# PhD defense: David Weirich

Event Type:

Colloquium

Speaker:

David Weirich

Event Date:

Monday, April 10, 2017 -

4:30pm to 6:00pm

Location:

SMLC 352

Audience:

Faculty/StaffStudents

### Event Description:

Title: Weighted inequalities for dyadic operators over spaces of homogeneous type.

Abstract:

A so-called space of homogeneous type is a set equipped with a quasi-metric and a doubling measure. We give a survey of results spanning the last few decades concerning the geometric properties of such spaces, culminating in the description of a system of dyadic cubes in this setting whose properties mirror the more familiar dyadic lattices in R^n. We then use these cubes to prove a result pertaining to weighted inequality theory over such spaces. We develop a general method for extending Bellman function type arguments from the real line to spaces of homogeneous type. Finally, we use this method to extend some recent results in the theory of weighted dyadic operators.

### Event Contact

**Contact Name: **David Weirich