Reaction-Diffusion Equations & Branching Brownian Motion
I am interested in the long-time behavior of reaction-diffusion systems with multiple interacting components.
I have studied systems of Fisher-KPP equations, which model ecological invasions.
My work on these systems focuses on determining the asymptotics of the location of their fronts.
There are interesting connections between the systems I have studied and multi-type Branching Brownian Motion.
Stochastic Partial Differential Equations
I am interested in applying Malliavin Calculus to stochastic reaction-diffusion equations to obtain regularity results for the solutions as random variables.
Malliavin Calculus provides tools to show the absolute continuity (with respect to the Lebesgue measure) of the law of the solution to an SPDE, and to study the regularity of the underlying density.
Physics-informed Neural Networks (PINNs)
I am interested in leveraging knowledge on the underlying PDE dynamics to optimize the performance of PINNs on extrapolation tasks and on inverse problems.
PUBLICATIONS & PREPRINTS
(with T.Papastathopoulos), ICANN 2025, Lecture Notes in Computer Science, vol 16071, Springer.
Malliavin Calculus for the stochastic heat equation and results on the density
(with G. Karali and D.Farazakis), 2024, Preprint arXiv:2410.10115, submitted.
Algebraic genericity of frequently universal harmonic functions on trees
(with V.Nestoridis and N.Biehler)
Journal of Mathematical Analysis and Applications, Volume 489, Issue 1, 2020,124132, ISSN 0022-247X.
Generic non-extendability and total unboundedness in function spaces
(with V.Nestoridis, A.Siskakis, S.Vlachos)
Journal of Mathematical Analysis and Applications, Volume 475, Issue 2,2019, Pages 1720-1731, ISSN 0022-247X.