Entrance hall of the ICMS 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.

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 (titles to follow);

Razvan Mosincat (University of Edinburgh)
Yue Wu, Technical (University Berlin)
Nikolay Barashkov  (University of Bonn) - 'Kinetic limit of the Schroedinger equation using rough paths'
Masahiro Ikeda (Kyoto University)
Justin Krometis (Virginia Tech)
Christian Zillinger (University of Southern California)  -  'On mixing for circular flows'
Liying Li (Courant Institute, New York University)
Jingyu Huang (University of Utah)

 

Public Lecture
On Tuesday 6 June , Professor James Ellis Colliander, Pacific Institute for the Mathematical Sciences, will give a Public Lecture. 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".

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 17:00-18:30.  Seats have been reserved in the Lecture Theatre for all the workshop participants so there is no need for you to book a seat.

 

 

 

 

 

Programme

Monday 5 June

08:45-09:30

Registration

09:40-09:50

Welcome Talk

09:40-10:40

Nikolay Tzvetkov (University of Cergy-Pontoise)                
Quasi-invariant gaussian measures for the 2d cubic defocusing wave equation

10:40-11:10

Tea/Coffee in the Chapterhouse, Level 1

11:10-12:10

Peter Constantin (Princeton University)                                   
The Lagrangian-Eulerian method

12:10-13:10

Franco Flandoli (Università di Pisa)                                 
Regularization by noise of PDEs in fluid mechanics

13:10-14:30

Lunch provided in the Chapterhouse, Level 1

14:30-15:00

Alexandre Boritchev (Université Lyon 1)                   
Turbulence and sharp estimates for solutions of the Burgers equation in 1d, multi-d and with a fractional dissipation

15:00-15:30

Nobu Kishimoto (Kyoto University)                   
Remark on global regularity for the rotating Navier-Stokes equations in a periodic domain

15:30-16:00

Tea/Coffee in the Chapterhouse, Level 1

16:00-17:00

Hendrik Weber (University of Warwick)                   
Ergodicity for parabolic $Phi^4_d$ dynamics

17:00-18:30

Poster session and informal wine reception in the Chapterhouse, Level 1

 

Tuesday 6 June

09:30-10:30

Scott McKinley (Tulane University)                   
Anomalous diffusion in thermally fluctuating viscoelastic fluids

10:30-11:00

Tea/Coffee in the Chapterhouse, Level 1

11:00-12:00

Nikolay Tzvetkov (University of Cergy-Pontoise)
Quasi-invariant gaussian measures for the 2d cubic defocusing wave equation

12:00-13:00

Bruce Turkington (University of Massachusetts Amherst)                   
Intrinsic closure for nonequilibrium statistical models via path optimization

13:00-14:30

Lunch provided in the Chapterhouse, Level 1

14:30-15:30

Herbert Koch (Universität Bonn)                   
Renormalization of 2 dimensional nonlinear stochastic wave equations

15:30-16:00

Tea/Coffee in the Chapterhouse, Level 1

16:00-16:30

Philippe Sosoe (Harvard University)                   
Some results on Gibbs-type measures

16:30-17:00

Yuzhao Wang (University of Edinburgh)                   
Invariance of white noise for the cubic fourth order nonlinear Schrödinger equation

17:30

Doors open to the public

18:00-19:00

Public Lecture by Professor James Ellis Colliander
The mathematical sciences infrastructure underpinning modern business

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)                
Quasi-invariant gaussian measures for the 2d cubic defocusing wave equation

10:30-11:00

Tea/Coffee in the Chapterhouse, Level 1

11:00-12:00

Arnaud Debussche (ENS Rennes)                   
Kolmogorov equations and weak order analysis for SPDEs with nonlinear diffusion coefficient

12:00-13:00

Jonathan Mattingly (Duke University)                   
Long time behaviour of Stochastic PDE

13:00

Free afternoon (Lunch will not be provided)

 

Thursday 8 June

09:30-10:30

Ivan Corwin (Columbia University)                   
Fluctuations of interacting particle systems

10:30-11:00

Tea/Coffee in the Chapterhouse, Level 1

11:00-12:00

Roger Temam (Indiana University)                   
To follow

12:00-12:30

David Herzog (Iowa State University)                   
Scalings and saturation in infinite-dimensional control problems with applications to stochastic partial differential equations

12:30-13:00

Vincent Ryan Martinez (Tulane University)                   
Asymptotic enslavement in hydrodynamic equations and applications to dynamics and data assimilation

13:00-14:30

Lunch provided in the Chapterhouse, Level 1

14:30-15:30

Ivan Corwin (Columbia University)                   
SPDE limits of interacting particle systems

15:30-16:00

Tea/Coffee in the Chapterhouse, Level 1

16:00-16:30

Juraj Foldes (University of Virginia)                   
Statistical solutions of Euler equation

16:30-17:00

Leonardo Tolomeo (University of Edinburgh)                   
Global well-posedness of the two-dimensional cubic stochastic nonlinear wave equation

17:00-17:30

Martina Hofmanova (Technical University Berlin)                   
Stationary solutions to the stochastic compressible Navier-Stokes system

19:00

Workshop Dinner (Venue TBC)

 

Friday 9 June

09:30-10:30

Anne de Bouard (CNRS and Ecole Polytechnique)
Long time behavior of the Gross Pitaevskii equation at positive temperature

10:30-11:00

Tea/Coffee in the Chapterhouse, Level 1

11:00-12:00

Sergei Kuksin (Université Paris)                   
Controllability, mixing and the Nash-Moser scheme for SPDEs

12:00-13:00

Yuri Bakhtin (Courant Institute of Mathematical Sciences, NYU)                   
Ergodic theory of the Burgers equation with random forcing

13:00

Close of workshop (Lunch will not be provided)

 

 

Presentations:

Presentation Details
Bakhtin, Yuri
Ergodic theory of the Burgers equation with random forcing
View Abstract Down
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 Down
Colliander, James Ellis
The mathematical sciences infrastructure underpinning modern business
View Abstract Down
Constantin, Peter
The Lagrangian-Eulerian method
View Abstract Down
Corwin, Ivan
Talk 1: Fluctuations of interacting particle systems Talk 2: SPDE limits of interacting particle systems
View Abstract Down
de Bouard, Anne
Long time behavior of the Gross Pitaevskii equation at positive temperature
View Abstract Down
Debussche, Arnaud
Kolmogorov equations and weak order analysis for SPDEs with nonlinear diffusion coefficient
View Abstract Down
Flandoli, Franco
Regularization by noise of PDEs in fluid mechanics
View Abstract Down
Foldes, Juraj
Statistical solutions of Euler equation
View Abstract Down
Herzog, David
Scalings and saturation in infinite-dimensional control problems with applications to stochastic partial differential equations
View Abstract Down
Hofmanova, Martina
Stationary solutions to the stochastic compressible Navier-Stokes system
View Abstract Down
Kishimoto, Nobu
Remark on global regularity for the rotating Navier-Stokes equations in a periodic domain
View Abstract Down
Koch, Herbert
Renormalization of 2 dimensional nonlinear stochastic wave equations
View Abstract Down
Kuksin, Sergei
Controllability, mixing and the Nash-Moser scheme for SPDEs
View Abstract Down
Li, Liying
POSTER: Inviscid limit of stationary solutions for the randomly forced Burgers equation in on R^1
View Abstract Down
Martinez, Vincent Ryan
Asymptotic enslavement in hydrodynamic equations and applications to dynamics and data assimilation
View Abstract Down
McKinley, Scott
Anomalous diffusion in thermally fluctuating viscoelastic fluids
View Abstract Down
Mosincat, Razvan
POSTER: Well-posedness theory of the three-dimensional stochastic beam equation with additive space-time white noise forcing
View Abstract Down
Sosoe, Philippe
Some results on Gibbs-type measures
View Abstract Down
Temam, Roger
Positive solutions of stochastic partial differential equations, and applications to the Shigesada-Kawasaki-Teramoto equations with white noise
View Abstract Down
Tolomeo, Leonardo
Global well-posedness of the two-dimensional cubic stochastic nonlinear wave equation
View Abstract Down
Turkington, Bruce
Intrinsic closure for nonequilibrium statistical models via path optimization
View Abstract Down
Tzvetkov, Nikolay
Quasi-invariant gaussian measures for the 2d cubic defocusing wave equation
View Abstract Down
Wang, Yuzhao
Invariance of white noise for the cubic fourth order nonlinear Schrödinger equation
View Abstract Down
Weber, Hendrik
Ergodicity for parabolic $Phi^4_d$ dynamics
View Abstract Down
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 ENS 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