Clay Mathematics Institute / PROMYS 2020 Research Projects

Mentoring of Research Projects:

The PROMYS/CMI mentors in 2020 were the following research mathematicians: Professor Jayadev Athreya (University of Washington), Dr. Henry Cohn (Microsoft Research Institute and MIT), Professor Diana Davis (Swarthmore College), Dr. Cameron Freer (MIT), Professor Paul Gunnells (University of Massachusetts at Amherst), Professor Kiran Kedlaya (University of California at San Diego), Professor Mike Mitzenmacher (Harvard University), Dr. Rehana Patel (Wesleyan University), Wayne Peng (University of Rochester), Professor Maya Saran (Ashoka University Delhi India), Professor Thomas Tucker (University of Rochester), and Dr. Joshua Zelinsky (The Hopkins School at New Haven). Each submitted research problems for advanced students to work on. The materials presented by the mentors included problem statements, hints for getting started and references to the pertinent literature.

Research Projects in the summer of 2020 were:

Beyond Pick’s Theorem: Ehrhart Polynomials and Mixed Volumes
Proposed by Kiran Kedlaya (University of California at San Diego)

Heapable Sequences
Proposed by Mike Mitzenmacher (Harvard University)

Continuous Functions and Notions of Smallness
Proposed by Cameron Freer (MIT), Rehana Patel (Wesleyan University), and Maya Saran (Ashoka University Delhi India)

Counting Matrices
Proposed by Jayadev Athreya (University of Washington)

Forgetful Fibonacci Sequences
Proposed by Joshua Zelinsky (The Hopkins School at New Haven)

Gerrymandering 1
Proposed by Diana Davis (Swarthmore College)

Gerrymandering 2
Proposed by Diana Davis (Swarthmore College)

Hypergraph Catalan Number
Proposed by Paul Gunnells (University of Massachusetts at Amherst)

Narain Lattices
Proposed by Henry Cohn (Microsoft Research Institute)

Open Problems Related to Voting Power
Proposed by Joshua Zelinsky (The Hopkins School at New Haven)

Some Counting Problems in Finite Fields
Proposed by Wayne Peng and Thomas Tucker (University of Rochester)