Workshop

Harmonic Analysis, Stochastics and PDEs

20 - 24 Jun 2022

Enquiries

ICMS, Bayes Centre, Edinburgh

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Organiser

Zdzislaw Brzezniak,University of York

Istvan Gyongy,University of Edinburgh

Tadahiro Oh,University of Edinburgh

Oana Pocovnicu,Heriot-Watt University

About

Harmonic Analysis, Stochastics and PDEs in Honour of the 80th Birthday of Nicolai Krylov

Harmonic analysis, stochastic analysis and PDEs are intimately related fields of great importance in mathematics. The relationship between harmonic analysis and PDE theory has a long and extremely successful history; harmonic analysis played a fundamental role in settling some of the central problems in the field of linear and nonlinear PDEs, including elliptic, parabolic, dispersive and hyperbolic equations and systems.
This workshop brought together researchers in different fields (analysis, probability and PDEs) to generate cross-disciplinary research interactions and an exchange of ideas and methods from PDEs, probability and harmonic analysis. There were participants ranging over elliptic, parabolic, dispersive and hyperbolic equations, and other PDEs, which allowed researchers in different PDE communities to interact as well.

Programme

Meet the speakers

Monday 20 June

Introductions

Michael Röckner

University of Bielefeld

On a Longstanding Open Problem in the Theory of Markov Processes.

Abstract

Hongjie Dong

Brown University

Sobolev estimates for degenerate Kolmogorov equations

Abstract

Máté Gerencsér

TU Wien

Regularisation by noise with subcritical drifts or multiplicative noise

Abstract

Leonardo Tolomeo

Hausdorff Center for Mathematics

Phase transitions of the focusing Φ^p_1 measures

Abstract

Bjoern Bringmann

Institute for Advanced Study/Princeton University

Invariant Gibbs measures for the three-dimensional cubic nonlinear wave equation.

Abstract

Tristan Robert

Université de Lorraine

Variational methods for some singular stochastic elliptic PDEs

Abstract

Poster Session

Tuesday 21 June

Kyeong-Hun Kim

Korea University

Sobolev regularity for PDEs with fractional Laplacian on $C^{1,1}$ open sets.

Abstract

Mikhail Safonov

University of Minnesota

On the boundary estimates for solution to second order elliptic and parabolic equations in irregular domains.

Abstract

Szymon Peszat

Jagiellonian University

Heat equation with Dirichlet white noise boundary conditions.

Abstract

Mario Maurelli

Università degli Studi di Milano

Non-explosion by Stratonovich noise for ODEs

Masato Hoshino

Osaka University

Paracontrolled calculus and regularity structures.

Abstract

Konstantinos Dareiotis

University of Leeds

Approximation of stochastic differential equations with irregular drifts

Chenmin Sun

Universtité Paris-Est Créteil

Weak Universality for a class of nonlinear wave equatoins

Abstract

Workshop Public Lecture

Wednesday 22 June

Lutz Weis

Karlsruhe Institute for Technology

A stochastic maximal function and regularity estimates for parabolic stochastic evolution equations.

Mark Veraar

Delft University of Technology

SPDE in critical spaces.

Abstract

Kijung Lee

Ajou University

Stochastic parabolic equation and Dirichlet boundary condition.

Abstract

Thursday 23 June

Neil Trudinger

Australian National University

Classical solvability of generated Jacobian equations.

Giuseppe Da Prato

Scuola Normale Superiore

Existence of the gradient for solutions of some Hypoelliptic Dirichlet problems (paper in collaboration of Luciano Tubaro).

Abstract

Enrico Priola

University of Pavia

Poisson process and sharp constants in $L^p $ and Schauder estimates for a class of degenerate Kolmogorov operators.

Abstract

Etienne Pardoux

Aix-Marseille Université

Uniqueness of the filtering equations in the space of measures

Abstract

Yuzhao Wang

University of Birmingham

Stochastic quantization of Liouville conformal field theory

Abstract

Mark Freidlin

University of Maryland

Long-time Influence of Small perturbations.

Abstract

Friday 24 June

Guopeng Li

University of Edinburgh

Convergence on the finite-depth fluid equation in the shallow water surface and infinitely deep water limits

Abstract

Justin Forlano

University of California Los Angeles

Global well-posedness and quasi-invariance of Gaussian measures for fractional nonlinear Schr”odinger equations

Doyoon Kim

Korea University

Lp theory for parabolic equations with local and non-local time derivatives.

Abstract

Alexander Veretennikov

University of Leeds

On ergodic properties of a diffusion with switching