Month: February 2020

Student Colloquium Talk by Professor Allison Lewis, Lafayette College

Abstract: How can mathematical modeling assist in the development of treatment protocols for cancer? Recent technological advances make it possible to collect detailed information about tumors, and yet clinical assessments of treatment responses are typically based on extremely sparse datasets. We propose a workflow for choosing an appropriate model for tumor growth and treatment response, verifying parameter identifiability, and assessing the amount of data necessary to precisely calibrate model parameters in order to make accurate predictions of tumor size at future times. Throughout this talk, we will discuss ways in which we can bridge the gap between mathematical modelers and clinical physicians to better harness the power of both worlds to meet a common goal.

Student Colloquium Talk by Professor Kenny Barrese, Bucknell University

Abstract: Rook theory is a branch of mathematics which considers how many ways you can put rooks on a board so that no two are attacking each other. Here a “rook” is the usual chess piece, but the “board” that we are placing on probably is not an eight by eight square. One way to consider the numbers you obtain is as coefficients of a polynomial, the rook polynomial. It is a key result in rook theory that, if you define the rook polynomial correctly, it always factors completely! In fact, we will see that this factorization arises not by algebraic manipulation, but by counting things in a clever way.