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Math & Stats Department Colloquium

Friday, November 19th, 2021

Time: 2:30 p.m.  Place: Jeffery Hall 234 & Online (via Zoom)

Speaker: Brad Rodgers (¾ÅÐãÖ±²¥)

Title: How random are arithmetic sequences?

Abstract: In this talk I will outline some of the ways that number theoretic sequences -- despite being deterministic -- can be fruitfully studied using the language of probability. Two fundamental number theoretic sequences I hope to discuss are the sequence of primes and the sequence of squarefree numbers (which are numbers whose prime factorization contains no repeated factors). I will focus especially on the statistical distribution of these sequences inside relatively small intervals. In the former case there is a conjectural link to random matrix theory, while in the latter case I will discuss forthcoming work with O. Gorodetsky and A. Mangerel which establishes a link to fractional Brownian motion.

Brad Rodgers is an Assistant Professor in the Department of Mathematics and Statistics at ¾ÅÐãÖ±²¥. He obtained his Ph.D. in Mathematics from the University of California, Los Angeles in 2013. He held a postdoctoral position at the Institut für Mathematik at University of Zurich from 2013 to 2015, and was a Postdoc Assistant Professor at the University of Michigan from 2015 to 2018. His research interests are in analysis, number theory and probability. He is especially interested in problems at the interface of random matrix theory and analytic number theory.