Graduate course (Spring 2018, Spring 2019, Spring 2020) at the University of Cergy-Pontoise:
Regularity for Partial Differential Equations: elliptic equations, homogenization and fluid mechanics
- Lecture 1: Caccioppoli's inequality and applications
- Lecture 2: Improved regularity in periodic homogenization and Liouville theorems
- Lecture 3: Harnack's inequality and Moser's proof of the De Giorgi-Nash-Moser theorem
- Lecture 4: De Giorgi's proof of the De Giorgi-Nash-Moser theorem
- Lecture 5: Calderón-Zygmund decomposition, BMO and John-Nirenberg's inequality
- Lecture 6: Epsilon regularity for the Navier-Stokes equations
Short graduate course (December 2017) at Kyoto University, Japan:
Blow-up, compactness and (partial) regularity in Partial Differential Equations
Watch videos: the link does not directly lead to the lectures, so search for
- Lecture 1: number 243, Compactness methods in homogenization, part 1
- Lecture 2: number 244, Compactness methods in homogenization, part 2
- Lecture 3: number 245, Partial regularity for Navier-Stokes, part 1
- Lecture 4: number 246, Partial regularity for Navier-Stokes, part 2
With
Baoping Liu I gave a series of
introductory classes to PDEs at the
REU 2015 of the Department of Mathematics at The University of Chicago.
Here is a list of the classes I taught at The University of Chicago (2013-2015):
- Math 27300, Basic Theory of Ordinary Differential Equations (Winter 2015)
- Math 20000, Mathematical Methods for Physical Science 1 (Fall 2014)
- Math 20400, Analysis 2 (Fall 2014)
- Math 20100, Mathematical Methods for Physical Science 2 (Winter 2014)
- Math 20500, Analysis 3 (Winter 2014)
- Math 20000, Mathematical Methods for Physical Science 1 (Fall 2013)
- Math 20400, Analysis 2 (Fall 2013)