Georgia Institute of Technology College of Sciences

This is a summer school (June 18th - July 6th) in computational algebraic geometry intended for graduate students, however, everyone is welcome to attend. For details and schedule see aga.gatech.edu. The first day's schedule has been slightly altered; we will give introductory lectures at 9:30 (Anton Leykin -- Computer Algebra and Numerical Algebraic Geometry), 11:30 (Greg Blekherman -- Convexity), and 2:00 (Josephine Yu -- Tropical Geometry).

This work is concerned with the Almost Axisymmetric Flows with Forcing Terms which are derived from the inviscid Boussinesq equations. It is our hope that these flows will be useful in Meteorology to describe tropical cyclones. We show that these flows give rise to a collection of Monge-Ampere equations for which we prove an existence and uniqueness result. What makes these equations unusual is the boundary conditions they are expected to satisfy and the fact that the boundary is part of the unknown. Our study allows us to make inferences in a toy model of the Almost Axisymmetric Flows with Forcing Terms.

There is little known about the existence of contact strucutres in high dimensions, but recently in work of Casals, Pancholi and Presas the 5 dimensional case is largely understood. In this talk I will discuss the existence of contact structures on 5-manifold and outline an alternate construction that will hopefully prove that any almost contact structure on a 5-manifold is homotopic, though almost contact structures, to a contact structure.