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The Dean-Kawasaki equation with non-local singular interactions and correlated noise will be introduced, which describes the evolution of the density function for a system of finitely many particles g...
In this talk, I will give a survey of results related to the problem of computing Hausdorff dimension of various dynamically defined sets, such as singular vectors. The aim is to try to describe the l...
We consider the combined mean-field and semiclassical limit for a system of the N fermions interacting through singular potentials. We prove the uniformly in the Planck constant h propagation of quant...
The geometric considerations enter in a decisive way in many questions of harmonic analysis. For example, the estimation of the Fourier transform of surface-carried measure, which played a key role in...
We study positive solutions of the Yamabe equation with isolated singularity and prove the existence of solutions with prescribed asymptotic expansions near singular points and an arbitrarily high ord...
We consider the combined mean-field and semiclassical limit for a system of the N fermions interacting through singular potentials. We prove the uniformly in the Planck constant h propagation of quant...
In this talk, I will show that (nontrivial) Lyapunov stable classes of vector fields far from homoclinic tangencies contain periodic orbits. This gives a partial answer for the Palis Weak Density Conj...
The regularity estimates have well-established for second-order elliptic and parabolic equations, as well as for equations with stable-like non-local operators. Whether similar results hold for non-lo...
The subject of Diophantine approximation studies how a real vector is approximated by rational vectors. Diophantine sets are subsets of real vectors defined by certain approximate functions. Among the...
In this talk, we first briefly review history of the geometric singular perturbation theory, then talk about the traveling pulses for a diffusive Rosenzweig MacArthur model. We show the existence of t...
Motivated by applications, like modeling of thin structures immersed in a fluid, we develop a well posedness theory for Newtonian and some non-Newtonian fluids under singular forcing in Lipschitz doma...
To claim that x was the cause of y (or x caused y) is 1) to assume that x was a contributing member of the group of factors that jointly brought about y, and 2) to deem x responsible for the occurrenc...
Singular Spectrum Analysis (SSA) is a powerful data decomposition/recomposition technique that can be used to reduce the noise in time series. Compared to existing solutions aiming at similar purposes...
It is shown that the singular set for the Yang-Mills flow on unstable holomorphic vector bundles over compact K¨ahler manifolds is completely determined by the Harder-NarasimhanSeshadri filtration of ...
In this paper we prove the existence of weak solutions for the thin film equation with prescribed non zero contact angle and for a large class of mobility coefficients, in dimension 1. The existence o...

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