Research Interest

My research interest lies at the interface of probability and analysis.

In particular, I am interested in the sharp and quantitative inequalities from probability and analysis, and their applications.

PhD Thesis: Stability for functional and geometric inequalities and a stochastic representation of fractional integrals and nonlocal operators (2019) [PDF]

My papers on arXiv can be found here.

Publications

1. Quantitative inequalities for the expected lifetime of Brownian motion
   Michigan Math. J. 70 (2021), no. 3, 615-634. [arxiv] [journal]
2. Instability results for the logarithmic Sobolev inequality and its application to related inequalities
   Discrete Contin. Dyn. Syst. 42 (2022), no. 9, 4297-4320. [arxiv] [journal]
3. Deficit estimates for the logarithmic Sobolev inequality
   (with Emanuel Indrei) Differ. Integral Equ. 34 (2021), no. 7-8, 437-466. [arxiv] [journal]
4. Hardy–Stein identity for non-symmetric Lévy processes and Fourier multipliers
   (with Rodrigo Bañuelos) J. Math. Anal. Appl. 480 (2019), no. 1, 123383. [arxiv] [journal]
5. Martingale transforms and the Hardy–Littlewood–Sobolev inequality for semigroups Potential Anal. 45 (2016), no. 4, 795–807. [arxiv] [journal]

Preprints

1. Curie–Weiss model under $\ell^p$-constraint and a Generalized Hubbard--Stratonovich Transform
   (with Partha Dey) submitted (2024). [arxiv]
2. On the principal eigenvalue for compound Poisson processes
   (with Hyunchul Park) preprint (2024).
3. On discrete second order Riesz transforms
   (with Rodrigo Bañuelos) preprint (2024).
4. Collaboration of random walks on graphs
   (with Partha Dey, Grigory Terlov) submitted (2023). [arxiv]
5. Sharp $\ell^p$ inequalities for discrete singular integrals on the lattice $\mathbb{Z}^d$
   (with Rodrigo Bañuelos, Mateusz Kwaśnicki) submitted (2022). [arxiv]
6. Fluctuation results for size of the vacant set for random walks on discrete torus
   (with Partha Dey) submitted (2021). [arxiv]

Talks

1. Analysis, PDE and Probability Seminar, KIAS, South Korea, January 2024.
2. Probability Winter School in Korea 2023, KIAS, South Korea, December 2023
3. Probability Seminar, Seoul National University, South Korea, December 2023
4. Analysis Seminar, University of Belgrade, Serbia, in Zoom, December 2023
5. SIAM Great Lakes Meeting, Michigan State University, October 2023
6. Stochastic Seminar, Georgia Institute of Technology, September 2023.
7. Probability seminar, Purdue University, May 2023.
8. Probability seminar, University of Illinois at Urbana–Champaign, May 2023.
9. Stochastic Seminar, Georgia Institute of Technology, November 2022.
10. Analysis, PDE and Probability Seminar, KIAS, South Korea, June 2022.
11. Probability Seminar, Seoul National University, May 2022.
12. Undergraduate Seminar, University of Illinois at Urbana-Champaign, April 2022.
13. AMS Spring Central Virtual Sectional Meeting, Special session on the Interface Between Nonlinear PDEs, Harmonic Analysis, and Quantitative Geometric and Functional Inequalities, Mar 2022.
14. AMS Spring Central Virtual Sectional Meeting, Special session on Spectral Estimation and Optimization, Mar 2022.
15. Analysis Seminar, University of Illinois at Chicago, Mar 2022.
16. Probability Seminar, University of Illinois at Urbana–Champaign, Oct 2021.
17. AMS Spring Central Sectional Meeting, Special session on Probabilistic and diffusion methods in analysis and geometry, University of Cincinnati, in Zoom, Apr 2021.
18. Theory of Markov Semigroups and Schrödinger Operators, Wrocław University of Technology, in Zoom, Mar 2021.
19. Geometric and functional inequalities and recent topics in nonlinear PDEs, Purdue University, in Zoom, Mar 2021.
20. Seminar on non-local operators, probability and singularities, in Zoom, Oct 2020.
21. International Conference on Elliptic and Parabolic Problems, Minisymposium, Gaeta, Italy, May 2019.
22. AMS Spring Eastern Sectional Meeting, Special session on Stochastic processes, University of Connecticut, Hartford, April 2019.
23. Probability seminar, University of Illinois at Urbana–Champaign, April 2019.
24. Probability seminar, Purdue University, February 2019.
25. Probability seminar, Seoul National University, March 2018.
26. Probability seminar, Purdue University, September 2017.
27. Probability seminar, University of Illinois at Urbana–Champaign, March 2017.
28. Probability seminar, Purdue University, February 2016.