**We kindly ask you to RSVP at the following link to get a headcount for food: https://forms.gle/DGkd4onizvu2Sby59 **

Overview

What: CHAT+

Who: All math faculty, staff, and graduate students

When: Tuesday November 30, 11:00AM-12:00PM + lunch provided after the discussion

Where: MATH 350

Why: Promoting the success of first-generation students in our classrooms

Moderators: Breeann Wilson and Jennifer Gensler

Event description

CHAT(+)s are discussion sessions for graduate students and faculty of the Department of Mathematics organized by the Diversity Committee. They are structured conversations about key issues, including discussions of issues relating to diversity, for graduate students (CHATs) and between graduate students and faculty (CHAT+s). The goal of the CHAT+ organized for November 30th is to address the challenges faced by first-generation students in higher education and discuss practices we can implement in our classrooms that promote the success of these students.

The discussion will be guided by the following short readings:

3) https://firstgen.naspa.org/files/dmfile/FactSheet-01.pdf (this is a graphic)

Faculty and students are asked to take a look at the above readings before the CHAT+. If you are unable to do the readings, however, please do not be deterred from participating. If you can only attend for part of the discussion, please join us when you are able to.

Here are some additional readings that may prove insightful:

If you have any questions, please reach out. We hope to see you there!

Breeann and Jennifer, on behalf of the Diversity Committee

Serving First-Generation Students in our Classrooms

Tue, Nov. 30 12pm (Zoom)

Grad Algebra Seminar

Michael Kompatscher (Charles University Prague)

X

Let $G$ be a permutation group on a $n$-element set. We then say that an algebra $A$ has a $G$-term $t({x}_{1},\dots ,{x}_{n})$, if $t$ is invariant under permuting its variables according to $G$, i.e. $A\vDash t({x}_{1},\dots ,{x}_{n})\approx t({x}_{\pi (1)},\dots ,{x}_{\pi (n)})$ for all $\pi \in G$. Since $G$-terms appear in the study of constraint satisfaction problems and elsewhere, it is natural to ask for their classification up to interpretability. In the first part of my talk I would like to share a few partial results on this problem.

In the second part I am going to discuss the complexity of deciding whether a given finite algebra has a $G$-term. The most commonly used strategy in showing that deciding a given Maltsev condition is in P, is to show that it suffices to check the condition locally (i.e. on subsets of bounded size). We show that this „local-global“ approach works for all $G$-terms induced by regular permutation groups $G$ (and direct products of them), but fails for some other „rich enough" permutation groups, such as $S\phantom{\rule{0}{0ex}}y\phantom{\rule{0}{0ex}}m(n)$ for $n\ge 3$.

This is joint work with Alexandr Kazda.

$G$-terms and the local-global property Sponsored by the Meyer Fund

Birkhoff and Mal'cev independently posed the problem: Describe all subquasivariety lattices. Nurakunov in 2009 showed that there are many unreasonable subquasivariety lattices where unreasonable means there is no algorithm to determine if a particular finite lattice is a sublattice. This sugests refinements of the original question are needed.

A subquasvariety lattice has a natural equaclosure operator. Adaricheva and Gorbunov in 1989 defined an equaclosure operator abstractly as having the properties that are known to hold in a natural equaclosure operator.

The soon-to-be-published book, A Primer of Quasivariety Lattices by Kira Adaricheva, Jennifer Hyndman, JB Nation, and Joy Nishida, refines the abstract definition of equaclosure operator and provides some answers to the refined question: When is a lattice with an equaclosure operator representable by a subquasivariety lattice and the natural equaclosure operator. This presentation explores some of this new approach.

A reader's guide to A Primer of Subquasivariety Lattices

In many settings, the Temperley-Lieb algebra is isomorphic to the endomorphism algebra on the tensor representation for $S\phantom{\rule{0}{0ex}}{L}_{2}$. In characteristic zero, the Jones-Wenzl projectors give descriptions at the morphisms level for tilting modules in characteristic zero. Their characteristic p versions provided by Burrull-Libedinsky-Sentinelli, describe the tilting category for $S\phantom{\rule{0}{0ex}}{L}_{2}$ and admit a quiver representation given by Tubbenhauer-Wedrich. Our project extends this result to the mixed case, i.e. a field with characteristic p containing all ?’th roots of unity, gives fusion rules for tensoring with the natural module regarding the objects as well as the morphisms. This is joint work with L. Sutton, D. Tubbenhauer, and P. Wedrich. (Zoom Meeting ID: 941 2691 8788, passcode: algebra)

The $S\phantom{\rule{0}{0ex}}{L}_{2}$ Tilting Category in Mixed Characteristic

Tue, Nov. 30 3pm (Zoom)

Topology

Katharine Adamyk (University of Western Ontarion)

X

One common application of topological methods to data analysis is the clustering of data sets. Many of the methods for clustering depend on the value of certain parameters, and as these parameters vary, they index what is known as a hierarchical clustering. Jardine introduced the notion of layer points as a condensed description of hierarchical clusterings in 2020, in the context of the 2-parameter clustering defined by path components of degree-Rips complexes. In this talk I will present recent work that develops the theory of multiparameter layer points more generally, as well as a specific application to the original context. A main theme will be stability—under what conditions do similar inputs for a clustering algorithm guarantee similar resulting clusterings? I will focus particularly on the stability problem with respect to subsampling a data set.