**Problem of the Week**

**Math Club**

**DST and GT Day**

**Number Theory Conf.**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

seminars:alge

Unless stated otherwise, the seminar meets Tuesdays in room WH-100E at 2:50 p.m. There will be refreshments served at 4:00 in room WH-102.

Organizers: Alex Feingold and Marcin Mazur

To receive announcements of seminar talks by email, please join the seminar's mailing list.

**August 29**

Organizational meeting

**September 5**

Dikran Karagueuzian (Binghamton University)

*Categories for the Skeptical Mathematician*

: Many find it hard to see the mathematical content in Category Theory. I will discuss ways of understanding this content and how I recently decided that it is relevant to a problem in Commutative Algebra which I have studied.*Abstract*

**September 12**

Hung Tong-Viet (Binghamton University)

*Real class sizes*

: An element $x$ in a finite group $G$ is said to be*Abstract***real**if there exists an element $g\in G$ such that $x^g=x^{-1}$. A real conjugacy class of $G$ is a conjugacy class which contains some real element and a real class size is the size of a real conjugacy class. Several arithmetic properties of the real class sizes can conveniently be stated using graph theoretic language. The**prime graph**on the real class sizes of a finite group $G$, denoted by $\Delta^*(G)$, is a simple graph with vertex set $\rho^*(G)$, the set of primes dividing some real class size of $G$, and there is an edge between two vertices $p$ and $q$ if the product $pq$ divides some real class size. In this talk, I will outline the proof that if the prime graph on the real class sizes of a finite group is disconnected, then the group is solvable.

**September 19**

Phillip Wesolek (Binghamton University)

*Elementary amenability and bounded automata groups*

: (Joint work with Kate Juschenko) The bounded automata groups are a natural family of groups, which are defined by a finite amount of information in the form of a certain type of finite automaton. A remarkable property of bounded automata groups is that they are necessarily amenable. On the other hand, the elementary amenable groups are groups that are amenable for `elementary reasons' and thus are somewhat uninteresting. One is thereby motivated to identify the non-elementary amenable bounded automata groups. We isolate three natural families of bounded automata groups, and in each family, we identify the elementary amenable groups.*Abstract*

**September 26**

Matt Evans (Binghamton University)

*Natural Dualities and BCK-algebras*

: BCK-algebras are generalizations of Boolean algebras. There is a well-known natural duality between Boolean algebras and Stone spaces (totally disconnected, compact, Hausdorff spaces), and one might wish to develop a similar type of duality for the class of BCK-algebras. In this talk I will briefly review some category theory before defining “natural duality,” and then discuss some progress on dualizing bounded commutative BCK-algebras.*Abstract***This talk has been canceled due to illness of the speaker**.

**October 3**

Joe Cyr (Binghamton University)

*Subdirectly Irreducible Medial Quandles of Set Type*

: This talk will be a continuation of my seminar talk last semester on medial quandles (though no prior knowledge will be assumed). We will explore some important aspects of the structure of this class of algebras and find that the subdirectly irreducibles of set type are quasi-reductive. This then allows one to fully classify this class of subdirectly irreducible medial quandles.*Abstract*

**October 10**

Luise-Charlotte Kappe

*On covering numbers of groups*

: A set of proper subgroups is a cover for a group if its union is the whole group. The minimal number of subgroups needed to cover a group is called its covering number. No group is the union of two proper subgroups. Tomkinson showed that the covering number of a solvable group has the form prime-power-plus-one and for each such integer there exists a solvable group having this integer as a covering number. In addition he showed that 7 is not a covering number. So far it has been shown that the integers < 27, which are not covering numbers, are 2,7,11,19,21,22 and 25. We extend this list by determining all integers < 129 which are covering numbers. This is joint work with Martino Garonzi and Eric Swartz.*Abstract*

**October 17**

Mark Skandera (Lehigh) (joint with the Combinatorics Seminar, 1:15 - 2:15 PM, WH-100E)

*Evaluations of Hecke Algebra Traces at the Wiring Diagram Basis*

: The (type A) Hecke algebra H*Abstract*_{n}(q) is a certain module over**Z**[q^{1/2},q^{-1/2}] which is a deformation of the group algebra of the symmetric group. The**Z**[q^{1/2},q^{-1/2}]-module of its trace functions has rank equal to the number of integer partitions of n, and has bases which are natural deformations of those of the trace module of the symmetric group algebra. While no known closed formulas give the evaluation of these traces at the natural basis elements of H_{n}(q), or at the Kazhdan-Lusztig basis, I present a combinatorial formula for the evaluation of traces induced by the sign character at a certain wiring diagram basis of H_{n}(q).

**October 24**

Hung Tong-Viet (Binghamton University)

*Title of Talk*

: Abstract for Talk*Abstract*

**October 31**

Eran Crockett (Binghamton University)

*Title of Talk*

: Abstract for Talk*Abstract*

**November 7**

Matt Evans (Binghamton University)

*Natural Dualities and BCK-algebras*

: BCK-algebras are generalizations of Boolean algebras. There is a well-known natural duality between Boolean algebras and Stone spaces (totally disconnected, compact, Hausdorff spaces), and one might wish to develop a similar type of duality for the class of BCK-algebras. In this talk I will briefly review some category theory before defining “natural duality,” and then discuss some progress on dualizing bounded commutative BCK-algebras.*Abstract*

**November 14**

Victor Protsak (Cornell University)

*Title of Talk*

: Abstract for Talk*Abstract*

**November 21**

Ian Payne

*Title of Talk*

: Abstract for Talk*Abstract*

**November 28**

Upstate Descriptive Set Theory and Group Theory Day

*Several Talks 1:00 - 6:00*

: Please follow this link for details about the special talks: Website for this meeting*Abstract*

**December 5**

Hung Nguyen(The University of Akron)

*Title of Talk*

: Abstract for Talk*Abstract*

seminars/alge.txt · Last modified: 2017/10/22 22:38 by mazur

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