The 2019 Mathematics Research Communities (MRC) summer conferences were held, at Whispering Pines Conference Center in West Greenwich, Rhode Island. The three week-long conferences drew 122 early-career mathematicians. Funded in part by the National Science Foundation, these conferences are part of the AMS MRC program, which also includes special sessions at the Joint Mathematics Meetings, a longitudinal study, and continued connections and collaborations.
"The focus on group work was unlike any other conference I've attended. But that was also the best part of the whole thing."
"It (MRC) was the most worthwhile conference/workshop that I've been to. I was able to talk to people who I was previously too shy to talk to, and I learned a lot from everyone. . . ."
- Organizers: Dan Berwick-Evans, University of Illinois at Urbana-Champaign; Emily Cliff, University of Illinois at Urbana-Champaign; Nora Ganter, University of Melbourne; Arnav Tripathy, Harvard University; Joshua Jeishing Wen, University of Illinois at Urbana-Champaign
One of the tried-and-true techniques in representation theory is to apply topological invariants to spaces built out of Lie groups. The workshop focused on this paradigm where the invariant is equivariant elliptic cohomology. Elliptic cohomology has deep roots in homotopy theory, algebraic geometry, and mathematical physics.
"I really enjoyed the close atmosphere as well as the diverse group of expertise and interests that were represented at the MRC."
- Gerandy Brito, Georgia Institute of Technology; Michael Damron, Georgia Institute of Technology; Rick Durrett, Duke University; Matthew Junge, Duke University, David Sivakoff, Ohio State University
The goal was to better understand the global behavior of random systems driven by local interactions.
- Organizers: Renee Bell, University of Pennsylvania; Julia Hartmann, University of Pennsylvania; Valentijn Karemaker, University of Pennsylvania; Padmavathi Srinivasan, Georgia Institute of Technology; Isabel Vogt, Massachusetts Institute of Technology
The focus was on problems in arithmetic geometry over fields of positive characteristic p that are amenable to an explicit approach, including the construction of examples, as well as computational exploration. Compared to algebraic geometry in characteristic 0, studying varieties over fields of characteristic p comes with new challenges (such as the failure of generic smoothness and classical vanishing theorems), but also with additional structure (such as the Frobenius morphism and point-counts over finite fields) that can be exploited.