Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Drew Sills**, Rutgers University, asills {at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: On Monochromatic Van der Waerden Triples

Speaker: **Aaron Robertson**, Colgate University

Date: Thursday, February 15, 2007 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

We show that the minimum number of monochromatic 3-term arithmetic progressions that any 2-coloring of [1,n] can have is between 0.0511 n^2 (1+o(1)) and 0.0534 n^2(1+o(1)). This disproves the conjectured answer of 0.0625 n^2 (1+o(1)) as well as a more general conjecture.