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# Algebra

## Fall 2022

Seminars are held in 358 Parker Hall on Tuesdays at 2:30pm.

**DMS Algebra Seminar**

Mar 23, 2023 02:30 PM

358 Parker Hall

**PLEASE NOTE SEMINAR IS ON THURSDAY**

**Fred Holweck**, Université de Technologie de Belfort-Montbéliard

**DMS Algebra Seminar**

Mar 21, 2023 02:30 PM

Speaker: **Edinah Gnang**, Johns Hopkins University

Title: Bounds on the Chow-rank of hypermatrices via Partial Differential Encoding of Boolean functions

Abstract: We introduce partial differential encodings of Boolean functions and their relaxations. These encodings enable us to determine the fraction of optimal encodings of some important Boolean functions. Our main result is a general method for deriving upper and lower bounds on the Chow-Rank of hypermatrices which underlie polynomial transformed by some group or semi-group actions. Our method is a discrete analog of representation theory methods which devise bounds on the border rank via Lie group actions.

The talk is based on joint work with Rongyu Xu.

**DMS Algebra Seminar**

Feb 21, 2023 02:30 PM

358 Parker Hall

Speaker: **Prashanth Sridhar,** Auburn,

Title: Periodicity of Fitting Ideals in Free Resolutions

Abstract: We examine the periodicity of ideals of minors in minimal free resolutions of finitely generated modules over local rings with a focus on their asymptotic behavior. The heuristics rely on the general principle that the initial part of the resolution is influenced by the module’s relations, while the singularities of the ring have a telling effect on the asymptotic behavior. For example, we show that for any finite module over a local complete intersection, the Fitting ideals of any size in its minimal free resolution are eventually 2-periodic (although the resolution is not). Moreover, if the stable value of a given size of minors is non-zero, it contains some power of the Jacobian ideal. Results of this type hold true in other settings as well (ex: Golod rings or residue field over any local ring), but do not hold in general.

This is joint work with Michael K. Brown and Hailong Dao.

**DMS Algebra Seminar**

Feb 14, 2023 02:30 PM

358 Parker Hall

**Luke Oeding**(Auburn)

**DMS Algebra Seminar**

Feb 07, 2023 02:30 PM

ZOOM

Speaker: **Qingyuan Jiang** (University of Edinburgh)

Title: Derived Grassmannians, derived Schur functors, and their applications.

Abstract: In this talk, we will revisit Grothendieck's theory of Grassmannians and flag schemes and the theory of Schur and Weyl module functors studied in $GL_n$-representation theory from the perspective of derived algebraic geometry (DAG). We will explain how to use the DAG framework to extend these theories from modules to complexes, and the numerous theoretical benefits of doing so. Next, we will show how these two new theories are connected by a derived generalization of the Borel--Bott--Weil theorem. Finally, we will discuss how this framework broadens the application range of classical theories and sheds new light on many classical problems, including the study of derived categories of singular schemes, and of Hilbert schemes and compactified Jacobians of integral curves, as well as their applications to a variety of recent research topics including Hecke correspondences for surfaces and two-dimensional categories. The talk will be based on papers arXiv:2202.11636 and arXiv:2212.10488.

**DMS Algebra Seminar Pretalk**

Feb 02, 2023 09:00 AM

ZOOM

Speaker: **Hang Huang**

Title: Derived Grassmannians, derived Schur functors, and their applications Abstract: In this talk, we will revisit Grothendieck's theory of Grassmannians and flag schemes and the theory of Schur and Weyl module functors studied in $GL_n$-representation theory from the perspective of derived algebraic geometry (DAG). We will explain how to use the DAG framework to extend these theories from modules to complexes, and the numerous theoretical benefits of doing so. Next, we will show how these two new theories are connected by a derived generalization of the Borel--Bott--Weil theorem. Finally, we will discuss how this framework broadens the application range of classical theories and sheds new light on many classical problems, including the study of derived categories of singular schemes, and of Hilbert schemes and compactified Jacobians of integral curves, as well as their applications to a variety of recent research topics including Hecke correspondences for surfaces and two-dimensional categories. The talk will be based on papers arXiv:2202.11636 and arXiv:2212.10488.

**DMS Algebra Seminar**

Jan 31, 2023 02:30 PM

358 Parker Hall

Speaker: **Doug Leonard** (Auburn University)

**DMS Algebra Seminar**

Jan 24, 2023 02:30 PM

358 Parker Hall

Speaker: **Matthew Speck**, Auburn University

**DMS Algebra Seminar**

Jan 17, 2023 02:30 PM

358 Parker Hall

Speaker: **Michael Brown**

**DMS Algebra Seminar**

Nov 29, 2022 02:30 PM

ZOOM

Speaker: **Mark Walker** (University of Nebraska)

Last Updated: 09/20/2022