Clay Mathematics Institute / PROMYS 2015 Research Projects

Mentoring of Research Projects:

The PROMYS/CMI mentors in 2015 were the following research mathematicians: Dr. Henry Cohn (Microsoft Research), Professor David Rohrlich (Boston University), Professor Victor Rotger (Universitat Politècnica de Catalunya, Barcelona), Professor Jared Weinstein (Boston University), Professor Lionel Levine (Cornell University), Professor Keith Conrad (University of Connecticut), Professor Paul Gunnells (University of Massachusetts, Amherst), and Professor Laurent Berger (École Normale Supérieure de Lyon). 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 2015 were:

Improved Bounds for Kissing Numbers in Dimensions 25-31
Proposed by: Dr. Henry Cohn (Microsoft Research)
Students: Kenz Kallal, Tomoka Kan, Eric Wang
Counselor: Claudia Feng

Sets of Pairwise Equidistant Points
Proposed by: Professor David Rohrlich (Boston University)
Students: Jeremy Taylor, Marc Isern Hacker, David Amirault
Counselor: Kevin Lin

Dynamical Systems and Number Theory
Proposed by: Professor Victor Rotger (Universitat Politècnica de Catalunya, Barcelona)
Students: Kara Luo, Sam Marks, Roshan Padaki
Counselor: Sam Mundy

Running Sums and Stopping Times
Proposed by: Professor Jared Weinstein (Boston University)
Students: Vanshika Jain, Dhruv Medarametla, Roshni Sahoo
Counselor: Petru Hlihor

Box-Ball System
Proposed by: Professor Lionel Levine (Cornell University)
Students: Victor de Fontnouvelle, Karthik Karnik, Mikaeel Yunus
Counselor: Samuel Zbarsky

Degrees and linear diophantine equations in F[x]
Proposed by: Professor Keith Conrad (University of Connecticut)
Students: Arthur Dennis, Kathryn Zhao
Counselor: Joseph Stahl

Heisenberg continued fractions
Proposed by: Professor Paul Gunnells (University of Massachusetts, Amherst)
Students: Ned Sanger, Nina Anikeeva
Counselor: Larson Linov

Modular representations of GL(2,F_p)
Proposed by: Professor Laurent Berger (École Normale Supérieure de Lyon)
Students: Michael Seaman
Counselors: Joseph Zurier, Yael Goldstein, Arjun Khandelwal