The IAS/Park City Mathematics Institute (PCMI) is a three-week summer school in the mathematical sciences, held each July in Park City, Utah. Its primary goal is to promote the development of mathematics students, teachers and researchers through concurrent overlapping programs of undergraduate and graduate study, teacher development, and mathematical research activities. This award supports five components of PCMI. Three of these components are the Research Program, the Graduate Summer School and the Undergraduate Summer School, that are organized around a single area of contemporary mathematical research. The Research Program and Graduate Summer School are led by world-renowned mathematicians. Lecturers in the graduate and undergraduate programs are world leaders in their specialties. All are chosen for their expository abilities. A fourth component, the Undergraduate Faculty Program, considers that year's mathematical research topic in light of undergraduate education. It is lead by a specialist who is an excellent teacher at the undergraduate level. PCMI contributes to the development of under-represented minorities in the STEM disciplines through the fifth funded component, a one-week Workshop for Mentors of Undergraduate Research by Minority Students. Workshop participants develop research projects suitable for use in undergraduate research programs. Workshop participants go on to lead undergraduate research programs for under-represented minorities after attending PCMI. One key goal is to build a pipeline of minority students who are prepared to participate in PCMI's undergraduate and graduate summer schools. The dissemination of PCMI activities to the wider mathematical community of graduate students and researchers is accomplished through its publication program. Polished versions of the lectures from each year's Graduate Summer School constitute a volume published by the American Mathematical Society (AMS). Quite often, one of the undergraduate lecture series, or the Undergraduate Faculty program leads to an innovative undergraduate text, also published by the AMS. PCMI is also now embarking on a series of volumes incorporating material developed in its program for secondary school teachers.
The research themes for PCMI vary from year to year. Each theme is chosen to reflect current trends of high importance in the mathematical community and is based on the identification of organizers who take seriously the synergistic nature of PCMI. The research themes for the first three programs that will be funded by this award and their organizers are as follows:
2015: Geometry of Moduli Spaces and Representation Theory; Roman Bezrukavnikov, Alexander Braverman, and Zhiwei Yun
2016: The Mathematics of Data; Anna Gilbert and Michael Mahoney
2017: Random Matrices; Alexei Borodin, Alice Guionnet, and Ivan Corwin.