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

Event Type: 
Colloquium
Speaker: 
Jose Conde Alonso (Brown University)
Event Date: 
Thursday, December 13, 2018 -
3:00pm to 4:00pm
Location: 
SMLC 124
Audience: 
Faculty/StaffStudents

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