It is impossible to be a mathematician without being a poet in soul
- Sofia Kovalevskaya
Research interests
My work focuses on investigating how probabilistic techniques and functional inequalities can be applied and extended to gain a better understanding of the connections between analytic, geometric and probabilistic aspects of stochastic processes in highly porous and non-smooth setting.
Examples of this kind of spaces include the Sierpinski gasket (hand-made picture), the Sierpinski carpet, the Vicsek set, diamond fractals, and more generally metric measure spaces with sub-Gaussian heat kernel estimates.
Preprints and publications
- Korevaar-Schoen p-energies and their Gamma-limits on Cheeger spaces (with F. Baudoin), submitted (2024). arXiv.
- Dirichlet forms on metric measure spaces as Mosco limits of Korevaar-Schoen energies (with F. Baudoin), Annali della Scuola Normale Superiore di Pisa (2024). arXiv.
- Oscillations of BV measures on nested fractals (with F. Baudoin), Journal of Fractal Geometry (2023). arXiv.
- Minimal gap in the spectrum of the Sierpinski gasket, International Mathematics Research Notices (2021). arXiV.
- Yet another heat semigroup characterization of BV functions on Riemannian manifolds (with F. Baudoin), Annales de la Faculte des Sciences de Toulouse (2021). arXiv.
- Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates (with F. Baudoin, L. Chen, L. Rogers, N. Shanmugalingam and A. Teplyaev), Cal. Var. and PDE's (2021) arXiv.
- Gagliardo-Nirenberg, Trudinger-Moser and Morrey inequalities on Dirichlet spaces (with F. Baudoin), Journal of Mathematical Analysis and Applications (2021). arXiv.
- Heat kernel analysis on diamond fractals, Stochastic Processes and their Applications (2021) arXiv.
- Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates (with F. Baudoin, L. Chen, L. Rogers, N. Shanmugalingam and A. Teplyaev), Cal. Var. and PDE's (2020) arXiv.
- Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities (with F. Baudoin, L. Chen, L. Rogers, N. Shanmugalingam and A. Teplyaev), Journal of Functional Analysis (2020) arXiv.
- Analysis on hybrid fractals (with Y. Chen, H. Gu, R.S. Strichartz and Z. Zhou), Comm. Pure App. Anal. (2020) arXiv.
- Explicit formulas for heat kernels on diamond fractals, Comm. Math. Phys. (2018) arXiv.
- Completely symmetric resistance forms on the stretched Sierpinski gasket (with U. Freiberg and J. Kigami), J. of Fractal Geometry (2018) arXiv.
- Entropy-based inhomogeneity detection in fiber materials (with E. Spodarev), Methodology and Computing in Applied Probability (2017) arXiv.
- Power dissipation in fractal Feynman-Sierpinski AC circuits, Journal of Mathematical Physics (2017) arXiv.
- Estimation of entropy for Poisson marked point processes (with E. Spodarev), Advances in Applied Probability (2017) arXiv.
- Weyl asymptotics for Hanoi atrractors (with U. Freiberg), Forum Mathematicum (2017) arXiv.
- The limit theorem for maximum of partial sums of exchangeable random variables (with A. Rakitko), Statistics & Probability Letters (2016) arXiv.
- Energy and Laplacian on Hanoi-type fractal quantum graphs (with D. Kelleher and A. Teplyaev), Journal of Physics A: Mathematical and Theoretical (2016) arXiv.