Oct

12

2015

The space of Euclidean/spherical/hyperbolic polyhedral metrics on a surface with cone points is the set of all equivalence classes of Euclidean/spherical/hyperbolic polyhedral metrics on the surface. The decorated Teichmüller space is the set of all decorated hyperbolic metric on the surface minus the cone points up to isometry isotopic to the identity map. The Teichmüller space of a surface with boundary is the space of all equivalence classes of hyperbolic metrics with geodesic boundary on the surface minus the cone points. The five spaces of metrics are C^1-diffeomorphic to each other.

Oct

12

2015

The 2-D Surface Quasi-Geostrophic Equations have been under

investigation due to some interesting ties between this 2-D model and the

3-D Euler equations. In this talk we will explore a blow-up condition on

solutions to the 2D Quasi-Geostrophic Equations that is analogous to the

well known Beale-Kato-Majda blow-up condition for solutions to 3D Euler.

Oct

12

2015

The dynamics of fluids, i.e. liquids and gases, is an important part of the continuum mechanics. This lecture is devoted to the qualitative analysis of mathematical models of motion of a viscous incompressible fluid around a compact body *B*, translating and rotating in the fluid with given time-independent translational and angular velocities *u _{∞}* and

Oct

13

2015

Following a strategy developed by Athreya and Cheung, we compute the gap distribution of the slopes of saddle connections on the octagon by translating the problem to a question about return times of the horocycle flow to an appropriate Poincare Section. This same strategy was used by Athreya, Chaika, and Lelievre to compute the gap distribution on the Golden L. The octagon is the first example of this type of computation where the Veech group has two cusps.

Oct

13

2015

We describe and characterize an extension to the classical path coupling method referred to as aggregate path coupling. In conjunction with large deviations estimates, we use this aggregate path coupling method to prove rapid mixing of Glauber dynamics for a large class of statistical mechanical models, including models that exhibit discontinuous phase transitions which have traditionally been more difficult to analyze rigorously.