Hi, I'm Xuerui Yang (杨学睿), and you can refer to me as Irving. I'm currently a PhD candidate in the Department of Mathematics at UIUC under the supervision of Xiaochun Li. My research interest lies in the broad intersection of Analytic Number Theory and Harmonic Analysis. I am also drawn to Additive Combinatorics problems using Fourier-analytic tools.

Email: xueruiy3 [at] illinois [dot] edu

Here is my CV.

Publications and preprints:

7. Some Mizohata-Takeuchi-type estimate for exponential sums. Preprint

6. Bessel functions and Weyl's law for balls and spherical shells (with J. Guo, T. Jiang and Z. Wang), Adv. Math. 484 (2026), 110715. Journal Preprint 

5. An improvement on Gauss's Circle Problem and Dirichlet's Divisor Problem (with X. Li). Preprint

4. Extreme values of the derivative of Blaschke products and hypergeometric polynomials (with L. Kovalev), Bull. Sci. Math. 169 (2021), 102979. Journal Preprint

3. Near-isometric duality of Hardy norms with applications to harmonic mappings (with L. Kovalev), J. Math. Anal. Appl. 487 (2020), no. 2, 124040. Journal Preprint

2. Algebraic structure of the range of a trigonometric polynomial (with L. Kovalev), Bull. Aust. Math. Soc. 102 (2020), no. 2, 251-260. Journal Preprint

1. Fourier series of circle embeddings (with L. Kovalev), Comput. Methods Funct. Theory 19 (2019), no. 2, 323-340. Journal Preprint

Here is the link to all my papers on arXiv.

Upcoming Talks:

1.

Past Talks:

4. Analysis Seminar, IU Bloomington, October 2025. 

3. Stochastics and Discrete Analysis Seminar, NC State University, Sep 2025.

2. Analysis Seminar, MIT,  April 2025.

1. AMS Spring Central Sectional Meeting, University of Kansas, March 2025.