# ACGT Seminar

The Algebra, Combinatorics, Geometry, and Topology (ACGT) Seminar meets on Tuesdays at 12:45-2:00pm in Room 164 of the Adel Mathematics Building. If you are interested/willing to give a talk, please contact Dana C. Ernst or Michael Falk, ACGT Co-coordinators.

# Schedule Fall 2017

Note that talks are listed in reverse chronological order.

### Permutation distributions from random walks

Speaker: Hugh Denoncourt (NAU)

Dates: 11/7/17

Abstract: A random walk on the real number line naturally gives rise to a permutation. With what probability does a given permutation arise? Which permutations arise most frequently in walks? In the talk, we’ll describe combinatorial approaches to these and related questions as well as recent applications of permutation entropy to time series analysis.

### Constructions for Self-dual codes: From Fields to Rings to Group Rings

Speaker: Bahattin Yildiz (NAU)

Dates: 10/17/17, 10/24/17, 10/31/17

Abstract: After giving a general background on Codes and some of the problems in Coding Theory, I will proceed to discuss a special class of codes named “self-dual codes”. I will give a chronology of different constructions for self-dual codes that have been used in the literature and will explain the recent constructions that I have been involved with. These constructions are quite algebraic in nature as they use some families of rings and most recently group rings. They have led to many new codes and in particular the group ring construction has generalized all the known construction methods.

### New Pathways and Pedagogies in Mathematics (Special Department Seminar)

Speaker: William Jaco (Oklahoma State University)

Date: 10/10/17

Abstract: There is a growing national program led by the Dana Center (DC) at U. of Texas and Complete College America (CCA) encouraging change in options and pedagogy in college entry-level mathematics. I will discuss the two central ideas of Math Pathways and Co-requisite Instruction central to the DC and CCA programs. In particular, I will discuss what I have been involved in for the state of Oklahoma and what I believe has been a fundamental role played by inquiry learning and what I envision as becoming an even greater role for inquiry learning for widespread fundamental systemic change.

### Impartial achievement and avoidance games for generating finite groups

Speaker: Dana Ernst (NAU)

Dates: 9/26/17, 10/3/17

Abstract: In this talk, we will explore two impartial combinatorial games introduced by Anderson and Harary. Both games are played by two players who alternately select previously-unselected elements of a finite group. The first player who builds a generating set from the jointly-selected elements wins the first game (GEN) while the first player who cannot select an element without building a generating set loses the second game (DNG). After the development of some general theory, we will discuss the strategy and corresponding nim-numbers of both games for several families of groups. This is joint work with Bret Benesh and Nandor Sieben.

### Discriminantal arrangements and permutations

Speaker: Michael Falk (NAU)

Dates: 9/5/2017, 9/12/17, 9/19/17

Abstract: We will define discriminantal arrangements and explain the connection with higher Bruhat orders, consider some examples, and attempt to sort out the relationship between certain discriminantal arrangements and factorizations of certain elements of the symmetric group.

In part 2, on 9/12, we will look carefully at the higher Bruhat order $B(n,2)$, in order to understand the bijection between its elements and the commutation classes of factorizations of the $n$-cycle $(1,2,\ldots,n)$ as a product of adjacent transpositions $(i,i+1)$.

In part 3, we will describe the higher Bruhat order and (in principle) explain the bijection between its elements and the commutation classes of factorizations of the longest element of the symmetric group (not an $n$-cycle) as a product of adjacent transpositions $(i,i+1)$.