Research

Research interests

My main research interest is the probabilistic nature of turbulence in fluid dynamics. I try to it approach from three different sides.

• the study of level sets and SPDEs. Here the initial motivation was the work Conformal Invariance in Inverse Turbulent Cascades [arxiv]. Some of these results might be explainable from the convergence of SPDEs to their invariant measure. So I explore the level sets for the stochastic heat equation using the technology of the Beltrami equation.
• the study of periodic KPZ equation and universality. The KPZ universality and the various statistical models that belong to it such as TASEP is one of the central phenomena in out-of-equilibrium statistical mechanics.
• the study of compact KPZ equation and Exciton-Polariton model. Here the motivation is the work Lattice duality for the compact Kardar-Parisi-Zhang equation [arxiv].

Articles

• A Left passage explorer model [arxiv]
• Inverse of the Gaussian multiplicative chaos: Moments with I.Binder [arxiv]
• Inverse of the Gaussian multiplicative chaos: an integration by parts formula [arxiv]
• Inverse of the Gaussian multiplicative chaos and Lehto welding with I.Binder [link]