At the end of May there was a two-day conference at MIT for the PRIMES program. About 30 high school students presented the research they’ve done over the last 6 months, as part of collaborative teams including grad students and sometimes undergrads, professors and post-docs at MIT and a few nearby universities. The quality of the work overall was quite impressive, even without taking into consideration that it was primarily performed by high school students. The talk abstracts are available on the PRIMES website; the papers that result will go online some time in December or January. You can read last years’ papers here.
Several contributors to this blog were mentors of PRIMES students: my students Ravi and Nihal presented some very nice work on generalizations of pattern avoidance in alternating permutations; this extends work in my thesis as well as work of Julian West and collaborators on shape-Wilf equivalence. Steven’s student Sheela presented work that’s a continuation of a project she began last year on the representation theory of Cherednik algebras. Yan’s student Aaron (who also is my coauthor in work based on his PRIMES project from 2011) presented his work studying the number of ways to put a graded poset structure on a given graph. As I understand it, this question comes from work of Yan on adinkras, and is both natural and apparently unstudied. The cutest result Aaron presented was the following: if G is a graph all of whose cycles are generated by its 4-cycles then the number of graded poset structures on G is , where is the chromatic polynomial of G.