PCMI 2025 Graduate Summer School
The Graduate 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 2025 Program: Extremal and Probabilistic Combinatorics
Organizers: Julia Böttcher (London School of Economics), Jacob Fox (Stanford University), Penny Haxell (University of Waterloo), Robert Morris (IMPA), and Wojciech Samotij (Tel Aviv University)
Extremal and probabilistic combinatorics are two central branches of contemporary discrete mathematics. The first of these two branches studies how large (or how small) a discrete structure can be given that it satisfies a certain set of restrictions; the second investigates random combinatorial objects using a blend of combinatorial methods and tools of probability theory. These two fields have been growing at a stunning rate over the last few decades and are nowadays considered to be an important part of mainstream mathematical research.
The aim of the planned summer graduate program at PCMI is to provide in-depth introduction to several preeminent themes and methods in extremal and probabilistic combinatorics, with particular emphasis on strong connections of these fields with other areas of mathematics such as analysis, geometry, number theory, statistical physics, and theoretical computer science. The core of the program will be nine graduate mini-courses taught by a diverse group of leading researchers in the field renowned for their clear and engaging lecturing styles. In parallel, we plan thematic workshops aimed at more senior researchers as well as activities for undergraduate students.
The PCMI Summer Session will be held July 6-26, 2025.
