Clay Mathematics Institute / PROMYS 2012 Research Projects

Mentoring of Research Projects:

The PROMYS/CMI mentors in 2012 were the following research mathematicians: Amanda Beeson (University of Rochester), Ira Gessel (Brandeis), Paul E. Gunnells (UMass Amherst), Ben Harris (Louisiana State University), and Kirsten Wickelgren (Harvard). 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.

Topics for Research Projects in the summer of 2012 were:

Hyperplane Arrangements
Proposed by Paul E. Gunnells
Students: Zach Izzo, Tony Qiao, Tony Zeng
Counselor: Erick Knight

Deformations of Symmetric Functions and Character Formulas
Proposed by Paul E. Gunnells
Students: Robin Zhang, Mitchell Harris, Luran He, Chris Kong, Pravina Samaratunga, Nic Trieu
Counselor: Tim Holland

Root Subsystems and Weyl Group Representations
Proposed by Ben Harris 
Students: Aditya Gopalan, Thomas Li, Erin McCloskey, Leo Tinone
Counselor: Qiaochu Yuan 

Random Involutions and the Distinct Prime Divisor Function
Proposed by Kirsten Wickelgren
Students: Uthsav Chitra, Eric Fegan, Zubin Mukerjee
Counselor: Zev Chonoles

Random Involutions and the Number of Prime Factors of an Integer 
Proposed by Kirsten Wickelgren 
Students: Sheela Devadas, Michael Dunn Goekjian, Hirsh Jain
Counselor: Zev Chonoles

The Fibonacci Numbers 
Proposed by Ira Gessel
Students: Larsen Linov, Lisa Kong, Hyun Jong Kim
Counselor: Tomer Reiter

Points on Parabolas 
Proposed by Amanda Beeson
Students: Ritwik Anand, John Lee, Bilyana Tzolova
Counselor: Ian Frankel