# Department of Mathematics Seminars

## Fall 2022

Location: UC 327

**Monday, August 15 ^{th}, 12:00-12:45pm**

- Organizational meeting

**Tuesday, August 23 ^{rd}, 12:00-12:45pm**

- Dr. David Plaxco, Clayton State University
- Abstract: Dr. Plaxco will discuss his experience traveling to the Bridges and MOVES conference during Summer 2022. This travel was funded by the President’s Research and Creative Endeavors Mini Grants initiative. In addition to a brief overview of the conferences, Dr. Plaxco will share the work that he presented at the conferences: Knot Theory on the nxnxn Rubik’s Cube.

**Monday, August 29 ^{th}, 12:00-12:45pm**

- Working seminar in discrete mathematics led by Elliot Krop. We will discuss Vizing's conjecture about the domination of Cartesian products of graphs and go over the proof of the result of Bartsalkin and German from 1979.

**Tuesday, September 6 ^{th}, 12:00-12:45pm**

- Dr. Dmitriy Beznosko, Clayton State University
- Abstract: What is Common Between Random Numbers and Cosmic Rays? In today’s world, random numbers are used in the multitude of the fields and areas. With that widespread use, the generation of the numbers starts to be an important question as the quality of the randomness becomes of the utmost importance. After an overview of the principles behind some generation methods, the example of the use of random numbers in high energy physics will be reviewed. PowerPoint slides

**Monday, September 12 ^{th}, 12:00-12:45pm**

- Working seminar in discrete mathematics led by Elliot Krop. We will continue our discussion of Vizing's conjecture about the domination of Cartesian products of graphs.

**Tuesday, September 20 ^{th}, 12:10-12:55pm **

- Working seminar on generating random matrices led by Dr. Brianna Vick.

**Friday, September 30 ^{th}, 12:00-12:45pm **

- Working seminar in discrete mathematics led by Elliot Krop. We continue our discussion of Vizing's conjecture, and will focus on the 2016 paper by Aziz Contractor (Clayton State student) and Elliot Krop that extended the result of Bartsalkin and German to broader classes of graphs. A copy of the paper can be found here.

**Tuesday, October 4 ^{th}, 12:00-12:45pm **

**Self-contracted****curves**, Tomás Merchán , Clayton State University- Abstract: A curve Γ : [0, 1] → R
^{n}is called self-contracted if for any 1 ≥ r ≥ s ≥ t ≥ 0, Γ satisfies that |Γ(r) − Γ(s)| ≤ |Γ(r) − Γ(t)|. In the talk we will study this class of curves and we will go over some recent results. - The talk will be accessible to undergraduate students!

**Monday, October 10 ^{th}, 12:00-12:45pm**

- Fall Break--No talk

**Tuesday, October 18 ^{th}, 12:00-12:45pm**

- No talk

**Monday, October 24th, 12:00-12:45pm**

- Seminar in discrete mathematics on Vizing's conjecture. We make our first natural generalization of the Contractor-Krop argument. This is a working seminar, in the form of a group discussion, so there will be no lead lecturer.

**Tuesday, November 1 ^{st}, 12:00-12:45pm**

**Is SVD the GOAT?**David Williams, Clayton State University-
ABSTRACT:

In numerical linear algebra, one of my favorite things is the singular value decomposition of a matrix (SVD). The SVD has an enormous number of applications and every matrix has one. I will briefly discuss some basic geometry related to the SVD and indicate some of the actual complexities of calculating the SVD for any given matrix. I will then discuss some of the many applications of the SVD which will include: image processing, classification problems in machine learning, and eigenfaces. Finally, I will introduce a topic I am really interested in because it lies at the intersection of data science, dynamical systems, and numerical linear algebra...the dynamic mode decomposition (DMD). The DMD and its variants have become increasingly versatile tools since the first appearance of the DMD in 2008. The DMD and its variants promise to be an exciting area of mathematical and computer science research for the foreseeable future (and the DMD starts with an SVD!)

- This talk will be accessible to undergraduate students (and there will be cookies)!

**Monday, November 7 ^{th}, 12:00-12:45pm**

- No talk

**Tuesday, November 15 ^{th}, 12:00-12:45**

- TBD

**Friday, November 18 ^{th}, 12:00-1:00pm**

**Mathematics Colloquium: Tom Kelley, Georgia Institute of Technology**

**Thresholds for Latin squares and Steiner triple systems**, Tom Kelley, Georgia Institute of Technology- Abstract: An order-n Latin square is an
*n*×*n*matrix with entries from a set of*n*symbols, such that each row and each column contains each symbol exactly once. Suppose that*L*⊆ [_{i,j}*n*] is a random subset of [*n*] where each*k*∈ [*n*] is included in*L*independently with probability_{i,j}*p*for each*i,**j*∈ [*n*]. How likely does there exist an order-*n*Latin square where the entry in the*i*th row and*j*th column lies in*L*? This question was initially raised by Johansson in 2006, and later Casselgren and Ha¨ggkvist and independently Luria and Simkin conjectured that log_{i,j}*n/n*is the threshold for this property. In joint work with Dong-yeap Kang, Daniela Ku¨hn, Abhishek Methuku, and Deryk Osthus, we proved that for some absolute constant*C*, if*p > C*log^{2}*n/n*, then asymptotically almost surely there exists such a Latin square. We also prove analogous results for Steiner triple systems and 1-factorizations of complete graphs.

**Monday, November 21st, 12:00-12:45pm**

- No talk

**Tuesday, November 29th, 12:00-12:45pm**

- No talk