The Gradate Summer School at PCMI consists of a series of several interwoven minicourses on different aspects of the main research theme of that summer. These courses are taught by leading experts in the field, chosen not only for their stature in the field but their pedagogical abilities. Each minicourse comprises three to five lectures. These minicourses vary in level of preparation needed, and the schedule is structured so there are good opportunities for students just entering the field as well as courses suitable for more advanced students. Each course is accompanied by a daily problem session, structured to help students develop facility with the material.
The GSS takes place within the broader structure of PCMI, so there are many researchers at all levels in the field in attendance, as well as participants in the other PCMI programs. This provides an outstanding way for graduate students to get to know leaders in their field and to interact with them in a leisurely way. There are also numerous group activities which allow participants in the GSS to interact with people in other groups, including formal and informal social events, and the PCMI Experimental Math Lab, which brings together small groups of participants to work on accessible and open-ended problems. Graduate students have many opportunities to get good advice about career paths after they complete their PhDs, and can meet mathematicians who are working at a wide variety of institutions, from top research centers to undergraduate-focused colleges.
There are three graduate minicourses scheduled each day (Wednesday afternoons are free) and problem sessions accompanying each minicourse. Participants may attend talks from the other programs as they see fit.
The 2020 Program: Number Theory Informed by Computation
Organizers: Jennifer Balakrishnan, Boston University; Kristin Lauter, Microsoft Research; Bjorn Poonen, MIT; and Akshay Venkatesh, Institute for Advanced Study
Number theory has always drawn inspiration from computational experiments; the importance and influence of computational number theory has steadily expanded over the last decades. The goal of the 2020 GSS is to bring together people working at the interface of number theory and computation, interpreted broadly. There will be minicourses on topics including algorithmic number theory, post-quantum cryptography, geometry of numbers, and arithmetic statistics; more advanced topics will include computation of zeta functions and computational arithmetic geometry.
Prerequisites: Most courses should be accessible to students who have completed graduate-level courses in algebraic number theory and algebraic geometry, including familiarity with elliptic curves. Advanced courses may require other prerequisites, which will be posted along with course descriptions.
The 30th Annual PCMI Summer Session will be held July 5 - July 25, 2020.