Applications for the 2023 American Mathematical Society Mathematical Research Communities are open including one on derived categories!

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.

This MRC is organized by Dr.’s Ballard, Katrina Honigs, Daniel Krashen, Alicia Lamarche, and Emanuele Macrì.