What is the maximum number of edges in a graph on n vertices without triangles? Mantel’s answer in 1907—that at most half of the edges can be present—started a new field: extremal combinatorics. More generally, what is the maximum number of edges in an n-vertex graph that does not contain any subgraph isomorphic to H? What about if you consider hypergraphs instead of graphs? I will introduce the technique of sums of squares and discuss how it can be used to attack such problems.
The Puddle Jumping Society is a celebrational collage of musical theater songs and original dance inspired by the 1952 MGM classic Singin’ in the Rain. Directed by Ron Bashford, music directed by Caroline Lee, adapted and choreographed by Anna Plummer. The show will run March 26-28 in Kirby Theater. Rehearsals begin in January (during Interterm) and continue through March 26.
Singer/actor auditions are Wednesday, November 6, from 7 to 9 p.m. and Saturday, November 9, from 1 to 4 p.m. in Webster Hall, Studio 2. Students from all five colleges are welcome. You should come prepared with a 32-bar cut of a song you just really enjoy singing or two contrasting 16-bar cuts. Please provide sheet music for the accompanist. Registration required.