Visits of scientific guests
Series of lectures given by Prof. Jacek Jendrej
About the lecturer
Jacek Jendrej, CNRS and Sorbonne Paris Nord University.
His research focuses on the long-term behavior of solutions to nonlinear wave equations, particularly on the study of multi-solitons. His work with A. Lawrie on the wave maps equation earned him the 'Cours de la Fondation Claude-Antoine Peccot' at the Collège de France in 2019, as well as the 'Juliusz Schauder Prize for Young Mathematicians' from Nicolaus Copernicus University in Toruń. He is a recipient of an ERC Starting Grant for his research in the field of nonlinear dispersive equations.
Course title: Dispersive partial differential equations
The aim of the course is to provide a brief introduction to the field of nonlinear dispersive equations.
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06.03.2024, 12:15 - 14:00, room no. 3250
Lecture 1 - Oscillatory integrals and stationary phase
In the first lecture, the notion of the Fourier Transform will be recalled and we will see a useful method from Harmonic Analysis called the "stationary phase approximation". -
08.03.2024, 10:15 - 12:00, room no. 5840
Lecture 2 - Linear wave equations and Strichartz estimates
The second lecture will be devoted to the linear wave equation and the Strichartz estimates, which provide a way of quantifying how waves spread in space as time passes. -
12.03.2024, 10:15 - 12:00, room no. 3260
Lecture 3 - Equivariant wave maps equation and its well-posedness in the energy space
In the final lecture, we will consider a particular nonlinear wave equation called the "equivariant wave maps equation". We will see that, thanks to the Strichartz estimates introduced in the previous lecture, well-posedness results for finite-energy initial data can be obtained as an easy application of the Banach fixed-point theorem.
The aim of the lecture series is to present the proof of A. Lawrie and myself of the soliton resolution for equivariant wave maps.
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03.04.2024, 12:15 - 14:00, room no. 3250
Lecture 4 - Overall strategy. Decay of energy in the self-similar region. -
05.04.2024, 10:15 - 12:00, room no. 5840
Lecture 5 - Linear and nonlinear profile decomposition. Small kinetic energy implies bubbling. -
09.04.2024, 10:15 - 12:00, room no. 4060
Lecture 6 - Modulation method. -
12.04.2024, 10:15 - 12:00, room no. 5840
Lecture 7 - Conclusion of the proof.