Maximal Functions Associated to Families of Curves in the Plane by Joshua Zahl

PROGRAM
MODERN TRENDS IN HARMONIC ANALYSIS

ORGANIZERS
Jotsaroop Kaur (IISER Mohali, India) and Saurabh Shrivastava (IISER Bhopal, India)
DATE & TIME
26 June 2023 to 07 July 2023
VENUE
Ramanujan Lecture Hall, ICTS Bengaluru
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 averages and the corresponding maximal functions.

There will be a dedicated lecture series on each of the above topics by the experts. These lectures will provide an introduction to the above methods in a self contained manner. One of the major aims of the lectures is to give an overview of these new techniques in solving problems related to harmonic analysis. Further some future prospects will also be discussed involving polynomial methods and discrete harmonic analysis. The program will help participants in following the recent developments in the field and undertake research projects in these exciting areas of harmonic analysis.

Thematic Lectures:

Theme 1 : Sharp restriction estimates
Speaker: Diogo Oliveira e Silva

Theme 2 : Quadrature rules on manifolds
Speaker: Giacomo Gigante

Theme 3: Discrete harmonic analysis
Speaker: Michael Lacey (Georgia Institute of Technology, US)

The program will also feature invited research talks with a focus on the above themes of the program.

List of Invited Speakers:

Benjamin Krause, King’s College, London UK (Online)
Blazej Wrobel,University of Wroclaw, Poland (Online)
Chandan Biswas, Indian Institute of Science, Bengaluru
David Beltran, University of Valencia, Spain (Online)
Diogo Oliveira e Silva, Instituto Superior Técnico, Lisboa, Portugal
Emanuel Carneiro, Abdus Salam International Centre for Theoretical Physics, Italy (Online)
Eyvindur Ari Palsson, Virginia Tech, US
Giacomo Gigante, University of Bergamo, Italy
Giuseppe Negro, Instituto Superior Técnico, Lisbon, Portugal
Jongchon Kim, City University of Hong Kong, Hong Kong
Joshua Zahl, University of British Columbia, Canada (Online)
Larry Guth, Massachusetts Institute of Technology, US (Online)
Malabika Pramanik, University of British Columbia, Canada (Online)
Neal Bez, Saitama University, Japan (Online)
Po Lam Yung, Australian National University, Australia (Online)
Sanghyuk Lee, Seoul National University, South Korea (Online)
Theresa Anderson, Carnegie Mellon University, US (Online)
ICTS is committed to building an environment that is inclusive, non discriminatory and welcoming of diverse individuals. We especially encourage the participation of women and other under-represented groups.

Eligibility Criteria:

All mathematicians are welcome. Preference will be given to researchers who work in areas related to the themes of the workshop.