Research

My research lies at the intersection between probability, analysis and geometry. 

In particular, I study functional inequalities, such as logarithmic Sobolev inequalities, and their applications to different fields on various geometric settings via both continuous and discrete approaches.

Papers:

1. Logarithmic Sobolev inequalities on non-isotropic Heisenberg groups

Joint with M. Gordina, Journal of Functional Analysis 283(2022), 33pp.

2. Logarithmic Sobolev inequalities on homogeneous spaces

Joint with M. Gordina, IMRN, 2024.

3. Construction of a Dirichlet form on metric measure spaces of controlled geometry

Joint with A. Butaev, N. Shanmugalingam, Potential Analysis, 2025.

4.  Non-Markovian maximal couplings and a vertical reflection principle on a class of sub-Riemannian manifolds

Joint with R.Neel, Transactions of the AMS, 2025.

5. Logarithmic Sobolev inequalities on infinite-dimensional reduced Heisenberg groups

Joint with M. Gordina, Submitted, 2025.

6. Heat content and spectral heat content of the subordinated Brownian motion on Carnot groups

Joint with M. Gordina, A. Pinamonti and R. Sarkar, In preparation, 2025.

7. Approximation of harmonic functions on metric measure spaces of controlled geometry via discrete graphs

     Joint with A. Butaev, N. Shanmugalingam, In preparation, 2025.

Invited talks:

1. Analysis, Probability, and Geometric Mapping Theory in Non-smooth Spaces, AMS Spring Eastern Sectional

Meeting, Boston College, March 28-29, 2026 (Expected)

2. Analytic–Geometric Synergies: Harmonic Analysis and Convexity, CMS Winter Meeting, Toronto, December,

2025 (Expected)

3. Recent Trends in Discrete and Continuous Probability, AMS Fall Central Sectional Meeting, St Louis University,

October 18, 2025

4. Prob/Stat seminar, Lehigh University, October 16, 2025

5. Progress in Discrete and Continuous Probability Conference, Union College, July 25, 2025

6. 8th Cornell Conference on Analysis, Probability, and Mathematical Physics on Fractals, Cornell University, June17, 2025

7. PDE and Applications Seminar, Queen’s University, October 25, 2024

8. PDE and Applications Seminar, Queen’s University, October 4, 2024

9. 8th Cornell Conference on Analysis, Probability, and Mathematical Physics on Fractals, Cornell Unive

10. Conference on New Developments in Probability, Centre de Recherches Math´ematiques (CRM) at Universit´e de Montr´eal, September 26, 2024

11. Stochastic and Geometry Workshop, Banff International Research Station for Mathematical Innovation and

Discovery (BIRS), September 10, 2024

12. Not Only Scalar Curvature Seminar (Online), June 5, 2024 

13. Interactions between Analysis, Geometric Measure Theory, and Probability in Non-smooth Spaces, AMS Spring Eastern Sectional Meeting, Howard University, April 6, 2024

14. Seminar, Hausdorff Center for Mathematics, Germany, December 8, 2023 (Online)

15. New Trends in Stochastic Analysis, The Casa Mathematica Oaxaca, Mexico, May 25, 2023

16. Interactions between Analysis, PDE, and Probability in Non-smooth Spaces, AMS Spring Central Sectional Meeting, University of Cincinnati, April 14, 2023

17. Analysis seminar, University of Cincinnati, October 20, 2022

18. Concentration Week on Geometry and Analysis on Nonsmooth Spaces, Texas A&M, August 12, 2022

19. MathFest, Philadelphia, August 5, 2022

20. Women in Analysis Research Network Event, AWM Research Symposium, University of Minnesota, June 18, 2022

21. Session on Stochastic Analysis and Applications, The 2022 Union College Mathematics Conference, Union College, June 5, 2022

22. Probability/Stat Seminar, University of Illinois Chicago, February 16, 2022 (Online)

23. Probability Seminar, University of Virginia, March 24, 2021 (Online)

24. Geometric Inequalities and Nonlinear Partial Differential Equations, AMS Fall Central Sectional Meeting, University of Texas at El Paso, September 12, 2020 (Online)

25. Probabilistic Methods in Geometry and Analysis, AMS Spring Southeastern Sectional Meeting, University of Virginia, March 13, 2020 (Cancelled due to COVID-19)

26. Probability Seminar, Wuhan University, China, July 2, 2019

27. International Conference on Stochastic Analysis and Related Fields, Jiangsu Normal University, China, June 26, 2019

Talks:

1. Poster Session, Frontiers in Sub-Riemannian Geometry, Centre International de Rencontres Math´ematiques

      (CIRM), Marseille, France, November 25-29, 2024

2. Poster Session, Seminar on Stochastic Processes, Rice University, March 7, 2024

3. Colloquium, Lehigh University, September 27, 2023

4. Poster Session, Seminar on Stochastic Processes, University of Arizona, March 9, 2023

5. Postdoctoral Day, Lehigh University, September 2, 2022

6. AGRS junior seminar, MSRI, April 25, 2022

7. Poster Session at Symposium on Stochastic Hybrid Systems and Applications, University of Connecticut, November 12-13, 2021

8. Poster Session, The 10th International Conference on Stochastic Analysis and its Application, Kyoto University, September, 2021 (Online)

9. Session for Early Career Participants, BIRS Workshop: Stochastic and Geometry, March 11, 2021 (Online)

10. AWM Graduate Student Poster Session, The 2021 Joint Mathematics Meetings, January 8, 2021 (Online)

11. 19th Northeast Probability Seminar, November 20, 2020 (Online)

12. 45th Annual New York State Regional Graduate/Undergraduate Mathematical Conference, March 28, 2020 (Online)

13. Poster Session, Seminar on Stochastic Processes, Michigan State University, March 5-7, 2020 (Did not attend due to COVID-19)

14. Research Seminar, Women and Math: Topics in Geometric Analysis, Institute for Advanced Study, May 28, 2019