Entrance hall of the ICMS Workshop

Shape optimization and spectral geometry

Jun 29, 2015 - Jul 03, 2015

ICMS, 15 South College Street, Edinburgh

Organisers

Name Institution
Bucur, Dorin Université de Savoie
Buttazzo, Guiseppe University of Pisa
Pratelli, Aldo Friedrich-Alexander-Universität Erlangen-Nürnberg
van den Berg, Michiel University of Bristol

The main purpose of this workshop is to bring together experts working on various topics involving partial differential equations on variable domains, with particular attention to the dependence of the solutions of the state equations (generally a partial differential equations) on the geometry of their domain of definition. Participants will include specialists on: shape optimization problems; spectral geometry; and isoperimetric inequalities and other geometric or functional inequalities.


The intention is to present the state-of-the-art on some celebrated open problems and conjectures, and try to make a step forward in the direction of solving them, or at least to obtain new partial information.

Group photographs of workshop participants can be found on the ICMS Flickr account 

This workshop is generously supported by the EPSRC, Foundaton Compositio and ERC grant 258685 Analisis of optimal sets and optimal constants.  


EPSRC logo   ERC Logo    Compositio Logo

 

Arrangements

The workshop will begin at 08:30 with registration on Monday morning 29 June and close around midday on Friday 3 July 2015.   Please take these timings into account when booking your travel. 

Participation
Participation for this event is by invitation only.   Invitees will have received an emailed invitation from ICMS, on behalf of the Scientific Organisers, in February 2015.

Venue and Talks
The workshop will be held at 15 South College Street, Edinburgh.  You may also find this map useful for the workshop.  All lectures will be held in the Newhaven Lecture Theatre.    The Lecture Theatre is equipped with a data projector, computer, visualiser (the new generation of overhead projectors) and two blackboards.  The projector and one board may be used simultaneously.  It is best to bring your presentation on a memory stick to use in our ICMS computer.   Alternatively, it is possible for you to use your own laptop with our dataprojector, but please be aware that you may have to alter your laptop resolutions/settings. 

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 that may occur on your trip.

A taxi directly from the airport will cost approximately 20.00 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 4.00 single or 7.00 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 and the workshop venue. 

Lothian buses charge £1.50 for a single, £3.50 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 meeting venue is an easy 10 minute walk over North and South Bridge.  The other railway stations are Haymarket and Edinburgh Park but please note that these stations are at the West End of the city centre.

Accommodation
ICMS will organise accommodation for all Invited Participants.

Public Lecture
On Tuesday 30 June, Bernd Kawohl will give a Public Lecture (title and abstract below).  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 at ICMS from 19.00-20.00.    Seats have been reserved in the Lecture Theatre for all the workshop participants so there is no need for you to book a seat.

On buttons and balls that cannot run away
When does a steel pipe have an exactly circular cross section? When it features constant exterior width from every angle? That could easily be verified with a big caliper or slide gauge, and this procedure was used in the process of assembling booster rockets for the space shuttle. The authors of the corresponding manuals had overlooked that there are geometric shapes, so-called sets of constant width, that are not circles. This was a contributing factor to the Challenger disaster in 1986. In my talk I will point out that these odd sets show up in our daily life, how their knowledge can be used to drill square holes, and that there are interesting mathematical questions connected with them. The talk is directed at a general audience. 

Organised historical tour of Edinburgh, Wednesday, 1 July, at 14:30
After lunch on Wednesday, 1 July,  14:30, ( the free afternoon of the workshop), a   historical tour of Edinburgh has been booked for all participants who wish to join it. The tour led by David Nish, a published historian, born and raised on Edinburgh's world famous Royal Mile, will take you round and show you a street full of hidden closes with hundreds of years of history (often dark) and inspired many famous literary figures and other national heroes. The tour will last approximately 60 - 90 minutes and is highly recommended. Please indicate on arrival to ICMS, at registration,  if you would like to come along to this exciting tour. The cost is covered by the workshop grant and is free to all participants.

Catering
The workshop grant will cover refreshments throughout the event, lunch on several days, an informal wine reception one evening and a Workshop Dinner.  

Wireless Access
The workshop venue, 15 South College Street, has wireless access throughout. On arrival at Registration you will be given instructions and a code for accessing the wireless network.  For those without laptops, there will also be a couple of computers available for you to check your emails. 

Registration Fee
There is no registration fee for this workshop.

 

 

Programme

HPlease continue to check the Programme until the time of the workshop as any updates will be notified here.

 

Monday 29 June 2015

08:30-09:30

Registration & coffee in the Chapterhouse, Level 1

09:30-10:20

Mark Ashbaugh (University of Missouri - Columbia)
A sharp lower bound for the first Eigenvalue of the vibrating clamped plate under compression

pdf of presentation

10:30-10:55

Ilaria Fragalà (Politecnico di Milano)
Mahler inequality for the first eigenvalue of the Dirichlet Laplacian

pdf of presentation

11:00-11:30

Coffee/Tea in the Chapterhouse, Level 1

11:30-12:20

Bruno Colbois (University of Neuchâtel)
The shape of Riemannian manifolds and submanifolds with large eigenvalues

12:30-14:00

Lunch provided in the Chapterhouse, Level1

14:00-14:50

Guido De Philippis (ENS Lyons)
Regularity of free boundaries in anisotropic capillarity problems and the validity of Young's law

15:00-15:50

Pedro Freitas (University of Lisbon)
Optimal Laplace determinants

16:00-16:30

Coffee/Tea in the Chapterhouse, Level 1

16:30-16:55

Peter Gilkey (University of Oregon)
Heat content asymptotics

pdf of presentation

17:00-17:25

Bozhidar Velichkov (Université Joseph Fourier)
TBA

17:30-19:00

Informal Wine Reception & buffet in the Chapterhouse, Level 1

 

Tuesday 30 June

09:00-09:50

Almut Burchard (University of Toronto)
To follow

10:00-10:50

Iosif Polterovich (Université de Montréal)
Spectral geometry for the Steklov problem

pdf of presentation

11:00-11:30

Coffee/Tea in the Chapterhouse, Level 1

11:30-11:55

Leonid Parnovski  (University College London)
Asymptotic behaviour of the local

pdf of presentation 

12:00-12:25

Carlo Nitsch (University of Naples)
On the elastic energy of Planar curves

pdf of presentation 

12:30-14:00

Lunch provided in the Chapterhouse, Level 1

14:00-14:50

Richard Laugesen (University of Illinois)
Steklov spectral inequalities through quasiconformal mapping

pdf of presentation 

15:00-15:50

Evans Harrell (Georgia Institute of Technology)
Semiclassically sharp bounds for sums of eigenvalues and heat traces

16:00-16:30

Coffee/Tea in the Chapterhouse, Level1

16:30-16:55

Jimmy Lamboley (University Paris-Dauphine)
Optimal compliance problem

pdf of presentation  

17:00-17:25

James Kennedy (University of Stuttgart)
Eigenvalue estimates for quantum graphs

pdf of presentation  

18:00-19:00

Public Lecture by Bernd Kawohl (University of Cologne)
On buttons and balls that cannot run away

19:00-20:00

Informal wine reception in the Chapterhouse, Level 1

 

Wednesday 1 July

09:00-09:50

Antoine Henrot (Université de Lorraine)
Towards the sharp constant in the quantitative isoperimetric inequality in the plane

pdf of presentation  

10:00-10:50

Nicola Fusco (University of Naples 'Federico II')
Stability and minimality fo a nonlocal variational problem

pdf of presentation  

11:00-11:30

Coffee/Tea in the Chapterhouse, Level 1

11:30-11:55

Lorenzo Brasco (Aix-Marseille Université)
An improved energy bound for Schrödinger operators

pdf of presentation  

12:00- 12:25

Alexandre Girouard (Université Laval)
The spectral gap of graphs and Steklov eigenvalues on surfaces

pdf of presentation  

12:30-14:00

Lunch in the Chapterhouse, Level 1

 

Thursday 2 July

09:00-09:50

Rafael Benguria (Pontificia Universidad Católica de Chile)
The Brezis-Nirenberg Problem on mathbb{S}^n, in spaces of fractional dimension

10:00-10:50

Nicolai Nadirashvili (CNRS France)
Extremals of conformal spectrum of the Laplacian

11:00-11:30

Coffee/Tea in the Chapterhouse, Level 1

11:30-11:55

Cristina Trombetti (University of Naples)
Best constants in some Sobolev Poincaré trace inequalities

pdf of presentation  

12:00-12:25

Emily Dryden (Bucknell University)
Can you hear the metric on a sphere?

12:30-14:00

Lunch provided in the Chapterhouse, Level 1

14:00-14:50

Michel Pierre (ENS Rennes and IRMAR)
Estimates of shape deriatives around nonsmooth domains

pdf of presentation  

15:00-15:50

Bernard Helffer (Université Paris-Sud)
On noal and minimal k-partitions

pdf of presentation  

16:00-16:30

Coffee/Tea in the Chapterhouse, Level 1

16:30-16:55

Virgininie Bonnaillie-Noel (CNRS, ENS Paris)
Minimal spectral partitions

19.00

Workshop Dinner at the Magnum, 1 Albany Street, Edinburgh

 

Friday 3 July

09:00-09:25

Julie Rowlett (Chalmers University)
When can one hear the shape of a drum?

09:30-09:55

Friedmann Brock (Leipzig University)
Isoperimetric inequalities with power weights

10:00-10:25

Dario Mazzoleni (University of Torino)
A surgery result for the spectrum of the Dirichlet Laplacian

10:30-11:00

Coffee/Tea in the Chapterhouse, Level 1

11:00-11:50

Susanna Terracini (University of Torino)
Existence and regularity of solutions to optimal partition problems involving Laplacian eigenvalues

pdf of presentation  

12:00

Close of workshop (no lunch provided)

 

Presentations:

Presentation Details
Ashbaugh, Mark
A Sharp Lower Bound for the First Eigenvalue of the Vibrating Clamped Plate under Compression
View Abstract Down
Benguria, Rafael
The Brezis--Nirenberg Problem on $mathbb{S}^n$, in spaces of fractional dimension
View Abstract Down
Bonnaillie-Noel, Virginie
Minimal spectral partitions
View Abstract Down
Brasco, Lorenzo
An improved energy bound for Schr"odinger operators
View Abstract Down
Brock, Friedemann
Isoperimetric inequalities with power weights
View Abstract Down
Colbois, Bruno
The shape of Riemannian manifolds and submanifolds with large eigenvalues.
View Abstract Down
De Philippis, Guido
Regularity of free boundaries in anisotropic capillarity problems and the validity of Young's law
View Abstract Down
Dryden, Emily
Can you hear the metric on a sphere?
View Abstract Down
Fragalà, Ilaria
Mahler inequality for the first eigenvalue of the Dirichlet Laplacian
View Abstract Down
Freitas, Pedro
Optimal Laplace determinants
View Abstract Down
Fusco, Nicola
Stability and minimality for a nonlocal variational problem
View Abstract Down
Gilkey, Peter
Heat Content Asymptotics
View Abstract Down
Girouard, Alexandre
The spectral gap of graphs and Steklov eigenvalues on surfaces.
View Abstract Down
Harrell, Evans
Semiclassically sharp bounds for sums of eigenvalues and heat traces.
View Abstract Down
Helffer, Bernard
On nodal and minimal k-partitions
View Abstract Down
Henrot, Antoine
Towards the sharp constant in the quantitative isoperimetric inequality in the plane
View Abstract Down
Kawohl, Bernd
On buttons and balls that cannot run away
View Abstract Down
Kennedy, James
Eigenvalue estimates for quantum graphs
View Abstract Down
Lamboley, Jimmy
Optimal compliance problem
View Abstract Down
Laptev, Ari
One-dimensional interpolation inequalities, Carlson-Landau inequalities and magnetic Schrödinger operators
View Abstract Down
Laugesen, Richard
Steklov spectral inequalities through quasiconformal mapping.
View Abstract Down
Mazzoleni, Dario
A surgery result for the spectrum of the Dirichlet Laplacian'
View Abstract Down
Nadirashvili, Nicolai
Extremals of conformal spectrum of the Laplacian
View Abstract Down
Nitsch, Carlo
On the Elastic Energy of Planar Curves
View Abstract Down
Parnovskii, Leonid
Asymptotic behaviour of the local density of states and the spectral function of multidimensional almost-periodic Schroedinger operators.
View Abstract Down
Pierre, Michel
Estimates of shape derivatives around nonsmooth domains.
View Abstract Down
Polterovich, Iosif
Spectral geometry of the Steklov problem
View Abstract Down
Rowlett, Julie
When can one hear the shape of a drum?
View Abstract Down
Terracini, Susanna
Existence and regularity of solutions to optimal partition problems involving Laplacian eigenvalues
View Abstract Down
Trombetti, Cristina
Best constants in some Sobolev Poincaré trace inequalities
View Abstract Down
Velichkov, Bozhidar
A free boundary problem arising in PDE optimization
View Abstract Down

Participants

Name Institution
Ashbaugh, Mark University of Missouri
Bandle, Catherine University of Basel
Benguria, Rafael Pontificia Universidad Católica de Chile
Bogosel, Beniamin Universite de Savoie
Bonnaillie-Noel, Virginie CNRS, ENS Paris
Brasco, Lorenzo Aix-Marseille Université
Brock, Friedemann Leipzig University
Buckley, Jerry King's College London
Bucur, Dorin Université de Savoie
Burchard, Almut University of Toronto
Buttazzo, Guiseppe University of Pisa
Colbois, Bruno University of Neuchâtel
De Philippis, Guido ENS Lyons
Dryden, Emily Bucknell University
Fragalà, Ilaria Politecnico di Milano
Freitas, Pedro University of Lisbon
Fusco, Nicola University of Naples 'Federico II'
Gilkey, Peter University of Oregon
Girouard, Alexandre Université Laval
Gittins, Katie University of Bristol
Harrell, Evans Georgia Institute of Technology
Hassannezhad, Asma Max-Planck Institute for Mathematics
Helffer, Bernard University Paris-Sud
Henrot, Antoine Université de Lorraine
Hoffmann-Ostenhof, Thomas University of Vienna
Jakobson, Dmitry McGill University
Karpukhin, Mikhail McGill University
Kawohl, Bernd University of Cologne
Kennedy, James University of Stuttgart
Lamboley, Jimmy University Paris-Dauphine
Laugesen, Richard University of Illinois
Levitin, Michael University of Reading
Malchiodi, Andrea Scuola Normale Superiore
Mazzoleni, Dario University of Torino
Nadirashvili, Nicolai CNRS France
Netrusov, Yuri University of Bristol
Nitsch, Carlo University of Naples
Parini, Enea Université Aix-Marseille
Parnovskii, Leonid University College London
Pierre, Michel ENS Rennes and IRMAR
Polterovich, Iosif Université de Montréal
Pratelli, Aldo Friedrich-Alexander-Universität Erlangen-Nürnberg
Radici, Emanuela Friedrich-Alexander Universität Erlangen-Nürnberg
Rowlett, Julie Chalmers University
Ruffini, Berardo École Polytechnique
Siudeja, Bartlomiej University of Oregon
Steinerberger, Stefan Yale University
Terracini, Susanna University of Torino
Trombetti, Cristina University of Naples
van den Berg, Michiel University of Bristol
Velichkov, Bozhidar Université Joseph Fourier
Wigman, Igor King's College London
Zeisler, Florian Friedrich-Alexander Universität Erlangen-Nürnberg