# ACGT Seminar

The Algebra, Combinatorics, Geometry, and Topology (ACGT) Seminar meets on Tuesdays at 1:00-1:50PM in Room 146 of the Adel Mathematics Building. If you are interested in giving a talk, please contact Dana C. Ernst, ACGT coordinator.

# Schedule Spring 2019

Note that talks are listed in reverse chronological order.

### Balanced partitions of cell networks supported by Cayley digraphs

Date: April 23

Speaker: Nandor Sieben (NAU)

Abstract: I am going to attempt to prove that the balanced partitions of a cell network on a Cayley color digraphs of the group $G$ are exactly the coset partitions of $G$.

### The Rapidly Changing Landscape in Statistics Education—Implications for the Preparation of Future Teachers

Note: This talk will be one of two talks that are given as part of our Honor’s Day celebration.

Date: April 16

Speaker: Roxy Peck (Professor Emeritus at California Poly)

Abstract: A careful look at changes over the last decade in the K-12 mathematics curriculum reveals a dramatic increase in statistical content. But higher education has been slow to recognize or respond to these changes, even though there are important implications for the college-level introductory statistics course and for the preparation of future teachers. This talk will explore these implications and the challenges mathematics and statistics faculty face in addressing them.

### Codes with a compact description: Linear transformation codes, Transpolizer codes

Date: April 2, April 9

Speaker: Bahattin Yildiz (NAU)

Abstract: Centralizer and twisted centralizer codes are special cases of what we now call linear transformation codes, codes that have a compact description and a new approach to the classical problems in coding theory. We will give some cryptographic motivation for such codes and then give the general properties of them. In particular we will talk about a new example of linear transformation codes, which we call “Transpolizer Codes” together with why we think they are important.

### On Generalizing the Scarpis Construction to Quaternary Complex Hadamard Matrices

Date: March 26

Speakers: Kaitlyn Lee and Mason Sargent (undergraduates at NAU)

Abstract: A complex Hadamard matrix H is a matrix of order n, with complex roots of unity for entries, that satisfies $H\cdot{\overline{H}^{T}}=n\cdot{I_{n}}$, where $\overline{H}^{T}$ denotes the complex conjugate transpose of $H$. In this talk, we will show that the Scarpis technique for constructing classic Hadamard matrices generalizes to Butson-type complex Hadamard matrices.

### An Alternative Approach to Hierarchical Secret Sharing

Date: February 26, March 5, March 12

Speaker: Jonathan Wheeler (undergraduate at NAU)

Abstract: We look to understand “Hierarchical Secret Sharing Schemes” and work on new methods of creating them. We begin with understanding Shamir’s secret sharing schemes and analyzing the incidence structures of fully democratic Shamir schemes. Matrices are constructed whose rows are labeled with scheme participants and whose columns represent the supports of minimal access sets of secret sharing schemes. These matrices allow a greater understanding of many properties of secret sharing schemes; using these matrices, we can consider complex structures such as weighted and multilevel hierarchical schemes. From understanding the properties of these types of hierarchical secret sharing schemes, we can use trees to express and construct hierarchical and weighted secret sharing schemes that consist of nested fully democratic Shamir schemes.

### Covering Spaces and the Fundamental Group

Date: February 5, February 12, February 19

Speaker: David Deville (NAU)

Abstract: In this talk I will introduce the fundamental group of a topological space, define covering spaces and outline a few basic connections between them. With a focus on explanatory examples from graph theory, this talk should be especially suitable for undergraduates.

### Tetravalent Tricirculant Graphs and the Woolly Hat graphs

Date: January 22

Speaker: Steve Wilson (NAU)

Abstract: Starting with the basics of graph symmetry, we will zoom into semi-regular symmetries and discuss diagrams of these symmetries. We will consider existing classifications of trivalent circulant, bicirculant and tricirculant graphs, of tetravalent circulant and bicirculant graphs and enter into the not-yet finished classification of tricirculant tetravalent graphs, including the most recalcitrant case, the Woolly hat graphs.