Organizing Committee
Abstract

The packing and covering of equal geometric shapes, such as spheres or convex polyhedra, are classical geometric optimization problems. They have a long mathematical tradition and were for instance part of Hilbert's famous twenty-three problems for the 20th century. Nevertheless, seemingly simple packing and covering problems are still extremely hard to solve and generally, far from a solution. Likewise, minimal energy problems for pair potentials, of which best-packing is a special case, have many such unresolved questions.

However, in recent years several new developments with computer assisted approaches have led to previously unexpected breakthrough results. These involve massive computer searches and techniques from numerical optimization, as well as the creation and application of new optimization techniques, such as specific semi-definite programming bounds. New techniques for computer assisted certified proofs allow one to obtain results that would otherwise have been difficult, if not impossible, to check.

During this workshop, we will bring together energy, packing and covering experts from these new computation-based research directions.

Image for "Computation and Optimization of Energy, Packing, and Covering"

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, April 9, 2018
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration121 South Main Street Providence RI 11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45am EDTHyperuniform Point Configurations - Salvatore Torquato, Princeton University11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:30 - 11:15am EDTPacking and Assembling Spheres in Cylindrical Confinement - Patrick Charbonneau, Duke University11th Floor Lecture Hall
11:30 - 12:15pm EDTRandom walks on perfect lattices and the sphere packing problem. - Antonello Scardicchio, International Centre for Theoretical Physics11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTLimit-periodic tilings in 1, 2, and 3 dimensions - Joshua Socolar, Physics Department, Duke University11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break 11th Floor Collaborative Space 
4:00 - 4:45pm EDTComplete positivity and distance-avoiding sets - Fernando de Oliveira Filho, Technical University Delft11th Floor Lecture Hall 
5:00 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, April 10, 2018
TimeEventLocationMaterials
9:00 - 9:45am EDTComputation of good point sets for separation, covering and polarization on the sphere - Robert Womersley, University of New South Wales11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:30 - 11:15am EDTApproximation of 1-qubit gates Energy and Discrepancy. - Steve Damelin, American Mathematical Society11th Floor Lecture Hall
11:30 - 12:15pm EDTPackings in spherical confinements - Marjolein Dijkstra, Debye institute for Nanomaterials Science, Utrecht University11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTPacking Liquid Crystal Domains - Randall Kamien, University of Pennsylvania11th Floor Lecture Hall
3:30 - 5:00pm EDTPoster Session Coffee/Tea Break 11th Floor Collaborative Space 
Wednesday, April 11, 2018
TimeEventLocationMaterials
9:00 - 9:45am EDTHyperuniformity on the sphere - Peter Grabner, Technische Universität Graz11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:30 - 11:15am EDTTammes' problem and irreducible contact graphs - Oleg Musin, University of Texas Rio Grande Valley11th Floor Lecture Hall 
11:30 - 12:15pm EDTGordian Configurations - Woden Kusner, Vanderbilt University11th Floor Lecture Hall
12:30 - 12:40pm EDTWorkshop Group Photo11th Floor Lecture Hall 
12:40 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTUniversal hidden order in amorphous cellular geometries - Gerd Schroeder-Turk, Murdoch University11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break 11th Floor Collaborative Space 
4:00 - 4:45pm EDTNew bounds for spherical finite distance sets - David de Laat, ICERM - MIT11th Floor Lecture Hall
6:30 - 8:00pm EDTPublic Lecture: Crowd Computing: Scientific discoveries by protein-folding game players - Firas Khatib, UMass Dartmouth11th Floor Lecture Hall 
Thursday, April 12, 2018
TimeEventLocationMaterials
9:00 - 9:45am EDTThe upper density of sets avoiding norm one in the real space of dimension n - Christine Bachoc, Université de Bordeaux11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:30 - 11:15am EDTSets with few distances and their optimality - Alexey Glazyrin, University of Texas Rio Grande Valley11th Floor Lecture Hall
11:30 - 12:15pm EDTLattice Coverings - Mathieu Dutour Sikiric, Institut Rudjer Boskovic11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTEnergy minimization for periodic sets in Euclidean spaces - Renaud Coulangeon, Université de Bordeaux11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break 11th Floor Collaborative Space 
4:00 - 4:45pm EDTSpherical designs, complex spherical designs, and unitary designs - Eiichi Bannai, Kyushu University11th Floor Lecture Hall
Friday, April 13, 2018
TimeEventLocationMaterials
9:00 - 9:45am EDTTBA - Henry Cohn, Microsoft Research New England11th Floor Lecture Hall 
10:00 - 10:30am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:30 - 11:15am EDTThe Gaussian core model in high dimensions - Matthew de Courcy-Ireland, Princeton University11th Floor Lecture Hall
11:30 - 12:15pm EDT5 Points on a sphere - Richard Schwartz, Brown University11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
3:30 - 4:00pm EDTCoffee/Tea Break 11th Floor Collaborative Space 

Associated Semester Workshops

Optimal and Random Point Configurations
Image for "Optimal and Random Point Configurations"

Lecture Videos

Lattice Coverings

Mathieu Dutour Sikiric
Rudjer Boskovic Institute
April 12, 2018