# Po Lam Yung

## Contacts

### Research interests

- Lie Groups, Harmonic And Fourier Analysis
- Partial Differential Equations

I work in a branch of mathematics called harmonic analysis, with particular focus on singular integrals, Sobolev embeddings, time-frequency analysis, oscillatory integrals and Fourier decoupling. The goal is to obtain delicate estimates for various operators between function spaces, often motivated by the study of partial differential equations, several complex variables, Cauchy-Riemann (CR) geometry and analytic number theory.

More precisely, I am interested in sharpening some results of Bourgain and Brezis about embeddings of certain critical Sobolev spaces, and some related cancelling / cocancelling L^1 estimates of Van Schaftingen. I am also developing a pseudodifferential calculus, involving operators of mixed homogeneities, with applications to several complex variables and CR geometry. Furthermore, I am interested in problems from time-frequency analysis, particularly those related to Stein-Wainger type oscillatory integrals. Recently I have been working on Fourier decoupling inequalities and related applications.

### Groups

- Researcher, Analysis & geometry

Teaching at the Chinese University of Hong Kong

- Math 1010A, University Mathematics, Fall 2018
- Math 4060, Complex Analysis, Fall 2018
- Math 6081A, Topics in Harmonic Analysis I, Fall 2017
- Math 1010B, University Mathematics, Fall 2017
- Math 1010A, University Mathematics, Fall 2017
- Math 4900F, Capstone Seminar, Fall 2016
- Math 4060, Complex Analysis, Fall 2016
- Math 1010C, University Mathematics, Fall 2016
- Math 4900E, Capstone Seminar, Fall 2015
- Math 4060, Complex Analysis, Fall 2015
- Math 1010C, University Mathematics, Fall 2015
- Math 2060B, Elementary Analysis II, Spring 2015
- Math 1010C, University Mathematics, Fall 2014

Teaching at Oxford (as a Teaching Assistant)

- 2 sets of B4b. Hilbert spaces, Hilary term, 2014
- 2 sets of B5b. Applied PDEs, Hilary term, 2014
- 2 sets of B4a. Banach spaces, Michaelmas term, 2013
- 2 sets of C2.1a. Lie Algebras, Michaelmas term, 2013

Teaching at Rutgers, the State University of New Jersey

- Math 494, Independent Study in Complex Analysis, Spring 2013
- Math 135, Calculus I, Sections 09-11, Fall 2012
- Math 244, Differential Equations for Engineering and Physics, Sections 01-03, Fall 2012
- Math 252, Elementary Differential Equations, Section 02, Spring 2012
- Math 350, Linear Algebra, Sections 01-02, Fall 2011
- Math 403, Introduction to Theory of Functions of a Complex Variable, Section 02, Spring 2011
- Math 152, Calculus II for the Mathematical and Physical Sciences, Sections 01-03 and 01-09, Fall 2010

Teaching at Princeton (as a Teaching Assistant)

- Princeton Summer School in Analysis and Geometry '09, Several Complex Variables, Summer 2009
- MAT 330, Fourier Analysis, Spring 2009
- MAT 218, Analysis in Several Variables, Fall 2008
- MAT 102, Calculus with Analytic Geometry II, Spring 2008
- Princeton Summer School in Analysis and Geometry '07, Harmonic Analysis, Summer 2007