### Sidebar

seminars:alge

The Algebra Seminar

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 Hung Tong-Viet

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

## Fall 2018

• August 28
Organizational Meeting
Title of Talk

Abstract: Please come or contact the organizers if you are interested in giving a talk this semester or want to invite someone.

• September 4
Casey Donoven (Binghamton University)
Covering Number of Semigroups

Abstract: A semigroup is a set $S$ equipped with an associative operation. The covering number of a semigroup $S$ is the minimum number of proper subsemigroups whose union is $S$. In this talk, I will introduce basic semigroup theory and some fundamental examples while proving the following theorem: If $S$ is a finite semigroup that is not a group nor generated by a single element, then the covering number of $S$ is 2. Similar questions have been studied for groups and loops. (Joint work with Luise-Charlotte Kappe and Marcin Mazur.)

• September 11
No Classes (University)
Title

Abstract: Abstract text

• September 18
Joe Cyr (Binghamton University)
Semilattice Modes

Abstract: A mode A is an algebra which is idempotent and in which every operation is a homomorphism from the appropriate power of A to A. We will explore some results on a particular class of modes which are constructed from semilattices. In particular, we will look at the question of when is a semilattice mode subdirectly irreducible, both in general and in the particular case of when the mode has a single binary operation.

• September 25
Matt Evans (Binghamton University)
Title

Abstract: Abstract text

• October 2
Mark Lewis (Kent State University)
Title

Abstract: Abstract text

• October 9
Fernando Guzman (Binghamton University)
Title

Abstract: Abstract text

• October 16
Luise-Charlotte Kappe (Binghamton University)
A generalization of the Chermak-Delgado lattice to words in two variables

Abstract: The Chermak-Delgado measure of a subgroup $H$ of a finite group $G$ is defined as the product of the order of $H$ with the order of the centralizer of $H$ in $G$, $|H||C_G(H)|$, and the set of all subgroups with maximal Chermak-Delgado measure forms a dual sublattice of the subgroup lattice of $G$. In this talk we step back from centralizers and consider four types of centralizer-like subgroups, defined using general words in the alphabet $\{x, y, x^{-1}, y^{-1} \}$ instead of the specific commutator word. We show that this generalization results in four sublattices of the subgroup lattice of a finite group, some of which may be equal to one another depending on the word. We consider which properties of the Chermak-Delgado lattice generalize to the new lattices, and which properties are specialized in the Chermak-Delgado lattice. (This work is joint with Elizabeth Wilcox.)

• October 23
Eran Crockett (Ripon College)
Title

Abstract: Abstract text

• October 30
Dan Rossi (Binghamton University)
Title

Abstract: Abstract text

• November 6
Speaker (University)
Title

Abstract: Abstract text

• November 13
Speaker (University)
Title

Abstract: Abstract text

• November 20
Hung Tong-Viet (Binghamton University)
Title

Abstract: Abstract text

• November 27
Nicholas Gardner (Binghamton University)
Title

Abstract: Abstract text

• December 4
Speaker (University)
Title

Abstract: Abstract text