# Spelman Mathematics Colloquium Series

All presentations take place on **Mondays **from **4:30 - 5:30 p.m. **in **Tapley 308 **unless otherwise noted.

## Spring 2018 Schedule

### Feb. 5: On Goldberg’s Conjecture

**Guantao Chen, Georgia State University**

Due to various applications, topics related to the chromatic index of a graph are important to both graph theory and computer science. Vizing's classic result shows that the chromatic index of a simple graph *G* is either Δ (G) or Δ(G)+1, which indicates that edge colorings unlike vertex colorings, usually have concise answers. Hence it is natural to consider whether similar phenomena would happen to the chromatic indices of multigraphs. In this paper, we will discuss progress on this conjecture.

### Feb. 12: A Topological Structure in Initial Algebras

**Mohammed Tesemma, Spelman College **

This talk will focus mainly on introducing the concept of topology, type of spaces, and examples. The latter part will introduce topologies derived from algebraic structures and a stated result about the natural topology defined on a family of algebras coming from invariant theory. This topological space has interesting properties. It is topologically homeomorphic to the cantor set.

### Thursday, Feb. 22: Etta Z. Falconer Mathematics Lecture

5 p.m. | NASA Auditorium

Speaker: Kelly-Ann Henry

### Feb. 26: An Uncertainty-Weighted ADMM Method for Large-Scale PDE Parameter Estimation

**Samy Wu, Emory University
**We are interested in estimating parameters of Partial Differential Equations (PDEs) that model real life phenomena such as blood-flow dynamics, seismic and electromagnetic wave propagation. We phrase the parameter estimation problem as an optimization problem, where given experimental data, we find the parameter that most accurately simulates the experiment. The optimization problem is very computationally intense since modern technology allows us to collect data at massive scales. In this work, we integrate concepts from probability/statistics into a distributed optimization method, the Alternating Direction Method of Multipliers (ADMM), to tackle these kinds of problems.

### Mar. 5:** **The SEE(Support, Encouragement, and Exposure) Principle: An examination on the K-12 science and math experiences of African American females

**Viveka Brown, Spelman College
**Voices of African American women in mathematics and other STEM fields have been limited. This presentation will explore the K-12 experiences of African American women in science and mathematics. In wanting to increase the number of African American women in STEM, this study will discuss the importance of support, encouragement, and exposure in STEM.

### Mar. 12:** **SPRING BREAK

### Mar. 19: Definitions of Quasi-Conformal Mappings

**Farouk Brania, Morehouse College **

A conformal mapping in the plane preserves angles between smooth curves. A quasi-conformal mapping in the plane is a natural generalization; it distorts the angle by a fixed amount. This talk will describe three definitions of quasi-conformality in R^n with possible extension to more general metric spaces.

### Mar. 26: On Spanning Trees with few Branch Vertices

**Warren Shull, Emory University
**A conjecture of Matsuda, Ozeki, and Yamashita posits that, for any positive integer

*k*, a connected claw-free

*n*-vertex graph must contain either a spanning tree with at most

*k*branch vertices or an independent set of 2

*k*+3 vertices whose degrees add up to at most

*n*-3. We prove this conjecture. This result is best possible, and generalizes a sufficient condition for traceability.

### Apr. 2:** **A lesson in symmetry: From triangles to quadratic forms (A time capsule from Pythagoras to Gauss via the February 2017 Problem of the Month)

**Eduardo Duenez, Spelman College
**Spelman's February 2017 Problem of the Month asked to find the side length of an equilateral triangle given the distances of its vertices to a fixed line. The study of this fun problem in successively more conceptual ways leads from purely algebraic approaches based on the Pythagorean Theorem towards an identification of the symmetries of the equilateral triangle triangle with those possessed by the quadratic form solving the problem (as once done by Gauss in his

*Disquisitiones Arithmeticae*) ultimately leading to concepts of group theory. The different viewpoints allow tackling generalizations of the problem more easily and illustrate the importance of striving for deeper understanding even of seemingly elementary questions.

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