## JOINT MATHEMATICS COLLOQUIUM

 Continuous linear combinations of polynomials

# János Kollár

Princeton University

### MIT

#### Tea from 4:00 - 4:30 p.m. in Room 2-290

 Abstract:   Let $f_1,\dots, f_r$ be polynomials in $n$ variables. We consider the following two questions: 1. Which continuous functions $\phi$ can be written in the form $\phi=\sum_i \phi_i f_i$ where the $\phi_i$ are continuous functions? 2. Which polynomials $g$ can be written in the form $g=\sum_i \phi_i f_i$ where the $\phi_i$ are continuous functions? (As a warm-up exercise, write $x^2 y^2=\phi_1 x^3+\phi_2 y^3$ where the $\phi_i$ are continuous functions.) After reviewing earlier work on similar questions, I plan to outline two answers to these problems. (Joint work with Charles Fefferman)

 Web page:  Alexandru I. Suciu Comments to:  alexsuciu@neu.edu Posted: February 17, 2011 URL: http://www.math.neu.edu/bhmn/kollar11.html