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) |
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) |
| Ruggero Gabbrielli (Princeton University) |
| Stefano Nardulli (Universidade Federal do Rio de Janeiro) |
12.00 - 13.30 | Lunch served in the Chapterhouse |
13.30 - 14.15 | Thomas Hales (University of Pittsburgh) |
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) |
| Aldo Pratelli (University of Pavia) |
| Miyuki Koiso (Institute of Mathematics for Industry) |
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) |
| Paul Sutcliffe (University of Durham) |
| Rafi Blumenfeld (Imperial College London & Cambridge University) |
Tuesday 20 March
09.30 - 10.15 | Andrew Kraynik (University of Erlangen-Nuremberg) |
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) |
| Sepehr Ravati (Ecole Polytechnique de Montreal) |
| Adil Mughal (Aberystwyth University) |
12.00 - 13.30 | Lunch served in the Chapterhouse |
13.30 - 14.15 | Robert Nurnberg (Imperial College London) |
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) |
| Emanuel Lazar (Princeton University) |
| Robert Nemeth (Budapest University of Technology and Economics) |
18.00 - 19.00 | PUBLIC LECTURE |
19.00 - 19.45 | Wine reception in the Chapterhouse |
Wednesday 21 March
09.30 - 10.15 | Gary Lawlor (Brigham Young University) |
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) |
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 |
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) |
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 | |
Cañete, Antonio | |
The isoperimetric problem in R^n for homogeneous densities | |
View Abstract | |
Cox, Simon | |
Enumeration of candidates to the minimal free cluster in 2D | |
View Abstract | |
Flikkema, Edwin | |
From clusters of particles to 2D bubble clusters | |
View Abstract | |
Gabbrielli, Ruggero | |
Ideas for an extension to the Frank-Kasper phases | |
View Abstract | |
Goldstein, Raymond E. | |
A soap-film Mobius strip changes topology with a twist singularity | |
View Abstract | |
Hales, Thomas | |
Computer assisted proofs and the Kelvin problem | |
View Abstract | |
Heppes, Aladar | |
Densest packing of translates of strings | |
View Abstract | |
Hilgenfeldt, Sascha | |
Order and disorder in tissues and tilings | |
View Abstract | |
Koiso, Miyuki | |
Bifurcation and stability for solutions of isoperimetric problems | |
View Abstract | |
Kraynik, Andrew | |
Structure of random polydisperse soap froth | |
View Abstract | |
Lawlor, Gary | |
New methods of proof for double and triple bubbles | |
View Abstract | |
Lazar, Emanuel | |
The "shapes" of some three-dimensional space filling patters | |
View Abstract | |
Morgan, Frank | |
Soap bubbles and mathematics | |
View Abstract | |
Mughal, Adil | |
Phyllotactic description of hard sphere packing in cylindrical channels | |
View Abstract | |
Nardulli, Stefano | |
Isoperimetry in non-compact Riemannian manifolds | |
View Abstract | |
Németh, Róbert | |
Pattern formation of lotus receptacles | |
View Abstract | |
Nurnberg, Robert | |
Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies | |
View Abstract | |
Pratelli, Aldo | |
Recent existence results for the isoperimetric problem in R^N with density | |
View Abstract | |
Ritoré, Manuel | |
Geometric inequalities and soap bubbles | |
View Abstract | |
Sullivan, John | |
Foams with small faces | |
View Abstract | |
Sutcliffe, Paul | |
Domain walls and double bubbles | |
View Abstract | |
Teixeira, Paulo | |
Surface energy of two-dimensional finite or periodic foams | |
View Abstract | |
Vaz, Fatima | |
Surface energy of two-dimensional finite or periodic foams | |
View Abstract | |
Weaire, Denis | |
Me and Kelvin: how bubbles brought me to Beijing | |
View Abstract |
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 |