When: Sunday, May 7,
10am
Where: Schreiber 309
Speaker: Shir Peleg-Priester, Tel Aviv
University
Title:
Sylvester-Gallai Type Theorems for Quadratic Polynomials
The Sylvester-Gallai (SG) theorem asserts that if a finite set of points has the property that every line passing through any two points in the set also contains a third point in the set then all the points in the set are colinear. Many variants of this theorem were studied: extensions to higher dimensions, colored versions, robust versions, and more. In this talk, we will see a polynomial version of SG theorem (and some of its variants) and prove generalizations to higher-degree polynomials (mainly quadratics). We will also show how we can use these theorems to obtain polynomial identity testing algorithms.
Based on Joint works with Amir Shpilka, Abhibhav Garg, Rafael Oliveira, Akash K Sengupta.