Clay Mathematics Institute / PROMYS 2014 Research Projects

Mentoring of Research Projects:

The PROMYS/CMI mentors in 2014 were the following research mathematicians: Professor Laurent Berger (École Normale Supérieure de Lyon), Dr. Henry Cohn (Microsoft Research), Professor Keith Conrad (University of Connecticut), Professor Paul Gunnells (University of Massachusetts, Amherst), Dr. Jonathan Hanke, and Dr. Victor Rotger (Universitat Politècnica de Catalunya, Barcelona).  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 2014 were:

The Casas-Alvero Conjecture
Proposed by: Professor Laurent Berger (École Normale Supérieure de Lyon)
Students: Vineet Gupta, Wentong Zhang, Joseph Zurier
Counselor: Akhil Mathew

Metacommutation and the Projective Line over Fp
Proposed by: Dr. Henry Cohn (Microsoft Research)
Students: Adam Forsyth, Jacob Gurev, Shakthi Shrima
Counselor: Raffael Singer

Metacommutation in the Hurwitz Integers
Proposed by: Dr. Henry Cohn (Microsoft Research)
Students: Christopher Zhang, Hyun Jong Kim, Suna Kim
Counselor: Joseph Stahl

Nonunique Factorization
Proposed by: Professor Keith Conrad (University of Connecticut)
Students: Yevgeniy Antipov, Calvin Lee, Anastasia Prokudina, Andreas Ravichandran
Counselor: Sam Mundy

Discriminants of Polynomials with Coefficients in Finite Fields
Proposed by: Professor Keith Conrad (University of Connecticut)
Students: Jonathan Chan, Steven Kwon, Michael Seaman
Counselor: Zhaorong Jin

Generalized Johnson Schemes and Eberlein Polynomials
Proposed by: Professor Paul Gunnells (University of Massachusetts, Amherst)
Students: Roger Van Peski, Uma Roy, Yael Goldstein
Counselor: David Mehrle

Full Flag and Type A Johnson Graphs
Proposed by: Professor Paul Gunnells (University of Massachusetts, Amherst)
Students: Linhan Chen, Arjun Khandelwal, Jongwon Kim, Bohan Yu
Counselor: Dylan Yott

Analysis of Various Portfolios and Their Generalizations
Proposed by: Dr. Jonathan Hanke
Students: Song Duong, Walter Li, Phillip Yoon
Counselor: Michael Greenberg

Portfolio Theory
Proposed by: Dr. Jonathan Hanke
Students: Bryan Zhu, Justin Yim, Nicholas Wu
Counselor: Hanna Astephan

The Art of Solving Equations
Proposed by: Dr. Victor Rotger (Universitat Politècnica de Catalunya, Barcelona)
Students: Angela Song, Leon Ochmann, In Hee Ho
Counselor: Petru Hlihor