IAS/Park City Mathematics Institute

Program ID: PCMI-GSS2019 [#724]
Program Title: Graduate Summer School 2019
Program Location: Park City, Utah 84060, United States [map]
Application Deadline: 2019/01/15 finished (2018/11/01, finished 2019/07/21, listed until 2019/01/15)
Program Description:    

*** this program has been closed, and no new applications will be accepted. ***

The Graduate Summer School bridges the gap between a general graduate education in mathematics and the specific preparation necessary to do research on problems of current interest. In general, GSS applicants will have completed their first year of graduate school, and in some cases, may already be working on a thesis. While most GSS participants will be graduate students, recent PhDs (PhD received less than 1 year ago) may also be interested in applying to the GSS. Some mobility is expected between the Graduate Summer School and the Research Program, but postdoctoral scholars who are more than one year after receipt of their PhD should consider applying to the Research Program, not to the Graduate Summer School.

The main activity of the Graduate Summer School will be a set of several interwoven minicourses offered by leading experts in the field, designed to introduce students to exciting, current research in mathematics. These minicourses will not duplicate standard courses available elsewhere. 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. Teaching assistants will be available for each minicourse.

Quantum field theory, a branch of high energy theoretical physics, has enjoyed a vigorous interaction with many parts of mathematics over the past several decades. The 2019 GSS will focus on invariants of smooth manifolds which arose in a broad sense from quantum field theory. There will be two introductory minicourses, one on mathematical gauge theory and the other on knot invariants. More advanced minicourses will cover such topics as Heegaard-Floer homology, knots and BPS states, characteristic classes for manifold bundles, BPS states and spectral networks, Higgs bundles, and applications of Floer homology. The goal of the program is to bring together students and researchers at all levels interested in these areas to share exciting recent developments in these subjects, stimulate further interactions, and inspire a new generation to pursue research at the interface of geometry and physics.

Student preparation: We seek motivated students interested in manifold invariants and in mathematical aspects of quantum field theory. Though familiarity with some of the topics listed above would be helpful, the formal general prerequisites are graduate-level courses in the basics of manifold theory, topology, and analysis. No formal training in physics is required. Additional prerequisites for individual courses are listed with the course descriptions.


1. Complete a Standard Coversheet for MathPrograms.Org. Your Standard Coversheet should include the name/s and email address/es of your reference writer/s. One letter of reference is REQUIRED (see below); you may submit up to two references in support of your application.

2. Provide one Reference Letter (REQUIRED). On the application, fill in the checkbox for your reference writer from the name you entered on your Standard Coversheet, then click on the green arrow next to the reference writer’s name so the writer will receive your reference request by email. When notified, your writers will then receive login info and upload instructions to come to the MathPrograms.org site to upload their letters. If your reference writer does not have access to a computer, he or she may submit the reference letter by mail no later than January 15, 2019.

3. Provide your Curriculum Vitae/Resume (REQUIRED): Applicants must upload their CV to their online application.

4. Provide a link to one preprint or publication.(OPTIONAL)

Application Materials Required:
Submit the following items online at this website to complete your application:
And anything else requested in the program description.

Further Info:
IAS/Park City Mathematics Institute
Institute for Advanced Study
1 Einstein Drive
Princeton, NJ 08540

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