Title: The transcendental Bézout problem and coarse zero count
Abstract:
By the Bézout theorem, for a generic collection of complex polynomials p_1, ..., p_n in C[z_1, ..., z_n], the number of their common zeroes is bounded above by the product of the degrees. The transcendental Bézout problem asks whether an analogous statement holds for analytic functions of several complex variables. The counterexample of Cornalba and Shiffman shows that in higher dimensions the answer is negative if one counts the common zeroes in the "usual way". In my talk I will introduce a coarse count of the common zeroes, and will explain how it leads to a positive answer to the transcendental Bézout problem.
Based on a work in progress joint with Iosif Polterovich, Leonid Polterovich, Egor Shelukhin and Vukašin Stojisavljević.