1.ICERM Semester Program: Phase Transitions and Emergent Properties |

Dates | 02 Feb 2015 → 08 May 2015 | [ID=592131] |

Location | Providence, United States |

Abstract | Emergent phenomena are properties of a system of many components which are only evident or even meaningful for the collection as a whole. A typical example is a system of many molecules, whose bulk properties may change from those of a fluid to those of a solid in response to changes in temperature or pressure. The basic mathematical tool for understanding emergent phenomena is the variational principle, most often employed via entropy maximization. The difficulty of analyzing emergent phenomena, however, makes empirical work essential; computations generate conjectures and their results are often our best judge of the truth.
The semester will include three workshops that will concentrate on different aspects of current interest, including unusual settings such as complex networks and quasicrystals, the onset of emergence as small systems grow, and the emergence of structure and shape as limits in probabilistic models. The workshops will (necessarily) bring in researchers in combinatorics and probability as well as statistical physics and related areas. We aim to have experimental contributors for workshops 1 and 2 where we will highlight the comparison between computational and theoretical modeling and the real world. This will be combined with computational modules for the student participants. |

Weblink | http://icerm.brown.edu/sp-s15 |

Related subject(s) | Courses and Events for Math Students and Early Career Researchers |

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2.ICERM Workshop: Crystals, Quasicrystals and Random Networks |

Dates | 09 Feb 2015 → 13 Feb 2015 | [ID=592229] |

Location | Providence, United States |

Abstract | The prototypical emergent phenomena are the bulk 'phases' of large collections of molecules, such as the fluid and solid phases. The solid phase is understood to emerge from an energy minimizing ideal crystal by the addition of random defects as energy increases from its minimum, the crucial/amazing fact being that the phase preserves something from the ideal crystal that unambiguously distinguishes it from the fluid phase. In this workshop we will focus on two significant variants of this classic picture: quasicrystals, and complex networks/random graphs. The analogue of energy minimizing crystals for quasicrystals are aperiodic tilings, such as the kite and dart tilings of Penrose, and for complex networks the analogue of energy minimizing crystals are (multi-partite) extremal graphs, graphs which minimize the number of subgraphs of some type. The workshop will focus on extremal graphs and aperiodic tilings and on the 'solid' phases they are believed to yield when random defects are introduced. It is hoped that progress can be made by pooling the expertise of researchers interested in the various aspects of these subjects. |

Weblink | http://icerm.brown.edu/sp-s15-w1 |

Related subject(s) | Applied Maths: Complex Networks |

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3.46th Southeastern International Conferences on Combinatorics, Graph Theory and Computing |

Dates | 02 Mar 2015 → 06 Mar 2015 | [ID=662708] |

Location | Boca Raton, FL, United States |

Abstract | Celebrating its 46th year, the Conference continues in the spirit of earlier conferences in Baton Rouge and Boca Raton. It brings together mathematicians and others interested in combinatorics, graph theory and computing, and their interactions. The Conference lectures and contributed papers, as well as the opportunities for informal conversations, have proved to be of great interest to other scientists and analysts employing these mathematical sciences in their professional work in business, industry, and government. |

Weblink | http://math.fau.edu/cgtc/CGTC46/ |

Related subject(s) | Information Theory, Foundations of Computer Science |

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4.ICERM Workshop: Small Clusters, Polymer Vesicles and Unusual Minima |

Dates | 16 Mar 2015 → 20 Mar 2015 | [ID=592195] |

Location | Providence, United States |

Abstract | This workshop will explore emergent phenomena in the context of small clusters, supramolecular self-assembly and the shape of self-assembled 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 non-spherical, or there are several types of components. Interactions vary from hard sphere repulsion to competition between coarse-grained liquid-crystalline 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 short-range 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 meso-scale building blocks for supermolecules and bulk materials (supramolecular chemistry) freed from the limited scope of atoms and quantum-mechanical 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 self-assembly of large numbers of units, block copolymers self-assemble into a wide variety of structures including vesicles, nano-fibers and tori. Many of the structures formed are essentially two-dimensional 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. |

Weblink | http://icerm.brown.edu/sp-s15-w2 |

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5.AIM Workshop: Dynamical algebraic combinatorics |

Dates | 23 Mar 2015 → 27 Mar 2015 | [ID=644242] |

Location | American Institute of Mathematics, Palo Alto, United States |

Abstract | This workshop, sponsored by AIM and the NSF, will focus on dynamical systems arising from algebraic combinatorics. |

Weblink | http://aimath.org/workshops/upcoming/dynalgcomb |

Related subject(s) | Applied Maths: Dynamic Systems, Control and Automation |

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6.ICERM Workshop: Limit Shapes |

Dates | 13 Apr 2015 → 17 Apr 2015 | [ID=592205] |

Location | Providence, United States |

Abstract | Since the days of Boltzmann, it has been well accepted that natural phenomena, when described using tools of statistical mechanics, are governed by various "laws of large numbers." For practitioners of the field this usually means that certain empirical means converge to constants when the limit of a large system is taken. However, evidence has been amassed that such laws apply also to geometric features of these systems and, in particular, to many naturally-defined shapes. Earlier examples where such convergence could be proved include certain interacting particle systems, invasion percolation models and spin systems in equilibrium statistical mechanics.
The last decade has seen a true explosion of "limit-shape" results. New tools of combinatorics, random matrices and representation theory have given us new models for which limit shapes can be determined and further studied: dimer models, polymer models, sorting networks, ASEP (asymmetric exclusion processes), sandpile models, bootstrap percolation models, polynuclear growth models, etc. The goal of the workshop is to attempt to confront this "ZOO" of combinatorial examples with older foundational work and develop a better understanding of the general limit shape phenomenon. |

Weblink | http://icerm.brown.edu/sp-s15-w3 |

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7.8th International Conference on Lattice Path Combinatorics & Applications |

Dates | 17 Aug 2015 → 20 Aug 2015 | [ID=679270] |

Location | Pomona, California, United States |

Abstract | 8th International Conference on Lattice Path Combinatorics & Applications. Researchers from all over the world come and present their work relating to lattice path combinatorics. These conferences were originally founded and organized (with loving care) by Sri Gopal Mohanty. For the most part, talks are presented sequentially over a 3-4 day period.
Sometimes tutorial sessions and special workshops are included on the program. Participants include a nice mix of regulars from past conferences and new reseachers who are warmly welcomed as part of the family. |

Topics | Conference Topics to be covered include (but are not limited to): • Lattice path enumeration • Plane Partitions • Young tableaux • q-calculus • Orthogonal polynomials • Random walks • Nonparametric statistical inference • Discrete distributions and urn models • Queueing theory • Analysis of algorithms • Graph Theory and Applications • Self-dual codes and unimodular lattices • Bijections between paths and other combinatoric structures |

Weblink | http://www.csupomona.edu/~math/CONFERENCE/index.html |

Contact | Email: latticepathcomb@cpp.edu |

Related subject(s) | Probability and Statistics, Game Theory; Applied Maths: Operational research |

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