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K-State Today

February 7, 2014

Mathematics Colloquium lecture today

Submitted by Reta McDermott

Tanya Firsova, Institute for Mathematical Sciences, Stony Brook University, will present "Generic Properties of Holomorphic Foliations" as part of the mathematics department Colloquium lecture series at 2:30 p.m. today in 122 Cardwell Hall.

The abstract for the lecture is: Holomorphic vector fields is an exciting subject exhibiting interesting chaotic behavior. This behavior can be seen even when the dimension of the ambient space is 2. In the talk we will concentrate on generic properties of holomorphic vector fields in C^2 or, more generally, of foliations on Stein manifolds, locally defined by vector fields. I will discuss the ideas of complex analysis and approximation theory that come into play. I will prove that a generic foliation is complex Kupka-Smale and completely describe the topology of leaves for generic foliations. I will also explain how some of these ideas can be used to study other foliations that naturally arise in dynamical systems, in particular the ones for polynomial utomorphisms of C^2.