This grant will fund the participation of early career mathematicians at a conference on Foliation theory in algebraic geometry to be held at the Simons Foundation's Gerald D. Fischbach Auditorium in New York City, September 3rd-7th, 2013. There will be lectures on recent advances in birational geometry, foliations, hyperbolicity and related subjects. This conference will give experts a chance to disseminate the many recent advances to young people working in these areas.
Algebraic geometry is the study of the solutions to a collection of polynomial equations. This began more than two thousand years ago, with the study of the geometry of conic sections, such as circles. However we still cannot completely answer many simple and fundamental questions, such as find the number of solutions. We know this number in many special cases, and these cases have interesting applications in engineering and biology. Foliation theory studies the solutions, or flow lines, to collections of differential equations. As differential equations model physical phenomena, foliation theory is useful in physics and engineering. When the collection of differential equations have polynomial coefficients, there is a rich interplay between algebraic geometry and foliation theory.
