Spring 2023
Feb 16 -- Katie Ragosta
Title: A Largest Acylindrical Action for Finite Type Artin Groups
Abstract: TBA
March 9 -- Tudor Popescu
Title: Additive Combinatorics via Sidon Sets
Abstract: I will give a brief overview of Additive Combinatorics and present a 2021 result of Balogh - Furedi - Roy on Sidon sets, improving the best bound on a conjecture by Erdos. The talk will be accessible to all graduate students (and Cauchy-Schwarz enjoyers).
March 16 -- Ray Maresca
Title: The Gabriel-Roiter Measure
Abstract: Of the two main methods to study representations of quivers (modules over algebras), the more well-known is Auslander-Reiten theory. The other method is called Gabriel-Roiter theory and has been useful in proving some conjectures in the theory. In this entirely expository talk, we will introduce GR theory and learn how it is useful in studying modules over algebras.
March 23 -- Dezhou Li (Northeastern University)
Title: Understanding the cohomology of unordered configuration space of R^n using spectral sequence.
Abstract: Fred Cohen in 1976 used Cartan-Leray spectral sequence to compute the cohomology of unordered configuration space of p points of R^n over a finite field F_p. Based on the idea provided by him, I hope that this can be generalized to arbitrary many points. In this talk, I will mention some strategies to approach the question and the work that has been done so far.
March 30 -- Rachmiel Klein
Title: Wallpaper patterns and their orbifolds
Abstract: Do you like beautiful designs with lots of symmetries? In this expository talk, I will be discussing symmetries of planar tessellations. There are exactly 17 symmetry types of planar tessellations (known as "the 17 wallpaper groups"), and this number seems to magically appear out of nowhere. I will present the general idea of “The Magic Theorem” which implies this fact. I will also explain what to call each of these 17 groups in what is known as "orbifold notation" and use that notation to visualize the geometry of each wallpaper group's orbifold. This is the topic for my DRP. Although not particularly challenging, it leads to some really beautiful visualizations of folding up everyday objects. There will be a lot of pictures along the way! My reference for this material is primarily from the book "The Symmetries of Things" by Conway, Burgiel, and Goodman-Strauss.
April 20 -- Jill Mastrocola
Title: Intersections of Parabolic Subgroups of Artin Groups
Abstract: Artin groups form a large and interesting class of groups. While there are many results about subfamilies of Artin groups, very little is known about Artin groups in general. One particularly useful tool for studying Artin groups is the behavior of their so-called parabolic subgroups. In this talk, I will give a general introduction to Artin groups and introduce the problem of intersections of parabolic subgroups.
April 27 -- Gus Schmidt
Title: Extending Riemann Roch via Spreading Out
Abstract: In general, the principle of “spreading out” is that for schemes of finite presentation, whatever happens over the generic point also happens over some open neighborhood of the generic point. We can use this principle to extend the Riemann-Roch theorem over global fields to other settings.