Gradient flows: challenges and new directions

ICMS, The Bayes Centre, 47 Potterrow, Edinburgh EH8 9BT

10 - 14 September 2018

ORGANISERS

Bertram Düring, University of Sussex
Carola-Bibiane Schönlieb, University of Cambridge
Yves van Gennip, University of Nottingham
Marie-Therese Wolfram, University of Warwick

This workshop is initiated by novel developments in gradient flow research in the various field of applied mathematics in the last years. It continues in the spirit of the previous “Gradient flows” workshop held at ICMS in 2015, by providing a venue for researchers from different fields to introduce and exchange ideas developed in their respective fields.

Nonlinear PDEs with an underlying energy structure, and in particular gradient flows in different metrics, have become a hot topic in mathematical research in recent years. Despite many advances in the analysis of their well-posedness and development of structure-preserving numerical approximations, important questions remain open, and pose challenging mathematical problems in various ways. The talks at this workshop will revolve around three main topics or themes which we describe in the following:

  • Gradient flows
  • Efficient numerical method for gradient flows
  • Gradient flows on discrete structures

The workshop will start on Monday morning and end on Friday at lunchtime. Based on the feedback from the last workshop there will be a mixture of one hour talks (including discussion) from leading experts in the field and 30 minutes talks (including discussion) from younger colleagues. This schedule ensures that participants have enough time to discuss and work during the workshop. Young researchers (PhD students or early postdocs) will also have the opportunity to present their work in a dedicated young researchers’ session. In this session each researcher will have five minutes to introduce their poster to the community. After this short session participants have the opportunity to discuss the posters in more detail.

The organisers gratefully acknowledge the financial contributions of the Alan Turing Institute (https://www.turing.ac.uk/)  and the Institute of mathematics and its applications  (https://ima.org.uk/).

    

Group photographs and images from the public lecture are now available in our Flickr account.

Arrangements

ICMS does NOT use third parties to arrange accommodation.  If you are approached by a third party (e.g. Business Travel Management) asking for booking details, please ignore.  If you have any concerns please contact ICMS.

PARTICIPATION

Invitations were sent out by ICMS in April 2018. 

VENUE

The workshop will be held at ICMS, The Bayes Centre, 47 Potterrow, Edinburgh EH8 9BT

TALKS AND AUDIO/VISUAL EQUIPMENT

All talks will be held in the Lecture Theatre.  The lecture theatre has a built in computer, data projector, and visualiser/document camera.  In addition, there are blackboards.  The projector and the blackboards 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 outside of the UK 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

Please note that it is your responsibility to have adequate travel insurance to cover medical and other emergencies 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 workshop venue.

Lothian buses charge £1.70 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.  If you alight at Edinburgh Waverley, the workshop venue is an easy 10 minute walk away.

Programme

Download the PDF of abstracts

Monday 10 September

10.00-11.00

Registration with coffee

11.00-12.00

Otto, Felix (Max Planck Insitute, Leipzig)
The thresholding scheme for mean curvature flow and De Giorgi's ideas for minimizing movements
PDF of presentation

12.00-14.00

Lunch provided in the catering space

14.00-15.00

Savare, Giuseppe  (Universitt of Pavia)
Singular perturbation of gradient flows

15.00-15.30

Coffee/Tea in the catering space

15.30-16.15

Rossi, Riccarda (Universita’ degli studi di Brescia)
On the Weighted Energy-Dissipation principle for gradient flows in metric spaces
PDF of presentation

16.15-17.00

Bruna, Maria (University of Oxford)
Asymptotic gradient flows for interacting particle systems

17.00-18.00

Informal wine reception  

 

Tuesday 11 September

09.00-10.00

Peyré, Gabriel (CNRS & ENS)
Computational optimal transport for data sciences

10.00-10.30

Coffee/Tea in the catering space

10.30-11.15

Cuturi, Marco   (CREST – ENSAE, Paris)  
Regularization for optimal transport and dynamic time warping

11.15-12.00

Schmitzer, Bernhard (Muenster)                                  
Numerical approximation of optimal transport type gradient flows

12.00-14.00

Lunch provided in the catering space

14.00-15.00

Fonseca, Irene  (Carnegie Mellon University)
Mathematical analysis of novel advanced materials: epitaxy and quantum dots
PDF of presentation

15.00-15.30

Coffee/Tea in the catering space

15.30-16.15

Budd, Chris (University of Bath)
Modified error estimates for discrete variational derivative methods

16.15-17.00

Discussions/Collaboration

17.00-20.00

Young Researchers at James Clerk Maxwell Foundation, 14 India Street, Edinburgh,
EH3 6EZ
PDFs of presentations
Kaiser | Keetch | Kreusser

 

Wednesday 12 September

09.00-10.00

Brenier, Yann (CNRS, Paris)                  
The arctangential heat equation: geometry and numerics
PDF of presentation

10.00-10.30

Coffee/Tea in the catering space

10.30-11.15

Matthes, Daniel (TU Munich)                           
A semi-implicit time discretization for fourth order diffusion equations with nonlinear mobility

11.15-12.00

Maas, Jan (IST Austria)
Gromov-Hausdorff convergence of discrete optimal transport

12.00-14.00

Lunch provided in the catering space

14.00-18.00

Discussions/Collaboration/Free afternoon

17.30-18.00

Doors open to public for public lecture

18.00-19.00

Public Lecture by Chris Budd (University of Bath)
Maths is coded in your genes
Presentation of this talk at Gresham College

 

Thursday 13 September

09.00-10.00

Mielke, Alexander (WIAS Berlin)                      
On notions of evolutionary Gamma convergence for gradient systems

10.00-10.30

Coffee/Tea in the catering space

10.30-11.15

Yarman, Evren (Schlumberger)
In search for an efficient multivariate data decomposition

11.15-12.00

Zygalakis, Konstantinos (University of Edinburgh)                               
Explicit stabilised Runge-Kutta methods for optimization

12.00-14.00

Lunch provided in the catering space

14.00-15.00

Zimmer, Johannes  (University of Bath)
From fluctuations in particle systems to gradient flows

15.00-15.30

Coffee/Tea in the catering space

15.30-16.15

Wirth, Benedikt (University of Muenster)
The spline energy on Riemannian manifolds                                

16.15-18.00

Discussions/Collaboration

19.00

Workshop dinner at Blonde Restaurant, 71-75 St. Leonard's St, Edinburgh EH8 9QR

 

Friday 14 September

09.00-10.00

Benamou, Jean-David (INRIA)             
An entropy minimization approach to second-order variational mean-field games

10.00-10.30

Coffee/Tea in the catering space

10.30-11.15

Lamacz, Agnes (University of Duisburg-Essen)
Overdamped limit of the Vlasov-Fokker-Planck equation: A variational approach
PDF of presentation

11.15-12.00

Poon, Clarice (University of Cambridge)           
On the total variation Wasserstein gradient flow and the TV-JKO scheme

12.00

Close of workshop

 

Download the PDF of abstracts