Workshop
Probabilistic perspectives in nonlinear PDEs
Jun 05, 2017 - Jun 09, 2017
ICMS, 15 South College Street
Organisers
Name | Institution |
---|---|
Friedlander, Susan | University of Southern California |
Glatt-Holtz, Nathan | Tulane University |
Oh, Tadahiro | University of Edinburgh |
Pocovnicu, Oana | Heriot-Watt University |
Richards, Geordie | Utah State University |
In recent decades there has been significant progress in the analysis of deterministic and stochastic partial differential equations (PDEs) through the usage and development of probabilistic methods and tools. In particular, exciting developments for dispersive equations and the equations of fluid mechanics have emerged through the connection with probability theory. Despite these developments, many important questions of dynamical significance remain unsolved in the analysis of PDEs. This workshop will bring together experts in probability, PDEs and stochastic analysis, all of whose work could address open problems in nonlinear PDEs which may benefit from a more probabilistic viewpoint. The organisers are confident that this workshop will generate interdisciplinary research directions, where new developments in one area will impact the other. A significant aim of this workshop is to provide an opportunity to deepen the involvement of the UK mathematicians, in particular, researchers at early stages, in this important research activity through interaction between probability and PDEs. This will benefit the entire mathematical analysis community in the UK.
In addition to the usual one-hour talks by the participants, there will be several mini courses. In each mini course, one topic will be explored in substantive details, giving a chance to non-experts and junior participants to discover new research ideas and opportunities.
Photographs from this workshop on our Flickr site
The organisers gratefully acknowledge the financial support of:
Arrangements
This workshop will commence with registration from 08:45-09:30 on Monday 5 June and will close at lunchtime on Friday 9 June.
Participation
- Invited participants received an invitation email from ICMS at the end of February/beginning of March
Venue
The workshop will be held at ICMS, 15 South College Street, Edinburgh.
Talks and Audio/Visiual Equipment
All lectures will be held in the Newhaven Lecture Theatre. The lecture theatre has a built in computer, data projector, and visualiser/document camera. In addition, there are two blackboards. The projector and one board may be used simultaneously. We advise Speakers that, where possible, you bring your talk on a memory stick/USB to put onto our computer in advance of your session - either at the start of the day or during coffee/lunch breaks. ICMS staff can help with this. It is possible for you to use your own laptops but it is then your own responsibility to ensure that resolutions are changed on the laptops if necessary (ICMS will not change the resolution on our equipment). If you use a MAC we expect you to bring your own adaptor.
UK Visas
If you are travelling from overseas you may require an entry visa. A European visa does not guarantee entry to the UK. Please use this link to the UK Visas site to find out if you need a visa and if so how to apply for one.
Travel
Information about travel to the UK and Edinburgh is available here.
Please note that it is your responsibility to have adequate travel insurance to cover medical and other emergencies (volcanic ash disruptions) that may occur on your trip.
A taxi directly from the airport will cost approximately 20.00 to 25.00 GBP to the city centre for a one-way journey. There is also a bus service direct from the airport to the city centre which will cost 4.50 GBP single or 7.50 GBP return - the Airlink 100. This is a frequent service (every 10 minutes during peak times) and will bring you close to Waverley Railway Station, only a short walk to the accommodation and the workshop venue (see map in 'Venue' section above).
Lothian buses charge £1.60 for a single, £4.00 for a day ticket. Please note that the exact fare is required and no change is given.
If travelling by train, please note that Edinburgh has several railway stations - Waverley Railway Station being the main station and closest to the workshop venue at 15 South College Street. If you alight at Edinburgh Waverley, the workshop venue is an easy 10 minute walk over North and South Bridge. The second large railway station is called Haymarket and is at the West End of the city centre. Please be aware that there is also an Edinburgh Park railway station but this is at the west side of the city some way from the city centre. For ICMS, use Edinburgh Waverley.
Poster Session
If you are presenting a poster at this workshop please note your poster should be A1 size (594x841mm), preferably in portrait format. These will be displayed all week in the Chapterhouse during the workshop, helping discussion during breaks as well as during the designated poster session. PLEASE hand this to a member of ICMS staff at registration.
Posters will be presented by the following;
Nikolay Barashkov (University of Bonn)
Kinetic limit of the Schroedinger equation using rough paths
We are exploring the possibility of viewing the convergence of a Schroedinger with time de-correlating random potential to the linear Bolzmann equation, as a limit of the corresponding rough drivers.
Jingyu Huang (University of Utah)
Dense blowup for parabolic SPDEs
We show that there are examples of stochastic partial differential equations of the type [ partial_t u=frac12Delta u +sigma(u)eta qquadtext{on $(0,,infty)times R^3$} ] such that the solution exists and is unique as a random field in the sense of Dalang and Walsh, yet the solution has unbounded oscillations in every open neighborhood of every space-time point. The proof consists of a local linearization of the solution, and with techniques from Gaussian analysis.
Masahiro Ikeda (Kyoto University)
Global dynamics below the ground state for the nonlinear Schr"odinger equation with a repulsive potential
We study global dynamics of the solution to the Cauchy problem for the focusing semilinear Schr¥"{o}dinger equation with a repulsive potential on the real line. Our aim in the presentation is to study global behavior of the solution and prove a scattering result and a blow-up result for NLS in the mass-supercritical case with the data whose mass-energy is less than that of the ground state, where the ground state is the unique radial positive solution to the stationary Schr¥"odinger equation without the potential.
Justin Krometis (Virginia Tech)
A Bayesian approach to estimating background flows from a passive scalar
We consider the statistical inverse problem of estimating a back- ground ow eld (e.g., of air or water) from the partial and noisy observation of a passive scalar (e.g., the concentration of a pollutant).
Here our unknown is a vector eld that is specied by large or in- nite number of degrees of freedom. Our work expands on frameworks developed in recent years for innite-dimensional Bayesian inference ([1],[2]). We approach the problem both analytically and computationally developing Metropolis-Hastings type algorithms to generate unbiased samples from the posterior distribution.
Liying Li (Courant Institute, New York University)
Inviscid limit of stationary solutions for the randomly forced Burgers equation in on R^1
We study the Burgers equation on R^1 with space-time stationary random kick-forcing. Despite the non-compact nature of the model, stationary solutions can be constructed from semi-infinite minimizers and variational formulas (in inviscid case) or infinite volume polymer measures and Feynman--Kac formula (in viscous case). Here we will show that the zero-temperature limits of infinite volume polymer measures are delta measures concentrating on semi-infinite minimizers, and then obtain a result on the inviscid limit of the stationary solutions.
Razvan Mosincat (University of Edinburgh)
Well-posedness theory of the three-dimensional stochastic beam equation with additive space-time white noise forcing
We consider the stochastic nonlinear beam equation (SNLB) with additive space-time white noise forcing posed on the three-dimensional torus. By studying the regularity property of the stochastic forcing term, we prove local-in-time well-posedness (existence, uniqueness and stability of solutions) for all power-type nonlinearities. Moreover, in the defocusing case, we also prove global-in-time well posedness when the degree of the nonlinearity is sufficiently small. This is joint work with Oana Pocovnicu (Heriot-Watt University), Leonardo Tolomeo (University of Edinburgh), and Yuzhao Wang (University of Edinburgh).
We also consider well-posedness of the nonlinear Schrödinger equations on d-dimensional tori with (either additive or multiplicative) stochastic forcing, white in time but smoother in space. This second part is joint work with Kelvin Cheung (Heriot-Watt University).
Yue Wu, (Technical University Berlin)
A randomized Milstein method for SDEs with non-differentiable drift
We presented a drift-randomized numerical method to approximate SDEs with non-differentiable drift with order of convergence 1.
Christian Zillinger (University of Southern California)
On mixing for circular flows
In recent years, following the seminal works of Villani and Mouhot on Landau damping, phase-mixing as a damping mechanism and
inviscid damping in fluid dynamics have attracted much interest. Here, mixing in physical space and weak convergence interact with the Biot-Savart law and results in damping of the velocity field. in this poster, I will discuss linear stability and damping with optimal decay rates around 2D Taylor-Couette flow between two concentric cylinders and similar circular flows. A particular focus will be on asymptotic singularity formation at the boundary and stability in weighted spaces.
Public Lecture
On Tuesday 6 June, Professor James Ellis Colliander, Pacific Institute for the Mathematical Sciences, will give a Public Lecture. Doors will open to the Public at 17.30, with the Lecture beginning at 18.00. The Public Lecture will be followed by an informal wine reception in the Chapterhouse, Level 1,at ICMS from 19:00-19:45. Seats have been reserved in the Lecture Theatre for all the workshop participants so there is no need for you to book a seat. Details of the talk title and abstract are as follows;
The mathematical sciences infrastructure underpinning modern business
"A 2012 report commissioned by EPSRC measured the enormous impact of mathematical sciences on the UK economy. Ideas from the mathematical sciences are transforming industry sectors. This talk will celebrate the human creativity driving these advances".
Programme
Monday 5 June
08:45-09:30 | Registration |
09:30-09:40 | Welcome talk |
09:40-10:40 | Nikolay Tzvetkov (University of Cergy-Pontoise) |
10:40-11:10 | Tea/Coffee in the Chapterhouse, Level 1 |
11:10-12:10 | Peter Constantin (Princeton University) |
12:10-13:10 | Franco Flandoli (Università di Pisa) |
13:10-14:30 | Lunch provided in the Chapterhouse, Level 1 |
14:30-15:0 | Alexandre Boritchev (Université Lyon 1) |
15:00-15:30 | Nobu Kishimoto (Kyoto University) |
15:30-16:00 | Tea/Coffee in the Chapterhouse, Level 1 |
16:00-17:00 | Hendrik Weber (University of Warwick) |
17:00-18:30 | Poster session with an informal wine reception in the Chapterhouse, Level 1 |
Tuesday 6 June
09:30-10:30 | Scott McKinley (Tulane University) |
10:30-11:00 | Tea/Coffee in the Chapterhouse, Level 1 |
11:00-12:00 | Nikolay Tzvetkov (University of Cergy-Pontoise) |
12:00-13:00 | Bruce Turkington (University of Massachusetts Amherst) |
13:00-14:30 | Lunch provided in the Chapterhouse, Level 1 |
14:30-15:30 | Herbert Koch (Universität Bonn) |
15:30-16:00 | Tea/Coffee in the Chapterhouse, Level 1 |
16:00-16:30 | Philippe Sosoe (Harvard University) |
16:30-17:00 | Yuzhao Wang (University of Edinburgh) |
17:30 | Doors open to the public |
18:00-19:00 | Public Lecture by James Ellis Colliander (Pacific Institute for the Mathematical Sciences) |
19:00-19:45 | Informal wine reception in the Chapterhouse, Level 1 |
Wednesday 7 June
09:30-10:30 | Nikolay Tzvetkov (University of Cergy-Pontoise) |
10:30-11:00 | Tea/Coffee in the Chapterhouse, Level 1 |
11:00-12:00 | Arnaud Debussche (École normale supérieure de Rennes) |
12:00-13:00 | Jonathan Mattingly (Duke University) |
13:00 | Free afternoon |
Thursday 8 June
09:30-10:30 | Ivan Corwin (Columbia University) |
10:30-11:00 | Tea/Coffee in the Chapterhouse, Level 1 |
11:00-12:00 | Roger Temam (Indiana University) |
12:00-12:30 | David Herzog (Iowa State University) |
12:30-13:00 | Vincent Ryan Martinez (Tulane University) |
13:00-14:30 | Lunch provided in the Chapterhouse, Level 1 |
14:30-15:30 | Ivan Corwin (Columbia University) pdf of presentation |
15:30-16:00 | Tea/Coffee in the Chapterhouse, Level 1 |
16:00-16:30 | Juraj Foldes (University of Virginia) |
16:30-17:00 | Leonardo Tolomeo (University of Edinburgh) |
17:00-17:30 | Martina Hofmanova (Technical University Berlin) |
19:00 | Workshop Dinner at Blonde Restaurant, St Leonard's |
Friday 9 June
09:30-10:30 | Anne de Bouard (CNRS and Ecole Polytechnique) |
10:30-11:00 | Tea/Coffee in the Chapterhouse, Level 1 |
11:00-12:00 | Sergei Kuksin (Université Paris) |
12:00-13:00 | Gideon Simpson (Drexel University) |
13:00 | Close of workshop |
Presentations:
Presentation Details | |
---|---|
Barashkov, Nikolay | |
POSTER: Kinetic limit of the Schroedinger equation using rough paths | |
Boritchev, Alexandre | |
Turbulence and sharp estimates for solutions of the Burgers equation in 1d, multi-d and with a fractional dissipation | |
View Abstract | |
Colliander, James Ellis | |
The mathematical sciences infrastructure underpinning modern business | |
View Abstract | |
Constantin, Peter | |
Remarks on high Reynolds number hydrodynamics | |
View Abstract | |
Corwin, Ivan | |
Talk 1: Fluctuations of interacting particle systems Talk 2: SPDE limits of interacting particle systems | |
View Abstract | |
de Bouard, Anne | |
Long time behavior of the Gross Pitaevskii equation at positive temperature | |
View Abstract | |
Debussche, Arnaud | |
Kolmogorov equations and weak order analysis for SPDEs with nonlinear diffusion coefficient | |
View Abstract | |
Flandoli, Franco | |
Regularization by noise of PDEs in fluid mechanics | |
View Abstract | |
Foldes, Juraj | |
Statistical solutions of Euler equation | |
View Abstract | |
Herzog, David | |
Scalings and saturation in infinite-dimensional control problems with applications to stochastic partial differential equations | |
View Abstract | |
Hofmanova, Martina | |
Stationary solutions to the stochastic compressible Navier-Stokes system | |
View Abstract | |
Huang, Jingyu | |
POSTER: Dense blowup for parabolic SPDEs | |
View Abstract | |
Ikeda, Masahiro | |
POSTER: Global dynamics below the ground state for the nonlinear Schr"odinger equation with a repulsive potential | |
View Abstract | |
Kishimoto, Nobu | |
Remark on global regularity for the rotating Navier-Stokes equations in a periodic domain | |
View Abstract | |
Koch, Herbert | |
Renormalization of 2 dimensional nonlinear stochastic wave equations | |
View Abstract | |
Krometis, Justin | |
POSTER: A Bayesian approach to estimating background flows from a passive scalar | |
View Abstract | |
Kuksin, Sergei | |
Controllability, mixing and the Nash-Moser scheme for SPDEs | |
View Abstract | |
Li, Liying | |
POSTER: Inviscid limit of stationary solutions for the randomly forced Burgers equation in on R^1 | |
View Abstract | |
Martinez, Vincent Ryan | |
Asymptotic enslavement in hydrodynamic equations and applications to dynamics and data assimilation | |
View Abstract | |
Mattingly, Jonathan | |
Long time behavior of Stochastic PDE | |
View Abstract | |
McKinley, Scott | |
Anomalous diffusion in thermally fluctuating viscoelastic fluids | |
View Abstract | |
Mosincat, Razvan | |
POSTER: Well-posedness theory of the three-dimensional stochastic beam equation with additive space-time white noise forcing | |
View Abstract | |
Simpson, Gideon | |
Gaussian approximations in Hilbert spaces | |
View Abstract | |
Sosoe, Philippe | |
Some results on Gibbs-type measures | |
View Abstract | |
Temam, Roger | |
Positive solutions of stochastic partial differential equations, and applications to the Shigesada-Kawasaki-Teramoto equations with white noise | |
View Abstract | |
Tolomeo, Leonardo | |
Global well-posedness of the two-dimensional cubic stochastic nonlinear wave equation | |
View Abstract | |
Turkington, Bruce | |
Intrinsic closure for nonequilibrium statistical models via path optimization | |
View Abstract | |
Tzvetkov, Nikolay | |
Talk 1(Mon & Tues) Quasi-invariant gaussian measures for the 2d cubic defocusing wave equation Talk 2 (Weds) Quasi-invariant gaussian measures for the 4th order NLS under | |
View Abstract | |
Wang, Yuzhao | |
Invariance of white noise for the cubic fourth order nonlinear Schrödinger equation | |
View Abstract | |
Weber, Hendrik | |
Ergodicity for parabolic $Phi^4_d$ dynamics | |
View Abstract | |
Wu, Yue | |
POSTER: A randomized Milstein method for SDEs with non-differentiable drift | |
View Abstract | |
Zillinger, Christian | |
POSTER: On mixing for circular flows | |
Participants
Name | Institution |
---|---|
Bakas, Odysseas | University of Edinburgh |
Barashkov, Nikolay | University of Bonn |
Boniece, Benjamin Cooper | Tulane University |
Boritchev, Alexandre | Université Lyon 1 |
Breit, Dominic | Heriot-Watt University |
Cheung, Kelvin | MIGSAA |
Colliander, James Ellis | Pacific Institute for the Mathematical Sciences |
Constantin, Peter | Princeton University |
Corwin, Ivan | Columbia University |
de Bouard, Anne | CNRS and Ecole Polytechnique |
de Kergorlay, Henry-Louis | University of Edinburgh |
Debussche, Arnaud | École normale supérieure de Rennes |
Dreher, Michael | University of Rostock |
Duong, Duc Lam | University of Sussex |
FAN, QIANZHU | University of Edinburgh |
Flandoli, Franco | Università di Pisa |
Foldes, Juraj | University of Virginia |
Forlano, Justin | MIGSAA |
Friedlander, Susan | University of Southern California |
Fuster Aguilera, Rosa Maria | Tulane University |
Glatt-Holtz, Nathan | Tulane University |
Hammersley, William | MIGSAA |
Herzog, David | Iowa State University |
Hofmanova, Martina | Technical University Berlin |
Huang, Jingyu | University of Utah |
Ignatova, Mihaela | Princeton University |
Ikeda, Masahiro | Kyoto University |
Jones, Felix | Drexel University |
Kishimoto, Nobu | Kyoto University |
Koch, Herbert | Universität Bonn |
König, Maximilian | TU Berlin & Berlin Mathematical School (BMS) |
Krometis, Justin | Virginia Tech |
Kuksin, Sergei | Université Paris |
Leahy, James-Michael | University of Southern California |
Li, Liying | Courant Institute, New York University |
Lord, Gabriel | Heriot Watt University |
Martinez, Vincent Ryan | Tulane University |
Mattingly, Jonathan | Duke University |
McKinley, Scott | Tulane University |
Mensah, Prince Romeo | Heriot-Watt University |
Mosincat, Razvan | University of Edinburgh |
Neelima, Neelima | University of Edinburgh |
Oh, Tadahiro | University of Edinburgh |
Ottobre, Michela | Heriot watt |
Pocovnicu, Oana | Heriot-Watt University |
Richards, Geordie | Utah State University |
Salkeld, William | University of Edinburgh |
Savostianov, Anton | Durham University |
Simpson, Gideon | Drexel University |
Siska, David | University of Edinburgh |
Sosoe, Philippe | Harvard University |
Szpruch, Lukasz | University of Edinburgh |
Tan, Shuren | University of Edinburgh |
Temam, Roger | Indiana University |
Tolomeo, Leonardo | University of Edinburgh |
Trenberth, William | MIGSAA |
Turkington, Bruce | University of Massachusetts Amherst |
Tzvetkov, Nikolay | University of Cergy-Pontoise |
Uda, Kenneth | University of Edinburgh |
Ugurcan, Baris Evren | Hausdorff Center for Mathematics |
Villa, Michele | Maxwell Institute Graduate School in Analysis |
Wang, Yuzhao | University of Edinburgh |
Weber, Hendrik | University of Warwick |
Wu, Yue | Technical University Berlin |
Yamazaki, Yohei | Cergy-Pontoise University |
Ying, Yik Keung | University of Edinburgh |
Zachhuber, Immanuel | University of Bonn |
Zhang, Xiling | University of Edinburgh |
ZHANG, YING | MIGSAA |
Zillinger, Christian | University of Southern California |