Scientific Organisers
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Zdzislaw Brzezniak, University of York
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Istvan Gyongy, University of Edinburgh
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Tadahiro Oh, University of Edinburgh
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Oana Pocovnicu, Heriot-Watt University
Local Assistant Organiser
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Guangqu Zheng, University of Edinburgh
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
| Monday 20 June | ||
| Introductions | ||
| Michael Röckner , University of Bielefeld | On a Longstanding Open Problem in the Theory of Markov Processes. | |
| Hongjie Dong , Brown University | Sobolev estimates for degenerate Kolmogorov equations | |
| Máté Gerencsér , TU Wien | Regularisation by noise with subcritical drifts or multiplicative noise | |
| Leonardo Tolomeo , Hausdorff Center for Mathematics | Phase transitions of the focusing Φ^p_1 measures | |
| Bjoern Bringmann, Institute for Advanced Study/Princeton University | Invariant Gibbs measures for the three-dimensional cubic nonlinear wave equation. | |
| Tristan Robert , Université de Lorraine | Variational methods for some singular stochastic elliptic PDEs | |
| Poster Session | ||
| Presented by F Cornalba, C Dietze, F Germ, J Lee, K Woo, S Wu, Y Zine, G Zheng | Poster links below: | |
| Tuesday 21 June | ||
| Kyeong-Hun Kim , Korea University | Sobolev regularity for PDEs with fractional Laplacian on $C^{1,1}$ open sets. | |
| Mikhail Safonov, University of Minnesota | On the boundary estimates for solution to second order elliptic and parabolic equations in irregular domains. | |
| Szymon Peszat, Jagiellonian University | Heat equation with Dirichlet white noise boundary conditions. | |
| Mario Maurelli , Università degli Studi di Milano | Non-explosion by Stratonovich noise for ODEs | |
| Masato Hoshino, Osaka University | Paracontrolled calculus and regularity structures. | |
| 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 | |
| Workshop Public Lecture | ||
| Ilya Chevyrev , University of Edinburgh | The rough journey of Brownian motion: from pollen particles, to Avogadro number, to stock markets. | |
| 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. | |
| Kijung Lee , Ajou University | Stochastic parabolic equation and Dirichlet boundary condition. | |
| 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). | |
| Enrico Priola, University of Pavia | Poisson process and sharp constants in $L^p $ and Schauder estimates for a class of degenerate Kolmogorov operators. | |
| Etienne Pardoux, Aix-Marseille Université | Uniqueness of the filtering equations in the space of measures | |
| Yuzhao Wang, University of Birmingham | Stochastic quantization of Liouville conformal field theory | |
| Mark Freidlin , University of Maryland | Long-time Influence of Small perturbations. | |
| 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 | |
| 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. | |
| Alexander Veretennikov, University of Leeds | On ergodic properties of a diffusion with switching |