Research

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

In particular, I study functional inequalities, such as logarithmic Sobolev inequalities, on various geometric settings.

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, Submitted, arxiv.

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

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

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

Joint with R.Neel, Submitted, arxiv.

Invited talks:

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

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

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

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

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

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

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

8. MathFest, Philadelphia, August 5, 2022

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

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

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

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

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

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

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

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

Talks:

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

2. Colloquium, Lehigh University, September 27, 2023

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

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

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

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

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

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

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

10. 19th Northeast Probability Seminar, November 20, 2020 (Online)

11. 45th Annual New York State Regional Graduate/Undergraduate Mathematical Conference, March 28, 2020 (Online)

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

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