Clay Mathematics Institute / PROMYS 2019 Research Projects

Mentoring of Research Projects:

The PROMYS/CMI mentors in 2019 were the following research mathematicians: Professor Jayadev Athreya (University of Washington), Professor Matthew Baker (Georgia Institute of Technology), Professor John Bergdall (Bryn Mawr), Dr. Jeremy Booher (University of Arizona), Professor Diana Davis (Swarthmore College), Dr. Erick Knight (University of Toronto), Professor Lionel Levine (Cornell University), Ryan McDermott (Cornell 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 2019 were:

Lower Bounds on a-Numbers of Artin Schreier-Curves
Proposed by Dr. Jeremy Booher (University of Arizona)

Exponents of Jacobians of Graphs and Regular Matroids
Proposed by: Professor Matthew Baker (Georgia Institute of Technology)

Metaheuristics For Optimizing Voter Distributions Against Partisan Gerrymandering
Proposed by: Professor Diana Davis (Swarthmore College)

Bernoulli Sandpiles On The Infinite Ladder Graph
Proposed by Professor Lionel Levine and Ryan McDermott (Cornell University)

Characterizing D for Integer-Solvable x2 − Dy2 = −1
Proposed by Dr. Erick Knight (University of Toronto)

Representation Theory and Dickson’s Theorem
Proposed by Professor John Bergdall (Bryn Mawr)

Ulam Sequences
Proposed by Professor Jayadev Athreya (University of Washington)