Undergraduate Work:
Title: Game Theory and an Exploration of 3 x n Chomp! Boards
Abstract: Chomp! is a two player game using a rectangular grid. We explored the game using a rectangular grid 3 x n where n is an integer to find a winning strategy for player one.
Graduate Work:
Title: Playing With Fire: My Adventures With Magma
Abstract: There has been no significant advances on the prime power conjecture for projective planes in approximately 30 years. We want to use group theory on the group, G, generated by the planar ternary rings of the plane, to obtain more results on this conjecture. This summer we focused on gathering computational results for the group G for Hall planes of small order.
Title: Secondary Constructions of PN and APN Functions.
Abstract: Highly nonlinear functions are important in differential cryptanalysis. We measure distance from linear by computing the differential uniformity of a function; so in order for a function to be far from linear it must have low differential uniformity. Optimal functions are called perfect nonlinear (PN) and almost perfect nonlinear (APN). The goal of our research is to develop a secondary construction for functions with low differential uniformity; in other words we want to take PN (or APN) function and manipulate it to obtain a new PN (or APN) function or a function with low differential uniformity. We will discuss previous research, including connections with orthogonal systems, our attempts at secondary constructions, and the residual questions left from these attempts.
