Algebra Seminar

Ari Shnidman, Temple University

During the spring semester, we will run an "arXiv seminar",  with talks on papers from the last five years or so in any area of algebra/number theory. Papers will be exposited over 1-3 talks with the first talks devoted to the background material. This will be a short organizational meeting. We will go over some ground rules and then people can volunteer or request papers/topics. The organizers are happy to help choose a topic and prepare for the talk.

Violet Nguyen, Temple University

In this talk, we will walk through a new elementary proof of a theorem of William Chen concerning Markoff triples. After this short proof, we will discuss applications to Nielsen equivalences on $SL_{F_p}$ and to generalized Markoff-like surfaces.

Vasily Dolgushev, Temple University

The main motivation to explore the Grothendieck-Teichmueller group GT and its versions comes from the connection of GT to the absolute Galois group $G_{\mathbb{Q}}$ of rational numbers. In my talk, I will recall the definition of GT and say a few words about the Ihara embedding from $G_{\mathbb{Q}}$ to GT. I will talk about interesting versions of GT and formulate known
results about the versions of this group. Finally, I will say a few words about open questions related to GT.

Sean O'Donnell, Temple University

The goal of this talk is to give a description of the action of the absolute Galois group of the rational numbers on the set of child's drawings. We give several definitions of child's drawings, discuss why they are categorically equivalent, and give examples to illustrate the action of the Galois group on each.

Vasily Dolgushev, Temple University

Sage (or SageMath) is free, open-source math software that supports research and teaching in algebra, geometry, number theory, cryptography and numerical computation. Although the syntax of Sage is similar to that of Python, it runs much faster than Python with its libraries (e.g. SymPy). During this Zoom session, I will show examples of using Sage in algebra and number theory. (I plan to hit the record button in the beginning of the session.) Here is the Zoom link for our session: 
https://temple.zoom.us/j/95281041454

Holly Miller, Temple University

In this third talk on the GT group, we introduce GT-shadows. After a reminder on profinite completions of groups, we recall the definition of the gentle version of the GT group as a subgroup of automorphisms of the profinite completion of the free group on two generators. It is natural to ask if the gentle GT group is itself profinite, and GT-shadows are discussed through the perspective that comes with this question. Along the way, a few open questions in the area will be mentioned.