~~META:title=Algebra Seminar~~ [[http://www-history.mcs.st-and.ac.uk/Biographies/Galois.html|{{http://www.win.tue.nl/~aeb/at/mathematicians/galois1.jpg?110*135 |Evariste Galois}}]] [[ http://www-history.mcs.st-and.ac.uk/Mathematicians/Noether_Emmy.html|{{ http://seminars.math.binghamton.edu/AlgebraSem/emmy_noether.jpg?110*135|Emmy Noether}}]] \\ \\ **#####The Algebra Seminar#####** **The seminar will meet in-person on Tuesdays in room WH-100E at 2:50 p.m. There should be refreshments served at 4:00 in room WH-102. Masks are optional.** **Anyone wishing to give a talk in the Algebra Seminar this semester is requested to contact the organizers at least one week ahead of time, to provide a title and abstract. If a speaker prefers to give a zoom talk, the organizers will need to be notified at least one week ahead of time, and a link will be posted on this page.** If needed, the following link would be used for a zoom meeting (Meeting ID: 93487611842) of the Algebra Seminar: [[https://binghamton.zoom.us/j/93487611842 | Algebra Seminar Zoom Meeting Link]] Organizers: [[:people:alex:start|Alex Feingold]], [[:people:daniel:start|Daniel Studenmund]] and [[:people:tongviet:start|Hung Tong-Viet]] To receive announcements of seminar talks by email, please email one of the organizers with your name, email address and reason for joining this list if you are external to Binghamton University. ---- =====Spring 2025===== * **January 21**\\ Organizational Meeting \\ \\ Please think about giving a talk in the Algebra Seminar, or inviting an outside speaker. * **January 28**\\ Daniel Studenmund (Binghamton University) \\ **//Piecewise isometry groups arising from Weyl groups//** \\ \\ **//Abstract//**: Here’s a fun way to build a group by cutting and pasting: Start with a Euclidean, spherical, or hyperbolic model geometry $X$ carrying a collection $\mathcal{H}$ of totally geodesic codimension-1 submanifolds determining a regular tessellation $\Delta$ of $X$. A piecewise isometry of $\Delta$ is defined by cutting out finitely many subspaces $S_1,\dotsc, S_k \in \mathcal{H}$ and isometrically mapping the components of what remains to the components obtained by cutting out another finite collection of subspaces $T_1,\dotsc, T_k \in \mathcal{H}$. The collection of all piecewise isometries is a group $PI(\Delta)$. When $\Delta$ is a tessellation of $\mathbb{R}$ by isometric line segments, $PI(\Delta)$ is an extension of Houghton’s group $H_2$. When $\Delta$ is a tessellation of the hyperbolic plane by ideal triangles, $PI(\Delta)$ naturally extends Thompson’s group $V$. Bieri and Sach studied $PI(\mathbb{Z}^n)$, where $\mathbb{Z}^n$ is the standard tessellation of Euclidean space by isometric cubes, obtaining lower bounds on their finiteness lengths and presenting a careful analysis of their normal subgroup structure. Our story will start with the piecewise isometry group of the tessellation of the Euclidean plane by equilateral triangles, and generalize to piecewise isometry groups of Euclidean tessellations associated with affine Weyl groups of type $A_n$. Pictures will be drawn and preliminary results on algebraic structure and finiteness properties will be discussed. Time permitting, we will connect our discussion to the tessellation of hyperbolic 3-space by regular ideal tetrahedra. This talk covers work in progress with Robert Bieri and Alex Feingold. * **February 4**\\ Dikran Karagueuzian (Binghamton University) \\ **//You Need a Yoneda//** \\ \\ **//Abstract//**: The Yoneda Lemma is widely regarded as the most-commonly-quoted result of category theory. This (expository) talk will discuss instances of the lemma appearing in the undergraduate mathematics curriculum, particularly linear algebra. * **February 11**\\ Hung Tong-Viet (Binghamton University) \\ **//Orders of commutators in finite groups//** \\ \\ **//Abstract//**: In this talk, I will discuss some problems concerning the orders of some commutators in finite groups and how they affect the structure of the group. * **February 18**\\ No Speaker, No Meeting \\ * **February 25**\\ No Speaker, No Meeting \\ * **March 4**\\ Thu Quan (Binghamton University) \\ **//Squaring a conjugacy class in a finite group//** \\ \\ **//Abstract//**: Let $G$ be a finite group and $K$ be a conjugacy class of $G$. Then $K^2$ consists of the products of any two elements in $K$. In this talk, we consider some equivalent conditions for $K^2$ to be a conjugacy class of $G$. This talk is based on the paper by Guralnick and Navarro in 2015. * **March 11**\\ No Meeting, Spring Break \\ * **March 18**\\ James Hyde (Binghamton University) \\ **//Title//** \\ \\ **//Abstract//**: Text of Abstract * **March 25**\\ Chris Schroeder (Binghamton University) \\ **//Title//** \\ \\ **//Abstract//**: Text of Abstract * **April 1**\\ Andrew Velasquez-Berroteran (Binghamton University) \\ **//Title//** \\ \\ **//Abstract//**: Text of Abstract * **April 8**\\ Edgar A Bering IV (San Jose State University) \\ **//Title//** \\ \\ **//Abstract//**: Text of Abstract * **April 15**\\ (? University) \\ **//Title//** \\ \\ **//Abstract//**: Text of Abstract * **April 22**\\ No Algebra Seminar - Monday Classes Meet \\ * **April 29**\\ (? University) \\ **//Title//** \\ \\ **//Abstract//**: Text of Abstract * **May 6**\\ (? University) \\ **//Title//** \\ \\ **//Abstract//**: Text of Abstract ---- ---- * [[http://seminars.math.binghamton.edu/AlgebraSem/index.html|Pre-2014 semesters]]\\ * [[seminars:alge:fall2014]] * [[seminars:alge:spring2015]] * [[seminars:alge:alge_fall2015]] * [[seminars:alge:alge-spring2016]] * [[seminars:alge:alge-fall2016]] * [[seminars:alge:alge-Spring2017|Spring 2017]] * [[seminars:alge:alge-Fall2017|Fall 2017]] * [[seminars:alge:alge-Spring2018|Spring 2018]] * [[seminars:alge:alge-Fall2018|Fall 2018]] * [[seminars:alge:alge-Spring2019|Spring 2019]] * [[seminars:alge:alge-fall2019|Fall 2019]] * [[seminars:alge:alge-Spring2020|Spring 2020]] * [[seminars:alge:alge-fall2020|Fall 2020]] * [[seminars:alge:alge-Spring2021|Spring 2021]] * [[seminars:alge:alge-fall2021|Fall 2021]] * [[seminars:alge:alge-Spring2022|Spring 2022]] * [[seminars:alge:alge-fall2022|Fall 2022]] * [[seminars:alge:alge-Spring2023|Spring 2023]] * [[seminars:alge:alge-fall2023|Fall 2023]] * [[seminars:alge:alge-Spring2024|Spring 2024]] * [[seminars:alge:alge-fall2024|Fall 2024]]