Problem of the Week
BUGCAT
Zassenhaus Conference
Hilton Memorial Lecture
BingAWM
Math Club
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. As of Saturday, March 26, 2022, 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: 981 8719 2351) 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 join the seminar's mailing list.
Please think about giving a talk in the Algebra Seminar, or inviting an outside speaker.
Abstract: It is a classical topic in finite group theory to understand a finite group through its simple composition factors. To this end, one would like to construct group invariants that distinguish the nonabelian finite simple groups. One heuristic for simple groups is that they have “few” inequivalent irreducible linear representations, as they have few normal subgroups. In this talk, we will construct invariants from this observation and show how they can be used to determine the structure of finite groups. Our talk aspires to be accessible and interesting to a wide mathematical audience.
Abstract: We study the relations between polynomial and random maps by computing the moments of the random variable of inverse image sizes. In the polynomial case, these moments are connected to the Galois Theory of the polynomial over a function field. For random maps, the moments can sometimes be computed using generating function techniques. These computations show both similarities and differences between the two cases.
Abstract: For an irreducible character $\chi$ of a finite group $G$, we define $f(\chi)$ as the `cyclotomic deficiency' of $\chi$. This deficiency is the degree of the field extension from the field of values of $\chi$ to its cyclotomic closure. Over thirty years ago, Cram proved that when $G$ is solvable, $f(\chi)$ is always a divisor of the character degree $\chi(1)$. In this talk, I will present strong evidence suggesting that for all finite groups, $f(\chi)$ is bounded above by $\chi(1).$
Abstract: The abstract commensurator of a group $G$, the group of isomorphisms between finite-index subgroups modulo equivalence, encodes symmetries of $G$ that may be ``hidden.'' When $G$ is a lattice in a simple Lie group incommensurable with $\operatorname{PSL}(2,\mathbb{R})$, work of Mostow, Prasad, Borel, and Margulis shows that the abstract commensurator of $G$ detects whether the group arises through arithmetic constructions. In this talk, I will discuss results on abstract commensurators of the other significant class of lattice in Lie groups, the solvable groups. This builds on classical work of Malcev for nilpotent groups and more recent rigidity results of Mostow, Morris, and Baues–Grunewald.
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