This workshop will explore emergent phenomena in the context of small clusters, supramolecular selfassembly and the shape of selfassembled structures such as polymer vesicles. The emphasis will be on surprises which arise when common conditions are not satisfied, for instance when the number of components is small, or they are highly nonspherical, or there are several types of components. Interactions vary from hard sphere repulsion to competition between coarsegrained liquidcrystalline ordering competing with shape deformation. Examples of this behavior are common in materials such as bulk homopolymers (rubber), copolymers, liquid crystals and colloidal aggregates. A basic mathematical setting would be to consider small clusters of hard spheres with isotropic shortrange attractions and study the shape of the clusters as a function of the number of components. One known surprise is that highly symmetric structures are suppressed by rotational entropy. This emphasizes the need to accurately count the number of particle configurations that lead to the same final state. Small clusters can also generate anisotropic building blocks which can in turn serve as nano or mesoscale building blocks for supermolecules and bulk materials (supramolecular chemistry) freed from the limited scope of atoms and quantummechanical bonding. These structures frequently possess topological defects in their ground states because they lower the energy. The challenge is to determine the shape and equilibrium defect structure of such superatoms and the number and geometry of their arrangement. The number of defects determines the effective valence of the super atoms and the global geometry of their arrangement determines the types of directional bonding possible when defects are linked together. The phenomenon of the appearance of singularities/defects because they are minimizers not necessarily required by topology or boundary conditions is also encountered in the study of harmonic maps. Moving up to selfassembly of large numbers of units, block copolymers selfassemble into a wide variety of structures including vesicles, nanofibers and tori. Many of the structures formed are essentially twodimensional surfaces embedded in R3. The mathematical challenge is to find both the shape and the order of the assembled object. This requires minimizing of a functional that depends on both the local and global order of the relevant matter fields and the shape of the surface.



Monday  March 16, 2015  

Time  Description  Speaker  Location  Abstracts  Slides 
8:30  8:55  ICERM Workshop Registration: Small Clusters, Polymer Vesicles and Unusual Minima  11th Floor Collaborative Space  
8:55  9:00  Welcome  ICERM Director  11th Floor Lecture Hall  
9:00  9:10  Theme of workshop  Mark Bowick, Syracuse University  11th Floor Lecture Hall  
9:10  10:10  Clusters with Shortrange Interactions a Tutorial  Miranda HolmesCerfon, Courant Institute of Mathematical Sciences  11th Floor Lecture Hall  
10:10  10:40  Discussion period  11th Floor Lecture Hall  
10:40  11:10  Coffee/Tea Break  11th Floor Collaborative Space  
11:10  12:10  Shape selection in frustrated elastic sheets  Eran Sharon, Hebrew University of Jerusalem  11th Floor Lecture Hall  
12:10  12:40  Discussion period  11th Floor Lecture Hall  
12:40  2:20  Break for Lunch  
2:20  2:50  From smooth manifolds to faceted polyhedra, and back  L. Mahadevan, Harvard University  11th Floor Lecture Hall  
3:00  3:30  The physics and geometry of colloidal sphere clusters  Vinothan Manoharan, Harvard University  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Lecture Hall  
4:00  5:00  Selfassembly with shaped particles  Sharon Glotzer, University of Michigan  11th Floor Lecture Hall  
5:00  6:30  Welcome Reception  11th Floor Collaborative Space 
Tuesday  March 17, 2015  

Time  Description  Speaker  Location  Abstracts  Slides 
9:00  10:00  Topology and Singularities  Robert Hardt, Rice University  11th Floor Lecture Hall  
10:00  10:30  Discussion period  11th Floor Lecture Hall  
10:25  10:30  Workshop Group Photo  11th Floor Lecture Hall  
10:30  11:50  Statistical Mechanics and Combinatorics (ongoing semester course)  Richard Kenyon, Brown University  10th Floor Classroom  
10:30  11:00  Coffee/Tea Break  11th Floor Collaborative Space  
11:00  12:00  Topology of Broken Translational Symmetry  Randy Kamien, University of Pennsylvania  11th Floor Lecture Hall  
12:00  12:30  Discussion period  11th Floor Lecture Hall  
12:30  2:30  Break for Lunch  
2:30  3:00  On vectorvalued singular perturbation problems involving potentials vanishing on curves.  Itai Shafrir, TechnionIsrael Institute of Technology  11th Floor Lecture Hall  
3:10  3:40  Nonspherical Bubble Clusters  John Sullivan, TU Berlin  11th Floor Lecture Hall  
3:40  4:00  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  4:30  Dr. Wrinkle and Mr. Hyde directing pattern formation in anisotropic elastic films  Elisabetta Matsumoto, Princeton University  11th Floor Lecture Hall 
Wednesday  March 18, 2015  

Time  Description  Speaker  Location  Abstracts  Slides 
9:00  10:00  Exploring the Energy Landscapes of Clusters and Unusual Minima  David Wales, Cambridge University  11th Floor Lecture Hall  
10:00  10:30  Discussion period  11th Floor Lecture Hall  
10:30  11:00  Coffee/Tea Break  11th Floor Collaborative Space  
11:00  12:30  Poster Session  11th Floor Lecture Hall and Collaborative Space  
12:30  2:15  Break for Lunch  
2:15  2:45  Metastability, Spectra, and Eigencurrents of LennardJones Clusters  Maria Cameron, University of Maryland  11th Floor Lecture Hall  
3:00  3:30  Numerical Methods and Uniqueness for the CanhamHelfrich Model of Biomembranes  Thomas Yu, Drexel University  11th Floor Lecture Hall  
3:30  3:50  Coffee/Tea Break  11th Floor Collaborative Space  
3:50  4:20  Geometric frustration in twisted filament assemblies Noneuclidean packing and morphology of selflimiting bundles  Greg Grason, University of Massachusetts  11th Floor Lecture Hall  
4:30  5:00  Random Organization, Hyperuniformity and Photonic Bandgap  Paul Chaikin, New York University  11th Floor Lecture Hall 
Thursday  March 19, 2015  

Time  Description  Speaker  Location  Abstracts  Slides 
9:00  10:00  Flavors of Rigidity for Sticky Spheres  Robert Connelly, Cornell University  11th Floor Lecture Hall  
10:00  10:30  Discussion period  11th Floor Lecture Hall  
10:30  11:50  Statistical Mechanics and Combinatorics (ongoing semester course)  Richard Kenyon, Brown University  10th Floor Classroom  
10:30  11:00  Coffee/Tea Break  11th Floor Collaborative Space  
11:00  12:00  The Duality between Floppy and Rigid Modes in the JammingUnjamming Transitions  Gustavo During, Instituto de Fisica, Universidad Catolica de Chile  11th Floor Lecture Hall  
12:00  12:30  Discussion period  11th Floor Lecture Hall  
12:30  2:15  Break for Lunch  
2:15  2:45  EASAL efficient atlasing, search and analysis of assembly landscapes under shortranged potentials using geometrization, stratification and Cayley convexification.  Meera Sitharam, University of Florida  11th Floor Lecture Hall  
2:55  3:25  Counting degrees of freedom in periodic frameworks  Louis Theran, Aalto University  11th Floor Lecture Hall  
3:25  3:50  Coffee/Tea Break  11th Floor Collaborative Space  
3:50  4:20  Topological soft matter from linkages to kinks  Bryan Chen, InstituutLorentz for Theoretical Physics, Leiden University  11th Floor Lecture Hall  
4:30  5:00  Dislocation modes and buckling in topological metamaterials  Jayson Paulose, Rijksuniversiteit te Leiden 
Friday  March 20, 2015  

Time  Description  Speaker  Location  Abstracts  Slides 
9:00  10:00  Inverse problems / packing&information theory  Henry Cohn, Microsoft Research  11th Floor Lecture Hall  
10:00  10:30  Discussion period  11th Floor Lecture Hall  
10:30  11:00  Coffee/Tea Break  11th Floor Collaborative Space  
11:00  12:30  Having a ball with sphere parking.  Beth Chen, Harvard University  11th Floor Lecture Hall  
12:30  2:00  Break for Lunch  
2:00  2:30  Tangent UnitVector Fields for Liquid Crystals and Nanoparticles  Dr Apala Majumdar, University of Bath, United Kingdom  11th Floor Lecture Hall  
2:30  3:00  Unusual Minima on Curved Surfaces  Mark Bowick, Syracuse University  11th Floor Lecture Hall  
3:00  3:30  Discussion period  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 