This course is aimed at introducing an area of mathematics at the forefront of current research in harmonic analysis. The solution of the so-called A2 conjecture in 2010 by Tuomas Hytönen was an impressive milestone in Calderón-Zygmund theory. The efforts to simplify the original proof led to the development of the theory of sparse domination. The philosophy of this theory is that the quantitative behavior of many operators in harmonic analysis can be understood by studying very simple averaging operators (called sparse operators) whose structure captures the complexity of the former. After a review of classical Calderón-Zygmund theory, in this course we will study sparse operators and how they can be used to answer questions about other important operators, including endpoint behavior and weighted inequalities, among others.

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This course is aimed at introducing an area of mathematics at the forefront of current research in harmonic analysis. Guest lecturer: José Manuel Conde Alonso (Researcher Ramón y Cajal, Universidad Autónoma de Madrid): He is a Spanish mathematician and Ramón y Cajal Tenure-Track Assistant Professor at the Universidad Autónoma de Madrid (UAM). He completed his Ph.D. in Mathematics at UAM and the Instituto de Ciencias Matemáticas (ICMAT) in 2015. He has held positions at Brown University and the Universitat Autňnoma de Barcelona, supported by ERC grants. He has received several awards, including the ‘Vicent Caselles’ Prize from the Spanish Royal Mathematical Society and the Junior Faculty Teaching Fellow Award from Brown University. His research focuses on harmonic analysis, geometric measure theory, and Calderón-Zygmund theory.

In presenza

Presentazione orale

P.D.1-1 - Novembre

November