Clay Mathematics Institute / PROMYS 2006 Research Projects

Mentoring of Research Projects:

The PROMYS/CMI mentors in 2006 were the following research mathematicians: Jonathan Hanke (Duke University), Kiran Kedlaya (MIT), Ira Gessel (Brandeis University), and Paul Gunnells (UMass Amherst). Mentors submitted research problems and worked with the advanced students. 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 2006 were:

Quaternion Algebras
Proposed by Jonathan Hanke
Students: Jason Bland, Dan Echlin, Dan Fudenberg, Ben Wolf
Counselor: Josh Zelinsky

Proposed by Ira Gessel
Students: Adam Kaye, Irina Kholodenko, Erick Knight, Michael Shu, Nick Slowey
Counselor: Ben Harris

Quadratic Forms and Quadratic Fields
Proposed by Jonathan Hanke
Students: Philip Engel, Athena Jiang, Chris Kennedy, Seohyung Kim, Sara Silberstein
Counselor: Thanos Papaioannou

Finiteness Theorems for Quadratic Forms
Proposed by Jonathan Hanke
Students: Hana Cho, Veena Ramakrishnan, Arthur Wang
Counselor: Agnés Beaudry

Purely Periodic Continued Fractions
Proposed by Kiran Kedlaya
Students: Brian Edwards, Ben Huan, Djordjo Milovic, Will Steadman, Norman Yu
Counselor: Ila Varma