I'm James Leng, a math graduate student at UCLA. Before coming to UCLA, I was an undergraduate student at UC Berkeley from 2017-2020. I am on the job market during the fall of 2024.
Contact:
email: jamesleng + "at" + math + "dot" + ucla + "dot" + edu
Office: MS 3965. You can often find me in MS 6620.
(replace "at", "dot" with appropriate symbols).
Teaching:
I have been a teaching assistant for the following classes:
Summer 2024: Math 31B: Integration and Infinite Series
Summer 2023: Math 31A: Differential and Integral Calculus.
Summer 2021: Math 170S, Introduction to Probability and Statistics
Spring 2021: Math 131A, Real Analysis
Winter 2021, Math 32B, Calculus of Several Variables
Fall 2020, Math 32B, Calculus of Several Variables
Research:
I'm working with Terence Tao. I'm interested in arithmetic combinatorics, dynamical systems, and Fourier analysis, focusing mostly on the field Higher Order Fourier Analysis. My research is supported by an NSF Graduate Research Fellowship Grant No. DGE-2034835.
Selected work:
J. Leng. Efficient equidistribution of periodic nilsequences and applications
J. Leng, A. Sah, and M. Sawhney. Quasipolynomial bounds on the inverse theorem for the Gowers U^{s+1}[N]-norm.
J. Leng, A. Sah, and M. Sawhney. Improved Bounds for Szemerédi's Theorem.
J. Leng. A Quantitative Bound for Szemeredi's Theorem for a Complexity One Polynomial Progressions over Z/NZ. https://arxiv.org/abs/2205.05540. Discrete Analysis 2024:3, 33 pp.
The rest of my work can be found here.
Talks:
ICMS conference in additive combinatorics Summer 2024
Stanford Analytic Number Theory Seminar Spring 2024
Harvard/MIT Richard P. Stanley Seminar in Combinatorics Spring 2024
Virginia Tech Analysis Seminar Spring 2024
JMM 2024 AIM Special Session on Multiplicative Number Theory and Additive Combinatorics
ETA Seminar Fall 2023
UCLA Analysis and PDE Seminar Fall 2023
AMS Southeastern Sectional on Discrete Analysis Spring 2023.
Caltech Discrete Analysis Seminar Spring 2023
UCLA Participating Analysis Seminar: Spring 2021, Fall 2021, Winter 2022, Spring 2022, Winter 2023, Spring 2023
JMM 2019
I have occasionally been mistaken (by the UC Berkeley architecture department, in fact) as James Leng, a lecturer of architecture at Berkeley.