New Mexico State University

Monday, November 3

•  No Events

Tuesday, November 4

•  No Graduate Student Seminar

Wednesday, November 5

•  No Events

Thursday, November 6

•  Algebra Seminar

Linear Quotients of Powers of Edge Ideals

Mario Stinson-Maas, NMSU

1:30PM – 2:30PM

SH 235 and Zoom. Link: https://nmsu.zoom.us/j/89765494169

Abstract: We construct an explicit and straightforward linear quotient ordering for any power of an edge ideal which admits linear quotients. This expands on a well-known result of Herzog, Hibi, and Zheng on quadratic monomial ideals, in the case of edge ideals. As a consequence, we give explicit formulae for the projective dimension and Betti numbers of the edge ideal of whisker graphs. Additionally, we prove that the second and higher powers of the edge ideals of anticycles admit linear quotient orderings, although the edge ideals themselves do not, thus resolving an open question of Hoefel and Whieldon in the affirmative and providing the first class of gap-free graphs whose edge ideals satisfy this property on their powers.

•  No Probability Seminar for Graduate Students

Friday, November 7

•  Analysis Seminar

Twisted Crossed Products of Banach Algebras

Alonso Delfin, University of Colorado, Boulder

10:30AM – 11:30AM

SH 235 and Zoom. Link: https://nmsu.zoom.us/j/86991740746

Abstract: The main goal of this talk is to introduce twisted crossed products of Banach algebras by locally compact groups. Classical crossed products of Banach algebras have been extensively studied for different classes of representations, including contractive representations on L^p-spaces. In this talk, we will give a general formulation for Banach algebras associated with twisted dynamical systems. Recent developments in L^p-twisted crossed products have mostly focused on situations where either the algebra is the complex numbers or when the group is discrete (more generally for étale groupoids). We present a universal characterization of the twisted crossed product when the acting group is locally compact and the Banach algebra has a contractive approximate identity. As an application, we focus on the case when the representations are contractive ones acting on L^p spaces. We briefly discuss a reduced version for L^p-operator algebras. Time permitting, we will present a generalization of the so called Packer–Raeburn trick to the L^p-setting, by showing that the universal L^p twisted crossed product is "stably'' isometrically isomorphic to an untwisted one.

•  Colloquium

What is Lean and Why Should I Care About Formal Methods?

Tyler Billingsley, Rose-Hulman Institute of Technology

12:00PM refreshments | 12:30PM – 1:20PM

SH 107 and Zoom. Link: https://nmsu.zoom.us/j/82329432705

Abstract: Lean is a theorem prover (software that can verify correctness of proofs) that has been adopted by some mathematicians as a platform in which to build a library of mathematical theorems. Using the so-called mathlib library, one can formalize complicated mathematical statements, similar to how software libraries assist with developing complicated programs. With the advent of large language models, mathlib is pushing formal methods in mathematics to be more mainstream than ever before, leading to possible wild applications like "vibe-coding" proofs and autoformalization. In this talk, I will introduce the audience to Lean assuming no background in formal methods or dependent type theory, instead highlighting its possible future role in the lives of mathematics practitioners and students.

•  Geometry and Topology Seminar

$Sigma_3$-equivariant Tate Spectral Sequences and $c_3$-equivariant Stable Stems

Yueshi Hou, University of California San Diego

2:00PM – 3:00PM

SH 107 and Zoom. Link: https://nmsu.zoom.us/j/96482605257

Abstract: In the category of Σ3-equivariant spectra, taking the Tate construction with respect to proper family yields, via the generalized Segal conjecture, the 2-completion of the classical sphere spectrum. Greenlees–May introduced a filtration on this Tate construction, producing another spectral sequence alongside the classical Tate spectral sequence. In contrast to the convergence target, the E1-pages of these Tate-type spectral sequences encode information at the primes 2, 3, and other odd primes. By computing the C3-equivariant stable stems, we determine the E1-pages explicitly within a certain range, and, despite this limitation, fully describe all differentials.

This is joint work with Shangjie Zhang.

Saturday, October 25

•  Applied Math Seminar

Zohreh Keivan, NMSU

12:15PM – 1:15PM

Zoom ONLY. Link: https://nmsu.zoom.us/j/88174028894