A finite geometry problem from some conjectures of Brauer Prof. Michael Geline Professor of Mathematics Northern Illinois University We will begin with a problem in "finite geometry" which captures at least some of the spirit of algebraic geometry in positive …
A Tree Approach to Solving Diophantine Equations Dr. Eva Goaedhart Visiting Scholar Franklin & Marshall College Diophantine equations are easy to state equations that often require complicated tools to solve. After introducing Diophantine equations, I will present a visual approach …
Julia Sets in Parameter Space for the Generalized McMullen Map Mrs. Kelsey Brouwer PhD Student University of Wisconsin – Milwaukee We will begin by introducing the field of complex dynamics and explaining the two types of pictures that dynamicists are …
Introduction to Topological Combinatorics Mr. Joe Paulson PhD Student University of Wisconsin – Milwaukee With the prominence of topology and combinatorics at 51ÁÔÆæ, we'll explore the intersection of these fields. This relatively new field originated with the solving of Kneser's …
Elementary Matrix Operations on a Napkin Dr. Bogdan Nica Assistant Professor Indiana University - Purdue University Indianapolis Atmospheric science provides excellent opportunities for encouraging student interest in all fields of STEM (Science, Technology, Engineering, Math). A model outreach program (“Chasing …
Representations of the Natural Numbers Using Box Arrangements Mr. Joakim Jakovleski PhD Student University of Wisconsin – Milwaukee Natural numbers can be presented as sums of numbers in boxes, where we are subject to certain rules about how we generate …
Games, Winning, and Nimbers Mr. John Museus PhD Student University of Wisconsin – Milwaukee The Nimbers are a particularly peculiar Field which arises naturally when studying the winning strategies of Impartial Games. In this talk, we will give a brief …
Combinatorial Resolutions of Monomial Ideals Dr. Selvi Kara Assistant Professor of Mathematics Bryn Mawr College One of the central problems in commutative algebra concerns understanding the structure of an ideal in a polynomial ring. Abstractly, an ideal’s structure can be …
Sandpile Group For Cones Over Trees Dorian Smith PhD Student University of Minnesota Twin Cities The sandpile group $K(G)$ of a graph $G$ is a finite abelian group, isomorphic to the cokernel of the reduced graph Laplacian of $G.$ We …