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 settings.
Examples of this kind of spaces include the Sierpinski gasket (hand-made picture), the Sierpinski carpet, the Vicsek set, diamond fractals,
general polygaskets and so-called fractional spaces.
A full list of my publications is available on arXiv.
Fall 2020 marked the start of the TAMU Fractals Research Team at Texas A&M.
Check out our website, our work may draw your interest!
- Minimal gap in the spectrum of the Sierpinski gasket.
to appear in International Mathematics Research Notices (2021) arXiV.
- Yet another heat semigroup characterization of BV functions on Riemannian manifolds (with F. Baudoin).
to appear in Annales de la Faculte des Sciences de Toulouse 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)
to appear in 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 497, no. 2, 124899 (2021) arXiv.
- Heat kernel analysis on diamond fractals.
Stochastic Processes and their Applications Vol. 131, 51-72 (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 No.3, Vol.59, Paper No.103, 32 pp (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).
J. of Functional Analysis Nr. 11, Vol. 278, 108459 (2020) arXiV.
- Analysis on hybrid fractals (with Y. Chen, H. Gu, R.S. Strichartz and Z. Zhou).
Comm. Pure App. Anal. Nr. 1, Vol. 19: 47-84 (2020) arXiV.
- Explicit formulas for heat kernels on diamond fractals
Comm. Math. Phys. Nr. 3, Vol. 364, 1305-1326 (2018) arXiv.
- Completely symmetric resistance forms on the stretched Sierpinski gasket (with U. Freiberg and J. Kigami)
J. of Fractal Geometry, Nr. 3, Vol. 5: 227-277 (2018) arXiv.
- Entropy-based inhomogeneity detection in fiber materials (with E. Spodarev)
Methodology and Computing in Applied Probability, 1-17 (2017) arXiv.
- Power dissipation in fractal Feynman-Sierpinski AC circuits
Journal of Mathematical Physics, Nr. 7, Vol. 58: 073503 (2017) arXiv.
- Estimation of entropy for Poisson marked point processes (with E. Spodarev)
Advances in Applied Probability, Nr. 1, Vol. 49: 258-278 (2017) arXiv.
- Weyl asymptotics for Hanoi atrractors (with U. Freiberg)
Forum Mathematicum 29, no. 5, 1003–1022, 2017 arXiv.
- The limit theorem for maximum of partial sums of exchangeable random variables (with A. Rakitko)
Statistics & Probability Letters, Vol. 119: 357-362 (2016) arXiv.
- Energy and Laplacian on Hanoi-type fractal quantum graphs (with D. Kelleher and A. Teplyaev)
Journal of Physics A: Mathematical and Theoretical, Nr. 4, Vol.49: 1501-1533 (2016) arXiv.
- Hanoi attractors and the Sierpinski gasket (with U. Freiberg)
Special issue of Int. J. Math. Modelling and Nonlinear Optimization on Fractals, Fractal-based Methods and Applications, Nr. 4, Vol. 3: 251-265, 2012
Research with students
Fall 2020 marked the start of the TAMU Fractals Research Team at Texas A&M!
Analysis on hybrid fractals (with Y. Chen, H. Gu, R.S. Strichartz and Z. Zhou). Comm. Pure App. Anal. Nr. 1, Vol. 19: 47-84, 2020. arXiV.