Lectures in Honor of Jean-Pierre Rosay on the occasion of his retirement

Lectures in honor of Jean-Pierre Rosay
on the occasion of his retirement

 
Complex Analysis Seminar            Wednesday, April 28, 4:00 PM, in B321 Van Vleck
            Dror Varolin (Stony Brook) will speak:
            “Interpolation of L2 data from a singular hypersurface”
 
Abstract. We present our results on extension of L2holomorphic functions from possibly singular hypersurfaces in complex Euclidean space. First we discuss some sufficient conditions for L2extension; these conditions are on (i) the density of the hypersurface, and (ii) the structure of its singularities. We then show that at least the conditions of type (ii) that we present are not necessary for extension.
 
Colloquium                                        Friday, April 30, 4:00 PM, in B239 Van Vleck           
            Dror Varolin (Stony Brook) will speak:
            “L2 methods in complex geometry”            

 
Abstract. The relation between complex analysis and algebraic geometry is the subject of a story that began a long time ago, has evolved along a number of interwoven strands, and is still far from fully told. In this talk we will tell a story along one particular strand involving the Laplace equation and equations that evolved from it. We will discuss several major results in the subject, beginning with Kodaira’s Embedding Theorem and ending with some more recent results in birational geometry.
 
Special Lecture                Saturday, May 1, 2:45 PM, in B139 Van Vleck
            Dror Varolin (Stony Brook) will speak:
 
            "Positive Hermitian Polynomials as Quotients of Squares"
 
Abstract. We discuss several notions of positivity of bihomogeneous Hermitian polynomials. These notions came up in the work of D'Angelo in proper holomorphic maps between balls.

Among these positivity notions is that of quotients of squares, which is the Hermitian analog of a real polynomial being a sum of squares of rational functions. In the real setting, Hilbert asked (in his 17th problem) whether every polynomial with only nonnegative values is a sum of squares of rational functions. Artin gave an affirmitive answer using methods that have since been developed considerably in Mathematical Logic. We will discuss the analogous result in the setting of Hermitian polynomials. Our methods, however, will be rather different, consisting of ideas from Bergman kernel asymptotics and elementary birational geometry.
 
Special Lecture                Saturday, May 1, 4:00 PM, in B139 Van Vleck
            John Erik Fornaess (University of Michigan) will speak:
 
            “Laminations by Riemann surfaces”       

 
Abstract. I will discuss recent joint work with Nessim Sibony and Erlend Wold on laminations by Riemann surfaces.
 
Schedule for Saturday, May 1
 
2:00 – 2:40 PM            Remarks on the career of Jean-Pierre Rosay, B139 Van Vleck
 
2:50 – 3:50 PM            Special lecture by Dror Varolin, B139 Van Vleck
 
4:00 – 5:00 PM            Special lecture by John Erik Fornaess, B139 Van Vleck