This workshop will be offered virtually. The in-person meeting has been cancelled due to the COVID-19 outbreak. A schedule for virtual talks will be posted soon. Accepted participants will be notified how to access the virtual presentations.
Organizing Committee

This workshop brings together two distinct streams of mathematics - on the one hand, the classical rigidity theory of bar-joint frameworks in combinatorics and discrete geometry, and on the other the theory of generalized circle packings that arose from the study of 3-manifolds in geometric topology.

Combinatorial and Geometric rigidity theory is concerned with the local and global uniqueness of congruence classes of frameworks as solutions to their underlying geometric constraint system.

The focal point of circle packing theory is the Koebe-Andre'ev-Thurston Theorem that gives conditions that guarantee the existence and rigidity of circle packings on closed surfaces in the pattern of a given triangulation of the surface.

A scattering of results in recent years has started to forge connections between these research areas. The main aim of the workshop is to develop a cross-fertilization of such ideas, with particular emphasis on the rigidity of inversive distance packings. As well as presentations on cutting edge research, the workshop will be an opportunity for new collaborations to emerge.

Image for "VIRTUAL ONLY: Circle Packings and Geometric Rigidity"

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, July 6, 2020
8:50 - 9:00am EDTWelcome - ICERM Director  
9:00 - 9:45am EDTFloppy Rigidity- circle packing via discrete schwarzian derivatives - Ken Stephenson, University of Tennessee Knoxville 
10:00 - 10:30am EDTCoffee/ Tea Break  
10:30 - 11:15am EDTAbstract 3-Rigidity and Bivariate Splines - Bill Jackson, Queen Mary University of London 
11:30 - 12:15pm EDTGeneric rigidity via many anisotropic subspaces, and higher Laman type theorems - Karim Adiprasito, Hebrew University of Jerusalem 
12:30 - 1:30pm EDTBreak for Lunch/ Free time  
1:30 - 2:15pm EDTDesign of hinged 3D auxetic mechanisms - Elisabetta Matsumoto, Georgia Institute of Technology 
2:30 - 3:00pm EDTCoffee/ Tea Break  
3:00 - 3:45pm EDTSome convergence results in discrete conformal geometry - Feng Luo, Rutgers University 
4:00 - 4:45pm EDTConnections - Robert Connelly, Cornell University 
Tuesday, July 7, 2020
9:00 - 9:45am EDTDensity of binary disc packings - Thomas Fernique, CNRS and Université Sorbonne Paris Cité 
10:00 - 10:30am EDTCoffee/ Tea Break  
10:30 - 11:15am EDTRigidity for sticky disks - Louis Theran, University of St Andrews 
11:30 - 12:15pm EDTPacking Disks Using Flipping and Flowing - Steven Gortler, SEAS Harvard University 
12:30 - 1:30pm EDTBreak for Lunch/ Free time  
1:30 - 2:15pm EDTAlmost-rigidity of frameworks - Miranda Holmes-Cerfon, Courant Institute of Mathematical Sciences 
2:30 - 3:00pm EDTCoffee/ Tea Break  
3:00 - 3:45pm EDTFlip Paths, Farey Sequences and Material Defects - Meera Sitharam, University of Florida 
4:00 - 5:00pm EDTLightning Talks - Zhen Zhang, Sean Dewar, Veit Elser, Eran Nevo, Elias Wegert, Aleksandr Kolpakov, Georg Grasegger, & Daria Pchelina  
Wednesday, July 8, 2020
9:00 - 9:45am EDTRigidity of Random Subgraphs - Shin-ichi Tanigawa, University of Tokyo 
10:00 - 10:30am EDTCoffee/ Tea Break  
10:30 - 11:15am EDTUniqueness of nonnegative matrix factorizations by rigidity theory - Kaie Kubjas, Aalto University 
11:30 - 12:15pm EDTOrthogonal ring patterns - Alexander Bobenko, Technische Universität Berlin  
12:30 - 1:30pm EDTBreak for Lunch/ Free time  
1:30 - 2:15pm EDTInfinitesimal periodic deformations and quadrics - Ileana Streinu, Smith College 
2:30 - 3:00pm EDTCoffee/ Tea Break  
3:00 - 3:45pm EDTAbel-Jacobi Condition for Quadrilateral Mesh Generation - David Xianfeng Gu, Stony Brook University 
4:00 - 4:45pm EDTThe spectrum of the Laplacian in a domain bounded by a flexible polyhedron in Euclidean space does not always remain unaltered during the flex - Victor Alexandrov, The Sobolev Institute of Mathematics 
Thursday, July 9, 2020
9:00 - 9:45am EDTCircle packings on surfaces with complex projective structures - Jean-Marc Schlenker, University of Luxembourg 
10:00 - 10:30am EDTCoffee/ Tea Break  
10:30 - 11:15am EDTRigidity of Intermingled Point and Sphere Configurations - Opal Graham, Florida State University 
11:30 - 12:15pm EDTDistinct Distances and Rigidity - Orit Raz, Hebrew University of Jerusalem 
12:30 - 1:30pm EDTBreak for Lunch/ Free time  
1:30 - 2:15pm EDTThe interplay between circle packings and subdivision rules - William Floyd, Virginia Tech 
2:30 - 3:00pm EDTCoffee/ Tea Break  
3:00 - 3:45pm EDTRigidity, associahedron graph and eigenvalues - Sebi Cioaba, University of Delaware 
4:00 - 5:00pm EDTLightning Talks - Tom Gilat, Lorenzo Ruffoni, Georg Nawratil, Daniel Bernstein, Tianqi Wu, Qays Shakir, & Alex Kontorovich  
Friday, July 10, 2020
8:00 - 9:00am EDTSpatial Chat Social Breakfast  
9:00 - 9:45am EDTGlobally rigid powers of graphs - Tibor Jordán, Eötvös University Budapest 
10:00 - 10:30am EDTCoffee/ Tea Break  
10:30 - 11:15am EDTDiscrete uniformization and ideal hyperbolic polyhedra - Boris Springborn, Technische Universität Berlin 
11:30 - 12:15pm EDTQuadratic differentials and deformation space of circle patterns on surfaces - Wai Yeung Lam, Université du Luxembourg 
12:30 - 1:30pm EDTBreak for Lunch/ Free time  
1:30 - 2:15pm EDTAuxetic bracing - Ciprian Borcea, Rider University 
2:30 - 3:00pm EDTCoffee/ Tea Break  
3:00 - 3:45pm EDTOn saturated bi-layered disk shaped tetrahedral packings - Brigitte Servatius, Worcester Polytechnic Institute 

Request Reimbursement

As this program is funded by the National Science Foundation (NSF), ICERM is required to collect your ORCID iD if you are receiving funding to attend this program. Be sure to add your ORCID iD to your Cube profile as soon as possible to avoid delaying your reimbursement.
Acceptable Costs
  • 1 roundtrip between your home institute and ICERM
  • Flights on U.S. or E.U. airlines – economy class to either Providence airport (PVD) or Boston airport (BOS)
  • Ground Transportation to and from airports and ICERM.
Unacceptable Costs
  • Flights on non-U.S. or non-E.U. airlines
  • Flights on U.K. airlines
  • Seats in economy plus, business class, or first class
  • Change ticket fees of any kind
  • Multi-use bus passes
  • Meals or incidentals
Advance Approval Required
  • Personal car travel to ICERM from outside New England
  • Multiple-destination plane ticket; does not include layovers to reach ICERM
  • Arriving or departing from ICERM more than a day before or day after the program
  • Multiple trips to ICERM
  • Rental car to/from ICERM
  • Flights on a Swiss, Japanese, or Australian airlines
  • Arriving or departing from airport other than PVD/BOS or home institution's local airport
  • 2 one-way plane tickets to create a roundtrip (often purchased from Expedia, Orbitz, etc.)
Reimbursement Request Form

Refer to the back of your ID badge for more information. Checklists are available at the front desk.

Reimbursement Tips
  • Scanned original receipts are required for all expenses
  • Airfare receipt must show full itinerary and payment
  • ICERM does not offer per diem or meal reimbursement
  • Allowable mileage is reimbursed at prevailing IRS Business Rate and trip documented via pdf of Google Maps result
  • Keep all documentation until you receive your reimbursement!
Reimbursement Timing

6 - 8 weeks after all documentation is sent to ICERM. All reimbursement requests are reviewed by numerous central offices at Brown who may request additional documentation.

Reimbursement Deadline

Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. Submissions after thirty days will incur applicable taxes. No submissions are accepted more than six months after the program end.

Lecture Videos

Auxetic bracing

Ciprian Borcea
Rider University
July 10, 2020

Orthogonal ring patterns

Alexander Bobenko
Technische Universität Berlin
July 8, 2020

Density of binary disc packings

thomas fernique
CNRS & Université Sorbonne Paris Cité
July 7, 2020


Robert Connelly
Cornell University
July 6, 2020