# overview
My research revolves around Analysis and Probability; in particular I am interested in the interconnections between probabilistic, analytic and geometric aspects of stochastic processes on spaces with a rough structure. Mostly I work on diffusion processes and heat kernels on metric measure spaces with fractal-like features. I also study related equations of interest in mathematical physics.

# keywords[]
4903 Numerical And Computational Mathematics

# educationAndTraining[].organization.label
University of Siegen - (Siegen, Nordrhein-Westfalen, Germany)

# educationAndTraining[].organization.label
Complutense University of Madrid - (Madrid, Spain)

# publications[].label
Canonical diffusions on the pattern spaces of aperiodic Delone sets

# publications[].label
Minimal Gap in the Spectrum of the Sierpinski Gasket

# publications[].label
Entropy-based inhomogeneity detection in porous media

# publications[].label
Explicit Formulas for Heat Kernels on Diamond Fractals

# publications[].label
Completely symmetric resistance forms on the stretched Sierpinski gasket

# publications[].publisher
European Mathematical Society - EMS - Publishing House GmbH

# publications[].label
Fractional Sobolev embeddings and algebra property: A dyadic view

# publications[].label
Heat kernel analysis on diamond fractals

# publications[].label
Entropy-based Inhomogeneity Detection in Fiber Materials

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A new graph-directed construction of nonlocal energies on the unit   interval

# publications[].label
The limit theorem for maximum of partial sums of exchangeable random  variables

# publications[].label
Power dissipation in fractal Feynman-Sierpinski AC circuits

# publications[].label
Completely Symmetric Resistance Forms on the Stretched Sierpinski Gasket

# publications[].label
Explicit formulas for heat kernels on diamond fractals

# publications[].label
Dirichlet forms on metric measure spaces as Mosco limits of  Korevaar-Schoen energies

# publications[].label
Yet another heat semigroup characterization of BV functions on   Riemannian manifolds

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Energy and Laplacian on Hanoi-type fractal quantum graphs

# publications[].label
ESTIMATION OF ENTROPY FOR POISSON MARKED POINT PROCESSES

# publications[].label
The limit theorem for maximum of partial sums of exchangeable random variables

# publications[].publisher
American Institute of Mathematical Sciences (AIMS)

# publications[].label
KorevaarSchoen p -energies and their  -limits on Cheeger spaces

# publications[].label
Minimal gap in the spectrum of the Sierpinski gasket

# publications[].label
Power dissipation in fractal Feynman-Sierpinski AC circuits

# publications[].label
Heat kernel analysis on diamond fractals

# publications[].label
Oscillations of BV measures on unbounded nested fractals

# publications[].publisher
European Mathematical Society - EMS - Publishing House GmbH

# publications[].label
Orlicz-Sobolev embeddings and heat kernel based Besov classes

# publications[].label
BV functions and Besov spaces associated with Dirichlet spaces

# publications[].label
Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities

# publications[].label
Yet another heat semigroup characterization of BV functions on  Riemannian manifolds

# publications[].label
Gagliardo-Nirenberg, Trudinger-Moser and Morrey inequalities on  Dirichlet spaces

# publications[].label
Besov class via heat semigroup on Dirichlet spaces III: BV functions and   sub-Gaussian heat kernel estimates

# publications[].label
Dirichlet forms on non-self-similar fractals: Hanoi attractors

# publications[].label
Minimal gap in the spectrum of the Sierpinski gasket

# publications[].label
Hanoi attractors and the Sierpiski gasket

# publications[].label
Iterative methods fail to solve NLS below the Sobolev embedding threshold on the Sierpinski gasket

# publications[].label
Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates

# publications[].label
Korevaar-Schoen $p$-energies and their $Gamma$-limits on Cheeger spaces

# publications[].label
Energy and Laplacian on Hanoi-type fractal quantum graphs

# publications[].label
BV functions and fractional Laplacians on Dirichlet spaces

# publications[].label
Oscillations of BV measures on nested fractals

# publications[].label
Gagliardo-Nirenberg, Trudinger-Moser and Morrey inequalities on Dirichlet spaces

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
CAREER: Heat semigroups and Strichartz estimates on fractals

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].awardedBy.label
Alexander von Humboldt Foundation - (Bonn, Germany)

# researcherOn[].label
Stochastic Processes on Rough Spaces and Geometric Properties of Random Sets

# researcherOn[].awardedBy.label
Directorate for Mathematical & Physical Sciences - (Arlington, Virginia, United States)