and its restriction. I’ll focus on several examples that served as inspiration for recent work with F. Holweck.

**DMS Algebra Seminar**

Aug 24, 2021 03:00 PM

250 Parker Hall

Speaker: **Michael Brown**

Title: Bounds on the shape of multigraded minimal free resolutions via exterior algebra methods

Abstract: It is a well-known result of Eisenbud-Goto that a sufficiently high degree truncation of a module over a standard graded polynomial ring has a linear free resolution. In this talk, we discuss an analogous result over polynomial rings with non-standard gradings. Modules over such rings are of interest in algebraic geometry, as they determine sheaves on toric varieties. The proof involves noncommutative techniques, namely a toric generalization of Eisenbud-Fløystad-Schreyer's theory of Tate resolutions over exterior algebras. This is joint work with Daniel Erman.

**DMS Nonlinear Algebra Seminar**

Jun 29, 2021 01:30 PM

Parker Hall 228

Topic:

*Invitation to Nonlinear Algebra*by Michalek and Sturmfels

**DMS Nonlinear Algebra Seminar**

Jun 22, 2021 01:30 PM

Parker Hall 228

Topic:

*Invitation to Nonlinear Algebra*by Michalek and Sturmfels

**DMS Nonlinear Algebra Seminar**

Jun 15, 2021 01:30 PM

Parker Hall 228

Topic:

*Invitation to Nonlinear Algebra*by Michalek and Sturmfels

**DMS Nonlinear Algebra Seminar**

Jun 08, 2021 01:30 PM

Parker Hall 228

Topic:

*Invitation to Nonlinear Algebra*by Michalek and Sturmfels

**DMS Algebra Seminar**

Apr 06, 2021 03:00 PM

Parker Hall 256 and ZOOM https://auburn.zoom.us/j/83583246175

Speaker: **Matthew Speck**

Title: Normal Tensors

Abstract: Normal matrices are an important tool in matrix analysis thanks to the role they play in the Spectral Decomposition Theorem. By contrast, normal operators in higher order tensor algebras receive much less attention. Motivated by the Marcus-de Oliveira determinantal conjecture, we will exposit on the Battacharya-Mesner tensor algebra with an eye towards generalized normality.

ZOOM: https://auburn.zoom.us/j/83583246175

**DMS Algebra Seminar**

Mar 16, 2021 03:00 PM

Parker Hall 236 and ZOOM https://auburn.zoom.us/j/83583246175

Speaker: **Bill Trok** (Auburn)

https://auburn.zoom.us/j/83583246175

Last Updated: 01/15/2021