Robert D. Hough

Robert "Bob" Daniel Hough is an American mathematician who specializes in probability theory, discrete mathematics, and analytical number theory.

Hough studied mathematics and computer science at Stanford University with a bachelor's degree in 2007 and a master's degree in computer science in 2008 and received his doctorate in mathematics with Kannan Soundararajan in 2012 (Distribution problems in number theory). As a post-doctoral student , he was at the Institute for Advanced Study and Ben Green in Oxford in 2015/16 . He is an Assistant Professor at the State University of New York at Stony Brook .

He deals with the applications of combinatorics and probabilistic methods in number theory (including distribution of extreme values ​​of L-functions) and random walk to groups (partly with Persi Diaconis ).

In 2017 he received the David P. Robbins Prize (MAA) for solving a problem from Paul Erdös . He showed that there is an upper limit of for the smallest modulus of a covering system of congruences. A system of covering congruences is a system ( ) with such that every natural number satisfies at least one of the congruences. Erdös asked whether there are systems whose smallest modulus is arbitrarily large. ${\displaystyle 10^{16}}$ ${\displaystyle a_{i}\mod m_{i}}$ ${\displaystyle i=1,\cdot \cdot \cdot k}$ ${\displaystyle 1<m_{1}<\cdot \cdot \cdot <m_{k}}$ ${\displaystyle m_{1}}$

Web links

• Homepage, Stony Brook
• Website at the IAS

Individual evidence

1. ↑ Robert D. Hough in the Mathematics Genealogy Project (English)
2. ^ Hough, Solution of the minimum modulus problem for covering systems, Annals of Mathematics, Volume 181, 2015, pp. 361–382, Arxiv
3. ^ Robbins Prize for Hough, IAS