# Colloquium on "Sparse bounds: history and open questions" by Jose Conde Alonso (Brown University)

### Event Description:

Title: Sparse bounds: history and open questions

Abstract: Calderón-Zygmund operators like the Hilbert transform

are nearly ubiquitous and appear naturally in many areas of Mathematics.

The general theory associated with them was first systematically studied

in the second half of the 20-th century and they remain very interesting

objects in harmonic analysis. The A2 theorem, originally proved in full

generality by Hytönen in 2010, closed a 15 year long effort by the mathematical

community to understand the precise dependence of the norm

of these operators in terms of the measures upon which they naturally

act. Later attempts to simplify the proof of this theorem led to the introduction

of sparse operators. It turns that these operators, which are

simple averaging objects (almost as simple as a conditional expectation)

govern the behavior of Calderón-Zygmund operators among many other

of interest to harmonic analysts. We will survey some of the exciting

recent developments in this area and their consequences, and we will explore

which questions remain open in this area and the consequences their

answer would entail.

### Event Contact

**Contact Name: **Cristina Pereyra

**Contact Phone: **(505) 307-9629

**Contact Email: **crisp@math.unm.edu