Graduate Student Seminars

Upcoming Graduate Student Seminar Seminars
Past Graduate Student Seminar Seminars
DMS Graduate Student Seminar
Sep 20, 2023 03:00 PM
108 ACLC


Speaker: Nicholas Gaubatz, Auburn University 

Title: Programming in Grad School: An Overview and an Algebra Project

DMS Graduate Student Seminar
Sep 06, 2023 03:00 PM
108 ACLC


Speaker: Elvan Ceyhan, Auburn University 

Title: Stochastic Obstacle Scene Problem on Spatial Networks


Abstract: The goal of this research is finding optimal or near-optimal solutions to the stochastic obstacle scene (SOS) problem using spatial network optimization. We will study two variants of the SOS problem: (i) Optimal Traversal Path (OTP) Problem: This is the original SOS problem which only considered a single navigating agent (NAVA) whose goal is choosing a path in the space containing “forbidden regions”, so as to minimize the cost sustained until arrival. (ii) Optimal Obstacle Placement (OOP) Problem: This second problem is recently introduced and considers an obstacle placing agent (OPA) inserting obstacles in the traversal window so as to maximize NAVA’s traversal length. Our research objectives are to (a) extend the SOS problem in various directions, e.g., high dimensional version and develop potential strategies to improve OTP and OOP algorithms, (b) introduce and develop the weight constraint versions of both SOS variants, study the solution strategies and develop a more comprehensive approach to network traversal optimization/obstruction all from the probabilistic/statistical and computational points of view, and (c) study the theoretical properties (including complexity) of the network traversal and obstruction algorithms together with the characterization of the cost functions for the OTP problem. 

DMS Graduate Student Seminar
Aug 30, 2023 03:00 PM
108 ACLC


Speaker: Isabel Harris, Auburn University 

Title: A Necessary Condition for Ark – Bounded Graphs


Abstract: Abstract: A simple graph with e = E(G) avoids a k-rainbow coloring if any color appears on at least k+1 edges of G. For k  P, ARk(G, n) is the maximum number of colors in an edge coloring of Kn so that in every copy of G, some color occurs on at least k+1 edges. G is ARk-bounded if ARk(G,n) ≤ c for some c  P and all n sufficiently large. This talk will discuss a necessary condition for classifying graphs into ARk-bounded or ARk-unbounded. 

DMS Graduate Student Seminar
Aug 23, 2023 03:00 PM
108 ACLC

Speaker: Dalton Bidleman

Title: Intersection Structures on Secants of Grassmannians


Abstract: Restricted secant varieties of Grassmannians are constructed from sums of points corresponding to k-planes with the restriction that their intersection has a prescribed dimension.  

This talk shows how to calculate dimensions of restricted, cyclic, and path geometric secants of Grassmannians and relates them to the analogous question for secants of Grassmannians via an incidence variety construction. It also demonstrates example calculations in Macaulay 2 and points out ways to make these calculations more efficient. 

DMS Graduate Student Seminar
Apr 26, 2023 03:00 PM
108 ACLC


Speaker: Dr. Steven Clontz (University of South Alabama)

Steven obtained his PhD in Math from Auburn in 2015 and currently holds a tenured associate professorship at the University of South Alabama.  During the seminar, he will share with us his experiences at Auburn and how they have influenced his career.  

DMS Graduate Student Seminar
Apr 19, 2023 03:00 PM
108 ACLC

Speaker: Stacie Baumann
Title: A Proof of the \((n,k,t)\) Conjectures
Abstract: An \((n,k,t)\)-graph is a graph on \(n\) vertices in which every set of \(k\) vertices contain a clique on \(t\) vertices. Turán's Theorem (complemented) states that the unique minimum \((n,k,2)\)-graph is a disjoint union of cliques. We prove that minimum \((n,k,t)\)-graphs are always disjoint unions of cliques for any \(t\) (despite nonuniqueness of extremal examples), thereby generalizing Turán's Theorem and confirming two conjectures of Hoffman et al. 
This is joint work with Joseph Briggs.

DMS Graduate Student Seminar
Apr 12, 2023 03:00 PM
108 ACLC


Speaker: Chinedu Eleh

Title:  Show Me A Function: More Than Meets The Eye

Abstract: Mathematics is a fascinating subject used to understand functions' properties and behavior. From simple precalculus to challenging graduate-level courses, there is an intricate web of functions to explore. Unfortunately, functions that arise from real life problems are elusive, hard to characterize and can often only be approximated. In this talk, we will discuss practical methods used to uncover valuable functions in a variety of applications.

Prerequisite: a curious mind!

DMS Graduate Student Seminar
Apr 05, 2023 03:00 PM
108 ACLC

Speaker: Dr. Junshan Lin
Title: Introduction to Mathematical Aspects of Inverse ProblemsAbstract: I will first give an overview of inverse problems arising from science and engineering and then use the example of the Electrical Impedance Tomograph (so-called Calderon problem) to explain how mathematicians can contribute to this area, especially in developing rigorous theories (such as uniqueness and stability for inverse problems) and computational algorithms (such as optimization and regularization methods to solve the inverse problems).

DMS Graduate Student Seminar
Mar 29, 2023 03:00 PM
108 ACLC


Speaker: Professor Pete Johnson 

Title: Euclidean Coloring Problems:  The Origin Story

Abstract:  The Four-Colour Conjecture begat not only graph theory but also "coloring problems."  For instance, around 1916 Issai Schur proved that if r > 1 and you color [N] = {1,,,,,N} with r colors, then for all N sufficiently large (depending on r) you cannot avoid the existence of integers a, b, and c in [N], all of the same color, such that a + b = c.  This is a coloring result that is only distantly related to graph theory results. In 1950 an 18-year-old student, Edward Nelson, asked a classmate:  What do you think is the smallest number of colors with which the points of the plane are colorable so that any two points (Euclidean) distance 1 from each other are colored differently? This question is still open, as are a great number of other questions that have germinated in certain human minds exposed to Nelson's question.

DMS Graduate Student Seminar
Mar 22, 2023 03:00 PM
108 ACLC

Speaker: Colby Muir 
Title : Word Representability and Hasse Diagrams
Abstract: Kitaev and Pyatkin posed several open problems regarding word representability and semi-transitive graphs during a talk in October 2022. We answer one of these problems and introduce a unique algorithm which was utilized in our solution.
This is joint work with Dr. Paul Horn (University of Denver), Dr. Andrew Owens (Widener University), and Zion Hefty (Grinnell College).

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