Mathematics Research Communities (MRC), a program of the American Mathematical Society (AMS), nurtures early-career mathematicians--those who are close to finishing their doctorates or have recently finished--and provides them with opportunities to build social and collaborative networks through which they can inspire and sustain each other in their work.

The structured program is designed to engage and guide all participants as they start their careers. For each topic,the program includes a one-week summer conference; a Special Session at the next Joint Mathematics Meetings; and a longitudinal study of early career mathematicians.

The summer conferences of the MRC are held in the scenic mountain setting of the Snowbird Resort, Utah, where participants can enjoy the natural beauty and a collegial atmosphere. Those accepted into this program will receive support (full room and board at the Snowbird Resort and up to $650 in airfare) for the summer conference, and will be partially supported for their participation in the Joint Mathematics Meetings which follow in January 2018.

ELIGIBILITY: Individuals within one to two years prior to the receipt of their PhDs, or up to five years after receipt of their PhDs, are welcome to apply. The MRC program is open to individuals who are U.S. citizens as well as to those who are affiliated with U.S. institutions. A few international participants may be accepted. Women and underrepresented minorities are especially encouraged to apply. All participants are expected to be active in the full MRC program.

For any program, fellowship, prize or award that has a maximum period of eligibility after receipt of the doctoral degree, the selection committee may use discretion in making exceptions to the limit on eligibility for candidates whose careers have been interrupted for reasons such as family or health. Therefore, an applicant who has had to slow down or temporarily stop his or her career for personal reasons may request to be considered for an extension in the amount of time after the PhD degree. Please send exception requests to ams-mrc@ams.org.

REQUIREMENTS: Completed on-line application form One (1) reference letter submitted by a professor or supervisor who knows the applicant and can address how the applicant will benefit from, and contribute to, the MRC program.

Individuals who can cover their MRC participation costs from other sources of funding should contact AMS Senior Program Coordinator Steven Ferrucci at sxf@ams.org for instructions on how to apply.

Note that all applicants will be notified of their status by May 1, 2017.

Week 1: June 4 – 10, 2017-- Homotopy Type Theory

Organizers:
J. Daniel Christensen, University of Western Ontario
Chris Kapulkin, University of Western Ontario
Daniel R. Licata, Wesleyan University
Emily Riehl, Johns Hopkins University
Michael Shulman, University of San Diego

Homotopy Type Theory is a new area of research, combining ideas from homotopy theory and dependent type theory (a formal system studied in mathematical logic and theoretical computer science). It is based on the idea that the logical notion of equality between two objects can carry more information beyond its truth value and as such may resemble the notion of path between two points. Homotopy Type Theory is a new and rapidly growing area, attracting the attention of many researchers with expertise in a wide variety of disciplines.

The goal of this workshop is to bring together students and postdocs having some background in one (or more) of related areas —algebraic topology, category theory, mathematical logic, or computer science — to learn more about how they come together in homotopy type theory, and to work together to prove new results. Basic knowledge of just one of these areas will be sufficient to be a successful participant. At the workshop, participants and organizers will work together to share background knowledge in their expertise, and the participants will also work together on a variety of interesting problems in synthetic and abstract homotopy theory, higher category theory, as well as mathematical logic, theoretical computer science, and formalization of mathematics. In particular, interested participants can gain some experience working with a computer proof assistant.