Abstract: Mr. Kyung-won Hwang
Title: A convex set in Z^k.
R. Graham, M. Simonovits, and V. T. Sos in 1980 posed the following question. Suppose S is a convex subset of Z^k, and let A_i be subsets of S whose pairwise intersections are non-empty and convex. If the A_i form a maximum such family, must the intersection of the A_i be non-empty? In this paper we answer this question in the negative by exhibiting a set S and a family of subsets of S for every dimension k>1. Then we will fix this question by asking a modified question, the answer to which we believe is in the affirmative. This is joint work with Naeem Shiekh.
Abstract: Prof. John E. Wetzel
Title: The worm problem - a status report
We report on some failed fits and starts on Leo Moser's well-known covering problem (especially having to do with the conjecture of long-standing that a 30 degree unit sector is a cover for all unit arcs in the plane); and we conclude with some positive recent developments hot off the press.