Analysis and Probability
Our research covers a broad spectrum from harmonic analysis and probability theory to pure and applied PDEs.
Interactions with number theory, combinatorics, discrete and integral geometry, geometric measure theory and PDEs, applications to elliptic BVPs and semilinear and linear PDEs with rough coefficients and/or domains; applications to nonlinear hyperbolic, dispersive and transport equations.
ODEs, PDEs and dynamical systems
Spectral theory of nonlinear (p-Laplacian-type) ODEs with jumping nonlinearities, nonlinear eigenvalue problems for ODEs and PDEs; spectral analysis of linear self-adjoint and non-self-adjoint operators and applications to mathematical physics.
Nonlinear PDEs and Applications
Free-boundary problems, PDEs and variational methods in nonlinear elasticity and other continuum theories, nonlinear dissipative equations including Navier-Stokes and reaction-diffusion equations, transport equations arising in mathematical biology (e.g. chemotaxis), mathematical general relativity, optimal transport theory, nonlocal PDEs, dispersive equations, and stochastic PDEs.
Development of new probabilistic methods and approaches to stability, performance and rare events analysis of complex stochastic processes.
Limiting behaviour of stochastic models for queueing systems and networks, and of objects from stochastic geometry and percolation theory; probabilistic analysis of algorithms and communication protocols; rare events analysis for stochastic models with heavy-tailed inputs; applications to (tele)communication and power systems, transport and risk.
Theoretical & Numerical Stochastic Analysis
Analysis of Markovian models; construction of Markovian projections of non-Markovian models; ordinary and partial stochastic differential equations; nonlinear filtering and stochastic control; development of efficient solvers for SDEs