Date: March 1
Title: Experimental Mathematics, a computational approach to number theory’s greatest challenges
Speaker: Romain Popescu
Abstract: In this talk I will generalize the euclidean algorithm and continued fractions to PSLQ/LLL algorithm. I will give some basic definitions and explanations for what an algorithm is but we will focus more on the number theoretic applications of PSLQ/LLL instead of the algorithm itself. I will begin by showing the power of PSLQ on simple problems like computing bounds on transcendence of constants or playing with systems of equations. Then we move on to important results of the field such as Spigot algorithms and their connection to normality of base representations in constants such as pi. Another famous problem we mention is the Riemann Hypothesis. As time permits I will touch upon other important number theory topics such as PV numbers or some applied math computations.