The goal of this program is to introduce some of the path breaking developments in harmonic analysis in recent years. In particular, the program is focused on polynomial methods in harmonic analysis and discrete harmonic analysis. Polynomial methods in harmonic analysis: In the recent years there have been remarkable developments in the direction of Fourier restriction and Bochner-Riesz conjectures using the polynomial method. This method involves using tools from algebraic geometry to solve problems in various areas of mathematics. In particular, the method has been fruitful in addressing outstanding open problems in harmonic analysis. Discrete harmonic analysis: The discrete analogues in harmonic analysis with connections to number theoretic problems have been an active area of research in harmonic analysis. It is quite remarkable that in the recent years the powerful technique of sparse domination in the continuous setting has been developed to address problems related to discrete a...
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