Xavier University Mathematics Department

Coming Wednesday, 11/17 @ 3:30pm:

Dr. Eric Bucher's "Introduction to cluster algebras and their applications"

Cluster algebras were first invented by Fomin and Zelevinsky in 2003. Since their inception, these mathematical objects have popped up in a large variety of seemingly unrelated areas including: combinatorics, topology, algebra and mathematical physics. In this talk we will lay the basic groundwork for working with cluster algebras as well as discuss a few of their applications to the above areas. This talk is intended to be introductory so no background or definitions will be assumed. The intention is to have everyone walk away having learned about this new and fascinating algebraic object.

Coming Wednesday, 11/17 @ 3pm:

Abby Brickner's "Mathematical Approach to Congressional Redistricting"

Gerrymandering has been a pertinent issue for politics and voting in the United States since its earliest days. In an attempt to analyze this political issue mathematically to automate a solution, we have created a number of simulations which run on the basis of four factors. These factors are fairness, competitiveness, equal population and compactness. The manipulation of these factors alongside a mutation algorithm allowed us to create maps which provide alternatives to the current districts. Further work focused more on the genetic algorithm and the idea of "survival of the fittest" regarding the crossover of the best parent maps to produce their offspring. Finally, manipulation of the fairness factor in combination with the genetic algorithm has allowed for simulations to show intentionally biased maps, either to favor the Republicans or the Democrats.