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We discuss applications of the Milnor-Thom Theorem, a result from AlgebraicGeometry concerning signs of polynomials, to the combinatorics of geometricconfigurations. In particular, we define an {it abstract lineconfiguration}, modelled on line configurations in $mathbb{R}^3$, and showthat there are many forbidden sub-configurations. We discuss theimplications for unavoidable "stacked" sets of lines via theErdH{o}s-Hajnal conjecture, and pose several open questions. Joint workwith Uli Wagner of ETH Z"{u}rich.

Baseball is a sport whose statistics are ingrained in the collectiveconsciousness of their fans. Ask any baseball fanatic to identify thesenumbers, and the response should be immediate: 56, 2130, 2632, 61 in 61,73, 4191, 4256, .406, 714, 755, 5714, 511, 7. Baseball fans also like toargue about which player or team is better, and the extensive history andrich landscape of numbers in the sport lends itself to spirited chats overa hot stove as well as mathematical analyses. It is not quite the HotStove season, but we will chat about some of the mathematics used toanalyze baseball statistics -- the study of baseball statistics is knownas "sabermetrics." Mathematical ideas like Markov chains, Monte Carlosimulation, and linear regression are used to shed new light on Americas sporting pastime. Some rudimentary knowledge of baseball and baseballstatistics is probably helpful, but not absolutely necessary.

We consider a two-dimensional weakly dissipative dynamical system withtime-periodic coefficients. Their time average is governed by a degenerateHamiltonian whose set of critical points has an interior. The dynamics ofthe system is studied in the presence of three time scales. Using themartingale problem approach and separating the involved time scales, weaverage the system to show convergence to a Markov process on a stratifiedspace. The corresponding strata of the reduced space are a two-sphere, apoint, and a line segment. Special attention is given to the domain of thelimiting generator, including the analysis of the gluing conditions at thepoint where the strata meet. The gluing conditions resulting from thehierarchy of the time scales are similar to the conditions on the domain ofskew Brownian motion.

In this talk I will present joint work with John Etnyre on classificationand structure theorems for Legendrian knots in the standard contact3-space. I will describe some of the unexpected phenomena that arise alongthe way.