Clay Mathematics Institute / PROMYS 2017 Research Projects

Mentoring of Research Projects:

The PROMYS/CMI mentors in 2017 were the following research mathematicians: Professor Jayadev Athreya (University of Washington), Professor Joshua Zelinsky (Birmingham-Southern College), Professor Paul Gunnells (University of Massachusetts, Amherst), Professor Jared Weinstein (Boston University), Professor Daniel Jerison (Cornell University), Professor Lionel Levine (Cornell University), Dr. Erick Knight (University of Toronto) and Professor Matt Baker (Georgia Tech). 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 2017 were:

Benford's Law in Linear Recurrences and Continued Fractions
Proposed by: Professor Jayadev Athreya (University of Washington)
Students: Michelle He, Brian Huang, Aadeesh Shastry, Mirilla Zhu
Counselor: Adam Block

Benford's Law and Ulam Sequences
Proposed by: Professor Jayadev Athreya (University of Washington)
Students: Nicholas Alvarez, Andrew Hwang, Aaron Kriegman
Counselor: Larsen Linov

Tau Ideals in Number Fields
Proposed by: Professor Joshua Zelinsky (Birmingham-Southern College)
Students: Kushagr Ahuja, Patrick Lei, Dylan Pentland
Counselor: Ishan Levy

Coxeter Nim
Proposed by: Professor Paul Gunnells (University of Massachusetts, Amherst)
Students: Niraek Jain-Sharma, Michelle Qin, Katherine Wu, Christianna Xu
Counselor: Kevin Lin 

Billiard Trajectories on Integrable Polygons and Cutting Sequences in Equilateral Triangles
Proposed by: Professor Jared Weinstein (Boston University)
Students: Sathwik Karnik, Steven Ma, Eugene Shao, Albert Xu
Counselor: Magda Hlavacek

Random Game Trees
Proposed by: Professor Daniel Jerison (Cornell University and Professor Lionel Levine (Cornell University)
Students: Sungwon Kim, Tarang Saluja, Arya Vadnere
Counselor: Samuel Marks

2-Torsion in Class Groups
Proposed by: Dr. Erick Knight (University of Toronto)
Students: Jeremy Chen, Johnny Coudsi, Adit Vishnu Pathirissery Manoj, Jonathan Yang
Counselor: Andreea Iorga

On the Gonality Conjecture for Graphs
Proposed by: Professor Matt Baker (Georgia Tech)
Students: Vandana Agarwala, Soumen Ghosh, Erik Jahn, Kenz Kallal, Philip Lamkin
Counselor: Stanislav Atanasov