1. Kelsey Hanser
Title : Greedy Kohnert Posets 
Abstract : K-Kohnert polynomials form a large family of polynomials which generalize Lascoux polynomials. Each K-Kohnert polynomial encodes a certain collection of diagrams which is formed from an initial seed diagram by applying what are called “Kohnert” and “ghost moves.” In particular, Kohnert polynomials are the restrictions of K-Kohnert polynomials to those diagrams obtained only by applying Kohnert moves. Much recent work has focused on these two families of polynomials, their combinatorics, and their appearances in other areas of mathematics. Of particular interest here is work related to the diagrams obtained by only applying ghost moves. Here we focus on the maximum number of ghost moves that can be applied to a diagram, as well as the structure of a corresponding natural ordering on the associated collection of diagrams.

2. Mathew Kushelman
Title : Morse theory: applications of Reeb’s theorem
Abstract : Morse theory is the study of critical points on manifolds. My aim here is to present the central ideas and techniques of the theory: Morse functions, Morse inequalities and connection to the Euler characteristic, and supply the examples, as well as mention an illustrative result: Reeb’s theorem. If time permits, I wish to touch on the study of exotic structures and how Reeb’s theorem allows us to prove the existence of exotic 7-spheres, due to Milnor (1956).
3. Logan Martyn
 
Title : Simulating Chemical Systems
Abstract : Chemical systems are often modeled using compartmental ordinary differential equation systems. We can instead examine reactions on a molecular level and use that framework to model chemical reactions using the stochastic simulation algorithm. This method provides a more detailed perspective that is accurate even with small systems. This paper aims to explore stochastic simulation and provide an investigation into the convergence of the stochastic simulation algorithm to the deterministic solutions through the thermodynamic limit. This involves numerical experiments on two chemical systems, the Michaelis-Menten system and the Schlogl model.