**Problem of the Week**

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**Math Club**

seminars:alge:alge-spring2020

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.

**January 21**

No Algebra Seminar Meeting

Please think about giving a talk in the Algebra Seminar, or inviting an outside speaker.

**January 28**

Organizational Meeting

**February 4**

Casey Donoven (Binghamton University)

*Thompson's Group V is 3/2-Generated*

: Every finite simple group can be generated by two elements and furthermore, every nontrivial element is contained in a generating pair. Groups with this property are said to be 3/2-generated. Thompson’s group V, a finitely presented infinite simple group, is one of a small number of examples of infinite noncyclic 3/2-generated groups. I will present a constructive proof of this fact and mention extensions of this theorem to generalizations of V.*Abstract*

**February 11**

Cancelled

**February 18**

Eran Crockett (Binghamton University)

*Universal algebra and constraint satisfaction problems*

: Constraint satisfaction problems (CSPs) form a class of combinatorial decision problems generalizing graph colorability and Boolean satisfiability. In this expository talk, I will explain how ideas from universal algebra have been instrumental in classifying the computational complexity of CSPs.*Abstract*

**February 25**

Fikreab Solomon Admasu (Binghamton University)

*Subgroups of the integer lattice $\mathbb{Z}^d$ and the higher rank discrete Heisenberg groups*

: A sublattice $L$ of the integer lattice $\mathbb{Z}^d$ is called co-cyclic when the quotient $\mathbb{Z}^d/L$ is a cyclic group. Approximately $85\%$ of sublattices of finite index in $\mathbb{Z}^d$ are co-cyclic. This can be proven by either counting solutions to linear congruence equations or using zeta function methods. We show a similar result holds for subgroups of the discrete Heisenberg groups $H_{2d+1}.$*Abstract*

**March 3**

Matt Evans (Binghamton University)

*Some recent results for spectra of commutative BCK-algebras*

: BCK-algebras are the algebraic semantics of a non-classical logic. Like for commutative rings, there is a notion of a prime ideal in these algebras, and the set of prime ideals is a topological space called the spectrum. By work of Stone (and later, Priestley), there is a close connection between these spectra and distributive lattices with 0.*Abstract*In this talk I will discuss some recent results on the interplay between commutative BCK-algebras, their spectra, and distributive lattices.

**March 10**

Aparna Upadhyay (University at Buffalo)

*The Benson-Symonds Invariant*

: Let $M$ be a finite dimensional $kG$-module for a finite group $G$ over a field $k$ of characteristic $p$. In a recent paper Dave Benson and Peter Symonds defined a new invariant $\gamma_G(M).$ This invariant measures the non-projective proportion of the module $M$. In this talk, we will see some interesting properties of this invariant. We will then determine this invariant for permutation modules of the symmetric group corresponding to two-part partitions and present a combinatorial formula for the same using tools from representation theory and combinatorics.*Abstract*

**March 17**

Cancelled

**March 24**

Cancelled

**March 31**

Cancelled

**April 7**

Spring vacation

**April 14**

Cancelled

**April 21**

Cancelled

**April 28**

Cancelled

**May 5**

Cancelled

seminars/alge/alge-spring2020.txt · Last modified: 2020/06/01 11:55 by alex

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