Congratulations to Duván Cardona for obtaining

The FWO Postdoctoral Fellowship

of The Research Foundation – Flanders (FWO).

About this fellowship: read more here!

The project: Fourier Integral Operators on Graded Lie groups.

About the project: the goal of this project is to contribute to the scientific program carried out for more than forty years (dating back to the works of Folland and Stein) in charge of extending the techniques from the Euclidean harmonic analysis to the more general setting of nilpotent Lie groups. The contribution of this project will be the construction of the theory of Fourier Integral operators (FIOs) on graded Lie groups. Developing a suitable theory of Fourier Integral Operators (FIOs) in this context will enable the solution of numerous unresolved problems in non-commutative harmonic analysis.

Keywords: Fourier Integral Operators, Microlocal Analysis, Control Theory, Harmonic Analysis, Partial Differential Equations.

Project Scope: the scope of this project involves the collaboration between the Ghent Analysis and PDE Center with a team formed by researchers from several foreign universities, including UCLA, University of Chicago, Cornell University, University of Wisconsin Madison, Queen Mary University of London, and the Imperial College London.

About Duván (visit his website here!). Duván Cardona earned his Bachelor’s degree in Mathematics from Universidad del Valle in 2015 under the supervision of Julio Delgado. He was associated as a Lecturer at different Colombian universities, such as Universidad de Los Andes and Pontificia Universidad Javeriana. In 2019, he began his doctoral studies under the supervision of Michael Ruzhansky. In 2018, he received an honorable mention from the Yu-Takeuchi Award, awarded by the Colombian Academy of Sciences. From 2022 to 2024, he will serve as the president of the scientific board for the continental project ICMAM Latin America. Adding to his achievements, he has been awarded this prestigious FWO Postdoctoral Fellowship by the FWO, Research Foundation, Flanders.

Read about Fourier Integral operators from Wikipedia here!.

Applications of Fourier Integral Operators in Real Life: Fourier integral operators serve as valuable tools for describing physical phenomena. They play a crucial role in understanding the evolution of waves over time as wave propagators. Waves, which are carriers of energy, can be observed in various domains, ranging from neuron pulses and blood flow in arteries to ocean waves. By employing Fourier integral operators, researchers can analyze and gain insights into diverse fields. For instance, in the medical field, these operators aid in the analysis of the cardiovascular system. In the realm of information theory, Fourier integral operators facilitate the study of waves like microwaves, radio waves, WiFi signals, and visible light. These operators are intrinsic mathematical objects that align with various numerical analysis techniques, enabling a comprehensive exploration of these phenomena and contributing to a deeper understanding of wave behavior and its implications in different areas of study.