Date and Time: Friday, Dec 3, 2021, 10:00-11:00 a.m. (China time)
Zoom ID: 913 0849 7114
Passcode: 471585
Zoom link: https://duke.zoom.us/j/91308497114?pwd=VzdXUldVM1VjQUJPM1lhckZ6NjZXZz09
Event/Title: Optimization Problems Arising in CR Geometry
Speaker: John P. D’Angelo – Professor from University of Illinois at Urbana-Champaign
Abstract:
This talk considers several optimization problems arising from solving systems of linear equations that arise when studying polynomial sphere maps. Given a source dimension n and a degree d, one studies the collection of real polynomials of degree d, with non-negative coefficients, that equal 1 on the hyperplane x1+x2+…+xn=1. Since the linear system is under-determined, one seeks solutions optimizing various expressions. Two of these problems lead to fascinating combination of analysis and combinatorial number theory. One of these problems can be solved in all dimensions except 2 but seems to be impossibly difficult in 2 dimensions. We conclude with some connections to CR Geometry.
