Y22- 23

YouTube Playlist of Year 2022 - 2023

Apr 19

Speaker: Jesus Omar Sistos Barron and Sungkon Chang
Title: Reflection on the 2022 William Lowell Putnam Mathematical Competition
Abstract: The William Lowell Putnam Mathematical Competition is annually held across the U.S. and Canada in December each year. Since 1970 the Armstrong Campus has participated in this nation-wide annual mathematical event, and in the fall semester each year, the department of mathematics offers students a seminar course on the competition problems. In this talk we introduce the seminar course, and discuss some of the problems of the past year's competition. All those who are interested are invited to join this presentation.

Mar 29

Speaker: Saeed Nasseh
Title: What's news with the Auslander-Reiten Conjecture?  
Abstract: There are several conjectures from representation theory of Artin algebras that have been transplanted to commutative algebra; this process has enriched both fields significantly. One of these conjectures, that is closely related to other important problems in commutative algebra, is the Auslander-Reiten Conjecture. In this talk, I will give the history of this conjecture and describe it from an algebraic topological point of view. 

Nov 30

Speaker: Modupe Ayewa, Jesus Sistos Barron, and Ana Rosales
Title: Data Integrity and scalability with zk-rollup 
Abstract: Applications of digital ledger technology (DLT) to data management is one of the most transformative innovations within the last decade.  We will discuss some of the applications such as decentralized digital identity, tracking supply chain data, and monitoring climate. The advent of DLT has caused a Cambrian explosion of immutable data monitoring, which poses a scalability problem with the base layer. We will see how elliptic curves and the Tate’s pairing can solve the scalability issue via Zero-Knowledge rollups (zk-rollups).

Nov 16

Speaker: Sabrina Hessinger
Title: A Tour of Differential Galois Theory via Undergraduate Differential Equations  
Abstract: In Differential Galois Theory one can associate a matrix group with a differential equation much as one associates a permutation group with a polynomial equation in the usual Galois Theory.  Since the vast majority of differential equations cannot be solved explicitly, being able to extract information about the solutions using characteristics of its Galois group becomes particularly valuable. The process of associating a matrix group with a linear differential equation beautifully integrates a range of mathematical subareas, including most obviously differential equations and abstract algebra, but also linear algebra, topology, representation theory, and computer algebra.  And yet, in the midst of all of that potential complexity, we’ve composed a set of surprisingly simple examples which illustrate several key characteristics of Differential Galois Groups and the information they provide about the solutions to the given equation, using basic undergraduate mathematics.  These examples as well as a recent result produced by my former undergraduate research team will be presented. 

Oct 12

Speaker: Paul Hadavas
Title: Extensions of the Bus Driver Sanity Problem
Abstract: In this talk we will take the theory out of graph theory and look at examples of applied problems dealing with transportation.  You model a network by assigning weights to the vertices and the edges of the corresponding graph.  Then, you find the optimal path on that network based on some objective, like minimizing cost or time or maximizing throughput.  We will present two examples of networks with counter-intuitive results.  One example sees the construction of a shortcut leading to longer average commute times.  The main example has the goal of saving the sanity of a bus driver, but this is not necessarily achieved with the fastest route. 

Sep 14

Speaker: James Brawner
Title: Drive-in Movies, Solar Panels, and Angle Optimization
Abstract: Have you ever wondered where to park at a drive-in movie?  Or where to place a solar panel between two buildings?  In this talk, we discuss these angle optimization problems, and focus on those that have integer solutions.  From the perspective of a calculus instructor, this is particularly relevant for creating variations of these problems with nice solutions, which can be used for an online homework database.  This is joint work with Georgia Southern alumna Nadou Lawson, from our recent article in the College Mathematics Journal.