Department of Mathematics

Indian Institute of Science

Bangalore 560 012

SEMINAR

 Speaker : R. Sivaguru Affiliation : TIFR Subject Area : Mathematics Venue : Department of Mathematics, Lecture Hall I Time : 04:00 p.m. Date : March 22, 2016 (Tuesday) Title : "Holomorphic Extensions and the Bergman Projection" Abstract : We will begin with a brief overview of when holomorphic functions of more than one complex variable extend to a larger domain (Hartogs' Theorem and Pseudoconvexity). We then proceed to discuss a recent result which shows that, on a class of domains with circular symmetries, the Bergman projection of conjugate holomorphic functions (also called the Friedrichs operator) extend holomorphically to a larger domain. The Bergman projection, on a domain $\Omega$, is the orthogonal projection from $L^2(\Omega)$ onto $L^2(\Omega)\cap\{\text{holomorphic functions in } \Omega\}$. We will use simple examples and geometric reasoning throughout the presentation. This is joint work with Yunus Zeytuncu.