About

My research has been focused on the analysis of partial differential equations, particularly describing fluid dynamics, and on Markov Chain Monte Carlo (MCMC) sampling algorithms applied to Bayesian inverse problems. Particularly, I have worked on the following topics: statistical solutions and long-time behavior of evolution equations; data assimilation schemes; mixing rates and design of MCMC algorithms with applications to fluid-related Bayesian inverse problems.

Publications and preprints (Google Scholar)

On the convergence of trajectory statistical solutions (with A. Bronzi and R. Rosa), submitted. arXiv

Sacred and Profane: from the Involutive Theory of MCMC to Helpful Hamiltonian Hacks (with N. Glatt-Holtz, A. Holbrook, J. Krometis, and A. Sheth), to appear as a chapter in Handbook of Markov Chain Monte Carlo, Second Edition (2024): Chapman & Hall/CRC. arXiv

On the locally self-similar blowup for the generalized SQG equation (with A. Bronzi and R. Guimarães), Journal of Differential Equations 415 (2025), pp. 266-302. arXiv

Long-term accuracy of numerical approximations of SPDEs with the stochastic Navier-Stokes equations as a paradigm (with N. Glatt-Holtz), IMA Journal of Numerical Analysis (2024). arXiv

Parallel MCMC algorithms: theoretical foundations, algorithm design, case studies (with N. Glatt-Holtz, A. Holbrook, and J. Krometis), Transactions of Mathematics and its Applications 8 (2024), no. 2. arXiv

On the accept-reject mechanism for Metropolis-Hastings algorithms (with N. Glatt-Holtz and J. Krometis), Annals of Applied Probability 33 (2023), no. 6B, pp. 5279-5333. arXiv

Mixing Rates for Hamiltonian Monte Carlo Algorithms in Finite and Infinite Dimensions (with N. Glatt-Holtz), Stoch PDE: Anal Comp (2021). https://doi.org/10.1007/s40072-021-00211-z. arXiv

Fully discrete numerical schemes of a data assimilation algorithm: uniform-in-time error estimates (with H. Ibdah and E.S. Titi), IMA Journal of Numerical Analysis 40 (2020), no. 4, pp. 2584-2625. arXiv

Downscaling data assimilation algorithm with applications to statistical solutions of the Navier-Stokes equations (with A.Biswas, C. Foias, and E.S. Titi), Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 2, pp. 295-326. arXiv

Uniform-in-time error estimates for the Postprocessing Galerkin method applied to a data assimilation algorithm (with E.S. Titi), SIAM J. Numer. Anal. 56 (2018), no. 1, pp. 78-110. arXiv

A discrete data assimilation scheme for the solutions of the 2D Navier-Stokes equations and their statistics (with C. Foias and E. S. Titi), SIAM J. Appl. Dyn. Syst. 15 (2016), no. 4, pp. 2109-2142. arXiv

Abstract framework for the theory of statistical solutions (with A. Bronzi and R. Rosa), J. Differential Equations 260 (2016), pp. 8428-8484. arXiv

Entropy measures based method for the classification of protein domains into families and clans (with N. Carels and R.P. Mondaini), BIOMAT 2013, World Sci. Publ. (2014), pp. 209-218.

Trajectory statistical solutions for three-dimensional Navier-Stokes-like systems (with A. Bronzi and R. Rosa), SIAM J. Math. Anal. 46 (2014), pp. 1893-1921. arXiv

Teaching

For the Fall 2024 term, I am teaching MATH 510 (Applied Probability and Statistics I). Course materials are available at learn.drexel.edu