Entrance hall of the ICMS

Isoperimetric problems, space-filling, and soap bubble geometry

Mar 19, 2012 - Mar 23, 2012

ICMS, 15 South College Street Edinburgh

Organisers

Name Institution
Cox, Simon Aberystwyth University
Morgan, Frank Williams College
Sullivan, John Technische Universitat Berlin

 

This workshop will address the following problems: 

• What are the main difficulties in trying to use the method of proof of the honeycomb conjecture to prove that the Kelvin cell is the least area tiling of space. Can similar tools be used to say anything about the Weaire-Phelan structure and its conjectured optimality?

• What are the optimal numerical procedures for determining conjectured minimizers for finite tilings? To what extent can they aid proofs of optimality?

• Where can this mathematics make an impact?

 The workshop will bring together experts in geometric measure theory, numerical computation, and foam structure and applications to make progress finding and proving the optimum area-minimizing cellular structures. It is anticipated that recent computational results may provide guidance in developing proofs, and results of the last 10 years will stimulate interest and further work in the area.

Each day the workshop will start with a plenary talk. Plenary speakers will be encouraged to focus on open questions to provoke discussion and debate amongst participants.  The organizers will ask participants to submit ideas for short talks on recent progress in the field to stimulate interaction and discussion. The remainder of the workshop will be made up of small group problem discussions. 

There are a limited number of spaces available at this workshop. If you would like to participate (and have not already received an invitation from ICMS by email) please apply using this application form. Completed applications must be submitted by Monday 20 February 2012 at the latest. Please note there is no financial support available from ICMS. 

A blog has been created by the workshop organisers to enable discussion in this medium ahead of the workshop. The blog can be found here.Frank Morgan also writes about the workshop here.

Photographs from the workshop can be seen on the ICMS Flickr account.

Arrangements

Venue
The workshop will take place at ICMS, 15 South College Street, Edinburgh, Scotland.

Lecture theatre facilities
The lecture theatre is fitted with data projection, visualiser (the new generation of over-head), smart-board and blackboard.  More information about the facilities are available from Helene Frossling.

Accommodation
Invited participants:
If your invitation included the offer of accommodation, then ICMS will arrange this and details will be in your letter of invitation. ICMS has reserved rooms for all delegates in University of Edinburgh en suite accommodation. All accommodation is no more than a twenty minute walk from ICMS. Please indicate on your booking form if you wish to take up the offer of these rooms or make your own arrangements. DELEGATES WILL RECEIVE INFORMATION ABOUT THEIR ACCOMMODATION IN THE FIRST WEEK OF MARCH 2012

Other participants:
ICMS cannot reserve accommodation for you. Suggestions for accommodation close to ICMS can be found here.

Meals and Refreshments
Morning and afternoon refreshments will be provided on each day of the workshop. A buffet lunch will be provided at ICMS in the Chapterhouse on the ground floor of 15 South College Street on Monday, Tuesday and Thursday. A workshop dinner will be held. The workshop grant will cover the cost of this catering.

Registration Fee and Financial Matters
A registration fee of £50 is payable by all speakers and participants. This can be paid by completing the details on this credit/debit card payment form.   As email is not secure, please print the form and return it by fax using the fax number at the top of the form.  ICMS will take your payment and a receipt will be given to you at Registration.  Alternatively, we can accept sterling cheques, made payable to Heriot-Watt University but sent to Helene Frossling , ICMS, 15 South College Street, Edinburgh, EH8 9AA.  If you have any difficulty in paying in advance, please email Helene Frossling.

Visas
ICMS asks attendees to check if they require a visa for entry to the United Kingdom. This government website gives more information. If you do require a visa ICMS will provide you with a letter in support of your application. 

Travel
Information about travel to the UK and Edinburgh is available here. Lothian buses charge 1.30 GBP for a single journey and 3.20 GBP for a day ticket. Please note that the exact fare is required and no change is given.

A taxi directly from the airport will cost approximately 18.00 to 20.00 GBP to the city centre for a one-way journey.

From the airport, you can take the airport bus Airlink to the city centre. It will cost you 3.50 GBP for a single ticket, or 6.00 GBP return. More details on the airport bus Airlink is available here. The bus will take you to Waverley Bridge (next to Waverley Railway Station).

If travelling by train, please note that Edinburgh has two railway stations - Waverley Railway Station being the main station and closest to the workshop venue at ICMS and George Square. If you alight at Edinburgh Waverley, the workshop venue is an easy 10 minute walk over North and South Bridge map. The second railway station is called Haymarket and is at the West End of the city centre.

Please note that it is your responsibility to have adequate travel insurance to cover medical and other emergencies that may occur on your trip.

Conference Co-ordinator
Helene Frossling is the conference co-ordinator for this workshop.  

 

Programme

Preliminary programme published Monday 27 February 2012. Last updated 14 March.

 

Monday 19 March

08.30 - 09.00

Registration and coffee

09.00 - 09.30

Welcome and logistics

09.30 - 10.15

Manuel Ritoré (Universidad de Granada)
Geometric inequalities and soap bubbles Link to slides (pdf)

10.15 - 10.30

Discussion

10.30 - 11.00

Coffee and tea (served in the Chapterhouse), time for private discussions

11.00 - 12.00

Contributed talks (15+5 minutes each, order may change)

 

Antonio Cañete (Universidad de Sevilla)
The isoperimetric problem in R^n for homogeneous densities Link to slides (pdf)

 

Ruggero Gabbrielli (Princeton University)
Ideas for an extension to the Frank-Kasper phases

 

Stefano Nardulli  (Universidade Federal do Rio de Janeiro)
Isoperimetry in non-compact Riemannian manifolds

12.00 - 13.30

Lunch served in the Chapterhouse

13.30 - 14.15

Thomas Hales  (University of Pittsburgh)
Computer assisted proofs and the Kelvin problem Link to slides (pdf)

14.15 - 14.30

Discussion

14.30 - 15.30

Contributed talks (15+5 minutes each, order may change)

 

Aladar Heppes (Alfred Renyi Institute of Mathematics)
Densest packing of translates of strings

 

Aldo Pratelli  (University of Pavia)
Recent existence results for the isoperimetric problem in R^N with density Link to slides (pdf)

 

Miyuki Koiso (Institute of Mathematics for Industry)
Bifurcation and stability for solutions of isoperimetric problems

15.30 - 16.00

Coffee and tea (served in the Chapterhouse), time for private discussions

16.00 - 17.00

Contributed talks (15+5 minutes each, order may change)

 

Raymond Goldstein(University of Cambridge)
A soap-film Mobius strip changes topology with a twist singularity Link to slides (pdf)

 

Paul Sutcliffe (University of Durham)
Domain walls and double bubbles Link to slides (pdf)

 

Rafi Blumenfeld (Imperial College London & Cambridge University)
Quadron tessellation, structural quantification and statistical mechanics of granular and cellular structures


Tuesday 20 March

09.30 - 10.15

Andrew Kraynik (University of Erlangen-Nuremberg)
Structure of random polydisperse soap froth Link to slides (PPTX)

10.15 - 10.30

Discussion

10.30 - 11.00

Coffee and tea (served in the Chapterhouse), time for private discussions

11.00 - 12.00

Contributed talks (15+5 minutes each, order may change)

 

Edwin Flikkema (Aberystwyth University)
From clusters of particles to 2D bubble clusters Link to slides (PPT)

 

Sepehr Ravati  (Ecole Polytechnique de Montreal)
Polymer droplet clusters

 

Adil Mughal   (Aberystwyth University)
Phyllotactic description of hard sphere packing in cylindrical channels

12.00 - 13.30

Lunch served in the Chapterhouse

13.30 - 14.15

Robert Nurnberg  (Imperial College London)
Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies Link to slides (external)

14.15 - 14.30

Discussion

14.30 - 15.30

Challenge problems: parallel session

15.30 - 16.00

Coffee and tea (served in the Chapterhouse), time for private discussions

16.00 - 17.00

Contributed talks (15+5 minutes each, order may change)

 

Simon Cox   (Aberystwyth University)
Enumeration of candidates to the minimal free cluster in 2D

 

Emanuel Lazar (Princeton University)
The "shapes" of some three-dimensional space filling patters

 

Robert Nemeth (Budapest University of Technology and Economics)
Pattern formation of lotus receptacles Link to slides (pdf)

18.00 - 19.00

PUBLIC LECTURE
Denis Weaire (Trinity College Dublin)
Me and Kelvin: how bubbles brought me to Beijing

19.00 - 19.45

Wine reception in the Chapterhouse



Wednesday 21 March

09.30 - 10.15

Gary Lawlor (Brigham Young University)
New proofs for double and triple bubbles Link to slides (PPT)

10.15 - 10.30

Discussion

10.30 - 11.00

Coffee and tea (served in the Chapterhouse), time for private discussions

 

FREE AFTERNOON

Schools outreach project: Frank Morgan - Soap Bubbles and Mathematics


Thursday 22 March

09.30 - 10.15

Sascha Hilgenfeldt  (University of Illinois at Urbana Champaign)
Order and disorder in tissues and tilings Link to slides (pdf)

10.15 - 10.30

Discussion

10.30 - 11.00

Coffee and tea (served in the Chapterhouse), time for private discussions

11.00 - 12.00

Time for private discussions

12.00 - 13.30

Lunch served in the Chapterhouse

13.30 - 14.15

Fatima Vaz and Paulo Teixeira  
Surface energy of two-dimensional finite or periodic foams Link to slides (PPT)

14.15 - 14.30

Discussion

14.30 - 15.30

Challenge problems: parallel session

15.30 - 16.00

Coffee and tea (served in the Chapterhouse), time for private discussions

16.00 - 17.00

Contributed talks (15+5 minutes each, order may change)

 

TBA

 

TBA

 

TBA

19.00

Workshop dinner at The Magnum Restaurant


 

Friday 23 March

09.30 - 10.15

John Sullivan (Technische Universitat Berlin)
Foams with small faces 

10.15 - 10.30

Discussion

10.30 - 11.00

Coffee and tea (served in the Chapterhouse), time for private discussions

11.00 - 12.00

Plenary summing-up / next steps

 


Presentations:

Presentation Details
Blumenfeld, Rafi
Quadron tessellation, structural quantification and statistical mechanics of granular and cellular structures
View Abstract Down
Cañete, Antonio
The isoperimetric problem in R^n for homogeneous densities
View Abstract Down
Cox, Simon
Enumeration of candidates to the minimal free cluster in 2D
View Abstract Down
Flikkema, Edwin
From clusters of particles to 2D bubble clusters
View Abstract Down
Gabbrielli, Ruggero
Ideas for an extension to the Frank-Kasper phases
View Abstract Down
Goldstein, Raymond E.
A soap-film Mobius strip changes topology with a twist singularity
View Abstract Down
Hales, Thomas
Computer assisted proofs and the Kelvin problem
View Abstract Down
Heppes, Aladar
Densest packing of translates of strings
View Abstract Down
Hilgenfeldt, Sascha
Order and disorder in tissues and tilings
View Abstract Down
Koiso, Miyuki
Bifurcation and stability for solutions of isoperimetric problems
View Abstract Down
Kraynik, Andrew
Structure of random polydisperse soap froth
View Abstract Down
Lawlor, Gary
New methods of proof for double and triple bubbles
View Abstract Down
Lazar, Emanuel
The "shapes" of some three-dimensional space filling patters
View Abstract Down
Morgan, Frank
Soap bubbles and mathematics
View Abstract Down
Mughal, Adil
Phyllotactic description of hard sphere packing in cylindrical channels
View Abstract Down
Nardulli, Stefano
Isoperimetry in non-compact Riemannian manifolds
View Abstract Down
Németh, Róbert
Pattern formation of lotus receptacles
View Abstract Down
Nurnberg, Robert
Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies
View Abstract Down
Pratelli, Aldo
Recent existence results for the isoperimetric problem in R^N with density
View Abstract Down
Ritoré, Manuel
Geometric inequalities and soap bubbles
View Abstract Down
Sullivan, John
Foams with small faces
View Abstract Down
Sutcliffe, Paul
Domain walls and double bubbles
View Abstract Down
Teixeira, Paulo
Surface energy of two-dimensional finite or periodic foams
View Abstract Down
Vaz, Fatima
Surface energy of two-dimensional finite or periodic foams
View Abstract Down
Weaire, Denis
Me and Kelvin: how bubbles brought me to Beijing
View Abstract Down

Participants

Name Institution
Blumenfeld, Rafi Imperial College London & Cambridge University
Cañete, Antonio Universidad de Sevilla
Cinti, Eleonora Università di Pavia
Cox, Simon Aberystwyth University
Flikkema, Edwin Aberystwyth University
Gabbrielli, Ruggero Princeton University
Goldstein, Raymond E. University of Cambridge
Hales, Thomas University of Pittsburgh
Heppes, Aladar Alfred Renyi Institute of Mathematics
Hilgenfeldt, Sascha University of Illinois at Urbana Champaign
Koiso, Miyuki Kyushu University
Kraynik, Andrew University of Erlangen-Nuremberg
Lawlor, Gary Brigham Young University
Lazar, Emanuel Institute for Advanced Study
Morgan, Frank Williams College
Mughal, Adil Aberystwyth University
Nardulli, Stefano Universidade Federal do Rio de Janeiro
Németh, Róbert Budapest University of Technology and Economics
Neumann-Chun, Nicholas Williams College
Nurnberg, Robert Imperial College London
Oudet, Edouard LJK, Universite Joseph Fourier
Pesci, Adriana University of Cambridge
Pratelli, Aldo Friedrich-Alexander-Universität Erlangen-Nürnberg
Ravati, Sepehr Ecole Polytechnique de Montreal
Ritoré, Manuel Universidad de Granada
Sullivan, John Technische Universitat Berlin
Sutcliffe, Paul Durham University
Taylor, Jean Courant Institute, NYU
Teixeira, Paulo Lisbon Polytechnic Institute and CFTC-UL
Tibor, Tarnai Budapest University of Technology and Economics
Vaz, Fatima ICEMS and Instituto Superior Tecnico, UTL
Vernadakis, Efstratios University of Granada
Weaire, Denis Trinity College Dublin