Unusual Configuration Spaces
(September 12-16, 2016)

Description

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.

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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.

Organizing Committee

= speaker    = poster presenter

Monday September 12, 2016
Time Description Speaker Location Abstracts Slides
8:45 - 9:15Registration121 South Main Street, Providence, RI; 11th Floor
9:15 - 9:30WelcomeBrendan Hassett, ICERM Director11th Floor Lecture Hall
9:30 - 10:15Spaces of non-k-equal configurations in a Euclidean space and the little discs operadVictor Turchin, Kansas State University11th Floor Lecture Hall
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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
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12:00 - 2:30Break for Lunch/Free Time
2:30 - 3:15Spaces of triangulations of a squareAaron Abrams, Washington and Lee University11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45Local multiplicity of continuous maps between manifoldsPavle Blagojevic, Free University Berlin and Mathematical Institute SASA Belgrade11th Floor Lecture Hall
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5:00 - 6:30Welcome Reception11th Floor Collaborative Space

Tuesday September 13, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:45The set of flexible nondegenerate polyhedra of a prescribed combinatorial structure is not always algebraicVictor Alexandrov, Sobolev Institute of Mathematics11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Periodic frameworks, deformation spaces and auxetic trajectoriesCiprian Borcea, Rider University11th Floor Lecture Hall
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11:30 - 12:15Algorithmic lattice kirigamiDaniel Sussman, University of Pennsylvania11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch/Free Time
2:30 - 3:15Mapping spaces on polyhedral productsJelena Grbic, University of Southampton, UK11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space

Wednesday September 14, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Equilateral Equiangular Polygons in the PlaneRobert Connelly, Cornell University11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Shape it as you wish- a minimal shapeable sheetNaomi Oppenheimer, Simons Foundation11th Floor Lecture Hall
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11:30 - 12:15Additive Lattice KirigamiToen Castle, UPenn11th Floor Lecture Hall
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12:30 - 12:40Group Photo 11th Floor Lecture Hall
12:40 - 2:30Break for Lunch/Free Time
2:30 - 3:15Mechanical linkages with chaotic dynamicsMickaël Kourganoff, Institut Fourier, Grenoble, France11th Floor Lecture Hall
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3:30 - 5:00Poster Session11th Floor

Thursday September 15, 2016
Time Description Speaker Location Abstracts Slides
11:30 - 12:15Configuration theorems and skewersSergei Tabachnikov, Pennsylvania State University11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch/Free Time
2:30 - 3:15The isomorphism problem for closed linkage spacesDirk Schuetz, Durham University11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45Counting embeddings of Laman graphsJosef Schicho, JKU Linz11th Floor Lecture Hall
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Friday September 16, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Multimode mechanical materialsGraeme Milton, University of Utah11th Floor Lecture Hall
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10:00 - 10:45Periodicity-changing deformations in infinite frameworksBryan 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
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12:30 - 1:15Free energy landscape of sticky-sphere clustersMiranda Holmes-Cerfon, Courant Institute of Mathematical Sciences11th Floor Lecture Hall
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