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 …
On the Lucky and Displacement Statistics of Stirling Permutations Dorian Smith PhD Student University of Minnesota Twin Cities Stirling permutations are parking functions. We investigate two parking function statistics in the context of these objects: lucky cars and displacement. Among …
A Primer on the Mathematics of Artificial Neural Networks Daniel Quigley PhD Student University of Wisconsin-Milwaukee Artificial neural networks (ANNs, or, simply, neural networks) are ubiquitous, not least of all in the context of modern machine learning. This presentation is …
On Combinatorial Problems of Generalized Parking Functions Kimberly Hadaway PhD Student Iowa State University In this talk, we study combinatorial problems related to generalized parking functions. Our work is motivated by two different research questions posed to us by Dr. …
Harmonize your Fractals Matt McClinton Graduate Student University of Wisconsin-Milwaukee The Sierpinski Gasket (SG) is a known fractal object. A simple observation shows that SG is path connected. Unfortunately, the infinitely jagged structure of the Gasket prevents these paths from …
Counting Orbits of Defective Parking Functions Alex Moon PhD Student University of Wisconsin-Milwaukee Parking functions are well-studied objects in combinatorics and representation theory which constitute tuples of preferred parking spots for cars under a linear parking scheme. This talk will …
On the Lucky Sets of Fubini Rankings Melissa Beerbower Loyola University Chicago Recall that Fubini rankings of length n are rankings of n competitors allowing for ties. We can say that the number of rankings, k, with k less than …
Introduction to (Partial) Z-Boundaries Joe Paulson PhD Graduate Student University of Wisconsin - Milwaukee In this talk, I'll share an abridged story of Z-boundaries and their utility in group theory. Throughout, we'll revisit some main characters (compactifications, homotopy groups, group …
Kohnert Properties of Northeast Diagrams Alexander Moon Graduate Student University of Wisconsin - Milwaukee Kohnert polynomials and posets are combinatorial objects with deep representation theoretic meaning, generalizing both Schubert polynomials and Demazure characters, i.e., key polynomials. In this talk I …
(t,r) Broadcast Domination of the Truncated Square Tiling Graph Jillian Cervantes Graduate Student University of Wisconsin - Milwaukee This talk will introduce graph domination theory and a generalization called (t,r) broadcast domination. We study a family of graphs that arise …