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seminars:alge
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:
Algebra Seminar Zoom Meeting Link
Organizers: Alex Feingold, Daniel Studenmund and 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)
Title
Abstract: Text of Abstract
- February 11
Hung Tong-Viet (Binghamton University)
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- February 18
(? University)
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- February 25
(? University)
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- March 4
Thu Quan (Binghamton University)
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- March 11
No Meeting, Spring Break
- March 18
James Hyde (Binghamton University)
Title
Abstract: Text of Abstract
- March 25
(? University)
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- April 1
Andrew Velasquez-Berroteran (Binghamton University)
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- April 8
(? University)
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- April 15
(? University)
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- April 22
No Algebra Seminar - Monday Classes Meet
- April 29
(? University)
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- May 6
(? University)
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Abstract: Text of Abstract
seminars/alge.txt · Last modified: 2025/01/22 15:34 by daniel