Probability in Number Theory

Les probabilités en théorie des nombres

May 14 – June 8, 2018

Organizers: Andrew Granville (Montréal), Dimitris Koukoulopoulos (Montréal), Maksym Radziwill (McGill)

The appearance of Probability in Number Theory can be traced back to a famous collaboration of Erdős and Kac. Nowadays, probabilistic techniques are routinely used in the study of integers and L-functions. However, until recently there had not been much room for modern and deep techniques of probability theory. During the past few years this has changed notably. Conversely, number theoretic techniques and heuristics have been proven effective in resolving standing problems in combinatorics and discrete probability theory. The goal of this month-long program is to bring together experts from Number Theory and Probability to highlight and facilitate the interactions between these two fields of mathematics.

During the first week of our program, there will be a workshop (an ISM discovery school) aimed at young researchers (postdocs and advanced graduate students) who work or are interested in the field of Probabilistic Number Theory. The workshop will consist of mini-courses given by Kevin Ford (Illinois), Adam Harper (Warwick), K. Soundararajan (Stanford) and Terence Tao (UCLA).

The remainder of the program will gather at CRM several of the leading experts in the fields of Probability and Number Theory. We also invite applications for five month-long postdoctoral positions (details to follow). Among other things, we will run a frequent research seminar for the participants of our program.