Clay Mathematics Institute / PROMYS 2013 Research Projects

Mentoring of Research Projects:

The PROMYS/CMI mentors in 2013 were the following research mathematicians: Arul Shankar (Institute of Advanced Study, Princeton University), Jacob Tsimerman (Harvard University), Paul E. Gunnells (University of Massachusetts, Amherst), David Rohrlich (Boston University), Ira Gessel (Brandeis University), Glen Hall (Boston University), and Jared Weinstein (Boston University). 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 2013 were: 

Lattices and Flags
Proposed by Arul Shankar and Jacob Tsimerman (Institute of Advanced Study at Princeton University and Harvard University)
Students: Tony Qiao,  Saarik Kalia, Erin McCloskey, and John Lee

A Generalization of Tokuyama's Formula to Hall-Littlewood Polynomials
Proposed by Paul E. Gunnells (University of Massachusetts, Amherst)
Students: Emma Xu, Uma Roy, Roger Van Peski, and Vineet Gupta

Adelic Integers
Proposed by David Rohrlich (Boston University)
Students: Calvin Qi, Danielle Kim, Justin Yim, and Yael Goldstein
Counselor: Sam Mundy

Lattice Paths
Proposed by Ira M. Gessel (Brandeis University)
Students: Stephanie Chin and Walter Ho 
Counselor: Michael Greenberg

Repeated Round-off Error
Proposed by Glen Hall (Boston University)
Students: Jiahan Liu, John Long, and Siddarth Seethepalli
Counselor: Sandy Neal

The Zeta Function of a Graph
Proposed by Jared Weinstein (Boston University)
Students: Sam Montgomery, Tim Ratigan, Gabriel Ravel, and Joseph Zurier
Counselor: Dylan Yott