Clay Mathematics Institute / PROMYS 2018 Research Projects

Mentoring of Research Projects:

The PROMYS/CMI mentors in 2018 were the following research mathematicians: Professor Matt Baker (Georgia Tech), Dr. John Bergdall (Michigan State University), Lila Greco (Cornell University), Professor Paul Gunnells (UMass Amherst), Professor Nathan Kaplan (UC Irvine), Dr. Michael King (Bowdoin College), Dr. Erick Knight (University of Toronto), Professor Lionel Levine (Cornell University), Professor Steven Miller (Williams College), Dr. Ananth Shankar (MIT), and Dr. Joshua Zelinsky (Iowa State 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 2018 were:

Characteristics of Hyperfields obtained as Quotients of Finite Fields
Proposed by: Professor Matt Baker (Georgia Tech)

Class Groups of Function Fields
Proposed by: Dr. Erick Knight (University of Toronto) and Dr. Ananth Shankar (MIT)

Expansions of Natural Numbers and of Real Numbers
Proposed by: Dr. Michael King (Bowdoin College)

Greedy Avoidance of Arithmetic Progressions
Proposed by: Lila Greco (Cornell University) and Professor Lionel Levine (Cornell University)

Left, Center, Right
Proposed by: Professor Nathan Kaplan (UC Irvine)

Averages of Divisors
Proposed by: Dr. Joshua Zelinsky (Iowa State University)

Permutation Statistics
Proposed by: Professor Paul Gunnells (UMass Amherst)