Richard Schwartz (Brown University) de 14h a 15h
The optimal paper Moebius band
If the number L is large you can take a 1xL rectangular strip, smoothly twist it in space, and glue the ends together so as to make an embedded paper Moebius band. If L is too small this is impossible. In this talk I will explain why L>sqrt(3) is a necessary and sufficient condition for the existence of a smoothly embedded paper Moebius band. This is the solution to the 1977 conjecture of B. Halpern and C. Weaver. I will also explain why a sequence of L-minimizing examples must converge to an equilateral triangle.
-------------------------
S. Filip (University of Chicago) de 15h30 a 16h30
Measure and Topological Rigidity Beyond Homogeneous Dynamics
To study the asymptotic behavior of orbits of a dynamical system, one can look at orbit closures or invariant measures. When the underlying system has a homogeneous structure, usually coming from a Lie group, with appropriate assumptions a wide range of rigidity theorems show that ergodic invariant measures and orbit closures have to be well-behaved and can often be classified. I will describe joint work with Brown, Eskin, and Rodriguez-Hertz, which establishes rigidity results for quite general smooth dynamical systems having some hyperbolicity. I will also explain some of the necessary assumptions as well as the homogeneous structures that emerge. | 
