About the Mathematics Research Communities:

Mathematics Research Communities (MRC), a program of the American Mathematical Society (AMS), nurtures early-career mathematicians--those who are close to completing 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; opportunities for support for collaborative travel; and guidance in career building. The program provides for 40 funded participants.

The 2023 summer conferences will be held at Beaver Hollow Conference Center, Java Center, NY, where participants can enjoy a private, distraction free environment conducive to research. Beaver Hollow is located in Western New York, 45 minutes from the Buffalo Niagara International Airport, one hour from Rochester or Niagara Falls.

Those accepted into this program will receive travel support for a summer conference, and will be partially supported for their participation in the Joint Mathematics Meetings which follow in January 2024 in San Francisco, CA. All participants are expected to be active in the full MRC program.

ELIGIBILITY: Individuals within one to two years prior to the receipt of their PhDs, and up to five years after receipt of their PhDs, are welcome to apply. Generally, applicants should apply to one of the programs that best matches their research interest. Applications to two MRCs are allowed, but an individual will not be selected to participate in more than one MRC. Individuals applying to three or more MRCs may be disqualified. Most of those supported by NSF funds to participate in the MRC program will be US-based, that is, employed by or a full-time student at a US institution at the time of the MRC summer conference. However, the terms of the grant allow for a limited number of individuals who are not US-based to be supported. Depending on space and other factors, a small number of participant slots may be available for self-funders. Applicants wishing to be considered as possible self-funded participants should email ams-mrc@ams.org at the time they apply and state that intention. Self-funders must satisfy the same criteria for admission as those who receive grant support. Individuals who have previously participated in an MRC will not be considered for admission without a clear rational articulated in the application for repeating, and in any event, no one may be an MRC participant more than twice.

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, applicants who have had to slow down or temporarily stop their 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.

Applications will close at 11:59 p.m. Eastern Time on Tuesday, February 15, 2023.

Note that all applicants will be notified of their status by May 1, 2023.

Week 2b: June 4-10, 2023 -- Derived Categories, Arithmetic and Geometry

Organizers:

Matthew Ballard, University of South Carolina
Katrina Honigs, Simon Fraser University
Daniel Krashen, University of Pennsylvania
Alicia Lamarche, University of Utah
Emanuele Macrì, Université Paris-Saclay

Since their introduction by Grothendieck and Verdier, derived categories have become an essential tool in the study of algebraic geometry. Their ability to bridge within subfields and to other areas of mathematics is compelling. At the same time, derived categories remain mysterious in many ways and our collective understanding is still in its very early stages. Tantalizing conjectures shimmer on the horizon and new paths branch every day.

This MRC will equip the participants with a solid foundation in the modern tools for studying derived categories in algebraic geometry and provide them a greater vista across the field. Even if a participant's interests are not directly in derived categories, they will see how derived categories can be a useful tool for and an insightful perspective into their own work.

Specific topics of focus include:

• Bridgeland stability
• Homological projective duality
• Enhancements
• Computational aspects

Those already interested in moduli problems, representation theory, non-commutative algebra, and birational geometry should find stimulating points of contact with these topics. We welcome all as participants and especially encourage those historically under-represented in the field. We aim to foster a welcoming environment.