Organizing Committee
Abstract

This workshop will bring together researchers interested in a panoply of unusual configuration spaces, arising in applied fields or in plausible models, to look for similarities or creative tensions between them.

Classical configuration spaces in mechanics are spaces of tuples of material points in Euclidean 3D space, sometimes constrained by the mutual distances or just precluding coincidences of any two particles. The no-k-equal configuration spaces and their generalizations relax the no-coincidence conditions allowing some number (greater than 1) of points to coincide. Linkages and origami (hinged structures) represent another well-established class of configuration spaces. Despite many spectacular results on the topology and geometry of the configuration (or moduli) spaces of such mechanical constructions, many natural questions are hard and remain unanswered. In general, neither the topology (even for generic structures), nor singularities of the configuration spaces are known beyond the simplest examples.

Beyond serial linkages (robot arms), configuration spaces in robotics are the source of many unsolved questions, such as the tantalizing question concerns caging a polygonal 2D shape by a finite collection of pointlike "fingers". Even more exotic are the configuration spaces of hard balls, arising from the archetypal model of statistical physics, Boltzmann gas. Their topology has not been addressed in any detail until very recently, and many basic questions such as the connectivity of the configuration spaces of the hard balls in the "gaseous" regime are unknown.

Along with the mathematical aspects, computational experimentation aspects will be highlighted, as well as applications ranging from path planning algorithms for robots, reconfiguration strategies for origami and protein folding.

Confirmed Speakers & Participants

Workshop Schedule

Monday, September 12, 2016
TimeEventLocationMaterials
8:45 - 9:15Registration121 South Main Street, Providence, RI; 11th Floor 
9:15 - 9:30Welcome - Brendan Hassett, ICERM Director11th Floor Lecture Hall 
9:30 - 10:15Spaces of non-k-equal configurations in a Euclidean space and the little discs operad - Victor Turchin, Kansas State University11th Floor Lecture Hall
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:45The toric geometry of triangulated polygons in Euclidean space. - John Millson, University of Maryland11th Floor Lecture Hall
12:00 - 2:30Break for Lunch/Free Time  
2:30 - 3:15Spaces of triangulations of a square - Aaron Abrams, Washington and Lee University11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Local multiplicity of continuous maps between manifolds - Pavle Blagojevic, Free University Berlin and Mathematical Institute SASA Belgrade11th Floor Lecture Hall
5:00 - 6:30Welcome Reception11th Floor Collaborative Space 
Tuesday, September 13, 2016
TimeEventLocationMaterials
9:00 - 9:45The set of flexible nondegenerate polyhedra of a prescribed combinatorial structure is not always algebraic - Victor Alexandrov, Sobolev Institute of Mathematics11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Periodic frameworks, deformation spaces and auxetic trajectories - Ciprian Borcea, Rider University11th Floor Lecture Hall
11:30 - 12:15Algorithmic lattice kirigami - Daniel Sussman, University of Pennsylvania11th Floor Lecture Hall
12:30 - 2:30Break for Lunch/Free Time  
2:30 - 3:15Mapping spaces on polyhedral products - Jelena Grbic, University of Southampton, UK11th Floor Lecture Hall
Wednesday, September 14, 2016
TimeEventLocationMaterials
9:00 - 9:45Equilateral Equiangular Polygons in the Plane - Robert Connelly, Cornell University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Shape it as you wish- a minimal shapeable sheet - Naomi Oppenheimer, Simons Foundation11th Floor Lecture Hall
11:30 - 12:15Additive Lattice Kirigami - Toen Castle, UPenn11th Floor Lecture Hall
12:30 - 12:40Group Photo 11th Floor Lecture Hall 
12:40 - 2:30Break for Lunch/Free Time  
2:30 - 3:15Mechanical linkages with chaotic dynamics - Mickaël Kourganoff, Institut Fourier, Grenoble, France11th Floor Lecture Hall
3:30 - 5:00Poster Session11th Floor 
Thursday, September 15, 2016
TimeEventLocationMaterials
9:00 - 9:45The glass transition as a mixture of random organization and athermal jamming - Michael Schmeideberg, Friedrich-Alexander University Erlangen-Nürnberg11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Cauchy rigidity of convex c-polyhedra - John C. Bowers, James Madison University11th Floor Lecture Hall
11:30 - 12:15Configuration theorems and skewers - Sergei Tabachnikov, Pennsylvania State University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch/Free Time  
2:30 - 3:15The isomorphism problem for closed linkage spaces - Dirk Schuetz, Durham University11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Counting embeddings of Laman graphs - Josef Schicho, JKU Linz11th Floor Lecture Hall
Friday, September 16, 2016
TimeEventLocationMaterials
9:00 - 9:45Multimode mechanical materials - Graeme Milton, University of Utah11th Floor Lecture Hall
10:00 - 10:45Periodicity-changing deformations in infinite frameworks - Bryan Chen, University of Massachusetts11th Floor Lecture Hall 
11:00 - 11:30Coffee/Tea Break11th Floor Collaborative Space 
11:30 - 12:15Symplectic invariants of the moduli space of polygons in R^3. - Alessia Mandini, PUC-RIO11th Floor Lecture Hall
12:30 - 1:15Free energy landscape of sticky-sphere clusters - Miranda Holmes-Cerfon, Courant Institute of Mathematical Sciences11th Floor Lecture Hall

Associated Semester Workshops

Topology in Motion
Stochastic Topology and Thermodynamic Limits
Topology and Geometry in a Discrete Setting

Lecture Videos

Free energy landscape of sticky-sphere clusters

Miranda Holmes-Cerfon
Courant Institute of Mathematical Sciences
September 16, 2016

Periodicity-changing deformations in infinite frameworks

Bryan Chen
University of Massachusetts Amherst
September 16, 2016

Multimode mechanical materials

Graeme Milton
University of Utah
September 16, 2016

Configuration theorems and skewers

Sergei Tabachnikov
University of Pennsylvania
September 15, 2016

Cauchy rigidity of convex c-polyhedra

John C. Bowers
James Madison University
September 15, 2016

Mechanical linkages with chaotic dynamics

Mickael Kourganoff
Institut Fourier, Grenoble, France
September 14, 2016

Additive Lattice Kirigami

Toen Castle
UPenn
September 14, 2016

Shape it as you wish- a minimal shapeable sheet

Naomi Oppenheimer
Simons Foundation
September 14, 2016

Equilateral Equiangular Polygons in the Plane

Robert Connelly
Cornell University
September 14, 2016

Mapping spaces on polyhedral products

Jelena Grbic
University of Southhampton, UK
September 13, 2016

Algorithmic lattice kirigami

Daniel Sussman
University of Pennsylvania
September 13, 2016

Local multiplicity of continuous maps between manifolds

Pavle Blagojevic
Free University Berlin and Mathematical Institute SASA Belgrade
September 12, 2016

Spaces of triangulations of a square

Aaron Abrams
Washington and Lee University
September 12, 2016