## Programs & Events

##### Limit Shapes

Apr 13 - 17, 2015

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,... (more)

##### Organizing Committee

- Marek Biskup
- Alexei Borodin
- Béatrice de Tilière
- Richard Kenyon
- Senya Shlosman

##### Public Lecture: Mathematics of Cooking

Mar 17, 2015

Members of the community are invited to attend a public lecture that will explore how cooking can illuminate some basic mathematical principles. Michael Brenner, Glover Professor of Applied Mathematics and Applied Physics, Harvard University, and eminent researcher in materials and modeling, will explain and demonstrate the scientific principles that form the foundation of cooking: from the everyday to haute cuisine.

The lecture will feature Mark Ladner, a 1990 graduate of Johnson & Wales University College of Culinary Arts and is now Executive Chef of the award-winning Del Posto Restaurant in New York City. Professor Brenner and Chef Ladner will demonstrate these mathematical principles through a fun and diverse tour of cooking demonstrations – from making fresh ricotta to blowing up marshmallows.

Please join us for this exciting evening of culinary and scientific experiments.

##### Small Clusters, Polymer Vesicles and Unusual Minima

Mar 16 - 20, 2015

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... (more)

##### Organizing Committee

- Mark Bowick
- Michael Brenner
- Miranda Holmes-Cerfon
- Rob Kusner
- Charles Radin

##### Crystals, Quasicrystals and Random Networks

Feb 9 - 13, 2015

The densest packing of unit disks in the plane is easily seen to be highly symmetric. This is exploited in statistical mechanics in arguing that as the density parameter is decreased from its optimum most packings at fixed density remain quite orderly ('solid'), changing only gradually until at a specific density they suddenly begin to 'melt' into the disordered ('fluid') packings of low density. This workshop will explore two variants of this fundamental phenomenon. One variant concerns packings of special shapes, such as the Penrose kites and darts of the accompanying figure, whose densest packings are aperiodic tilings. The other concerns complex networks for which the optima are certain extremal graphs. These optimization problems, and especially their associated solid phases and solid/fluid phase transitions, are the subject of the workshop.

In summary, our workshop will explore two optimization problems on which there is active mathematical... (more)

##### Organizing Committee

- Mark Bowick
- Persi Diaconis
- Charles Radin
- Peter Winkler

##### Phase Transitions and Emergent Properties

Feb 2 - May 8, 2015

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... (more)

##### Organizing Committee

- Mark Bowick
- Béatrice de Tilière
- Richard Kenyon
- Charles Radin
- Peter Winkler

##### 11th DIMACS Implementation Challenge in Collaboration with ICERM

Dec 4 - 5, 2014

The DIMACS Implementation Challenges address questions of determining realistic algorithm performance where worst case analysis is overly pessimistic and probabilistic models are too unrealistic: experimentation can provide guides to realistic algorithm performance where analysis fails.

The 11th Implementation Challenge is dedicated to the study of Steiner Tree problems (broadly defined), bringing together research in both theory and practice. Broadly speaking, the goal of a Steiner Tree problem is to find the cheapest way of connecting a set of objects. In most common variants, these objects are either points in a metric space or a subset of the vertices of a network, and the goal is to find a tree that connects all of them.

The main aim of the challenge is to create a reproducible picture of the state-of-the-art in Steiner Tree problems. Phases 1 and 2 of this challenge - the collection and improvement of testbeds and algorithm development and evaluation - began in June 2013.... (more)

##### Organizing Committee

- David Johnson
- Thorsten Koch
- Renato Werneck
- Martin Zachariasen

##### Public Lecture: Mathematics of Crime

Nov 20, 2014

Law enforcement agencies across the country have discovered that partnering with a team of mathematicians and social scientists from UCLA can help them determine where crime is likely to occur. Dr. Bertozzi will talk about the fascinating story behind her participation on the UCLA team that developed a “predictive policing” computer program that zeros-in on areas that have the highest probability of crime.

In addition, the use of mathematics in studying gang crimes and other criminal activities will also be discussed. Commercial use of the "predictive-policing" program allows communities to put police officers in the right place at the right time, stopping crime before it happens.

##### Computational Topology and Data Analysis Workshop (in Johannesburg, South Africa)

Nov 17 - 21, 2014

The review of Mathematical Sciences research at South African universities commissioned by the National Research Foundation highlighted the isolation of South African mathematics from its applications and related disciplines and not being fully distributed across different areas of mathematics. In particular it noted that there are contemporary mainstream subfields that are not represented and some research is disconnected from areas of contemporary interest. The newly established Centre for Mathematical and Computational Sciences and the African Institute for Mathematical Sciences are collaborating to address some of these gaps by co-organising workshops that will introduce new areas of study to the South African Mathematical Sciences Research landscape.

There is heightened awareness and renewed interest in (Big) Data Analysis since the announcement that South Africa together with Australia would be hosting the Square Kilometre Array project. One of the programmes to be pursued by... (more)

##### Research Cluster: Computational Challenges in Sparse and Redundant Representations

Nov 3 - 21, 2014

Harmonic analysis provides the mathematical backbone for modern signal and image processing. It also constitutes an important part of the foundation several scientific and engineering areas, including communication theory, control science, fluid dynamics, and electromagnetics, that underpin a much broader set of current applications. Although computer implementation of concepts from harmonic analysis is prevalent, relatively little attention is given to computational and numerical aspects of the discipline in its own literature. Further, many of the most capable young mathematicians working in this area have only modest exposure to the roles of such crucial computational considerations as finite data effects; e.g., How much error is introduced by truncating this infinite-series representation of a function in terms of a frame, and where will it be manifested?

On the other hand, new tools and ideas have entered the mainstream of harmonic analysis in recent years that have not yet... (more)

##### Organizing Committee

- Ben Adcock
- Doug Cochran
- Anne Gelb
- Karlheinz Gröchenig
- Yang Wang

##### Discrepancy Theory

Oct 27 - 31, 2014

Discrepancy theory deals with the problem of distributing points uniformly over some geometric object and evaluating the inevitably arising errors. The theory was ignited by such famous early results as Herman Weyl's equidistribution theorem and Klaus Roth's theorem on the irregularities of point distributions.

The subject has now grown into a broad field with deep connections tomany areas such as number theory, combinatorics, approximation theory, harmonic analysis, and probability theory, in particular empirical and Gaussian processes. The computational aspects of the subject include searching for well-distributed sets and numerical integration rules. Despite years of research, many fundamental questions, especially in high dimensions, remain wide open, although several important advances have been achieved recently.

The participants of this workshop will share a wide range of views on topics related to discrepancy with an eye towards the recent developments in the subject. The... (more)

##### Organizing Committee

- Dmitriy Bilyk
- William Chen
- Aicke Hinrichs
- Michael Lacey
- Mikhail Lifshits
- Friedrich Pillichshammer

##### Mathematics of Data Analysis in Cybersecurity

Oct 22 - 24, 2014

The goal of this workshop is to bring mathematicians and cybersecurity practitioners together to outline the key challenges in the mathematics of cybersecurity data analysis. The expected outcome of the workshop will be a roadmap for investment in specific mathematical topics that will directly impact the advancement of the science of cybersecurity.

Mathematicians have long been involved in information security through cryptography, and thus algebra and number theory. But modern cyber security is a much larger field, and the perspectives and methodologies of other parts of the mathematical sciences have been only rarely been brought to bear. Given the complexity and dynamics of cyberspace it is essential to have a formal scientific basis for the field of cybersecurity. Indeed, a variety of sources have called for the creation of a "science of cybersecurity", and mathematical methods should play a critical role in such a science.

The purpose of this workshop is to bring together... (more)

##### Organizing Committee

- Edoardo Airoldi
- Paul Barford
- Henry Cohn
- John Harer
- John Johnson
- Mauro Maggioni
- Jill Pipher

##### Approximation, Integration, and Optimization

Sep 29 - Oct 3, 2014

The workshop is devoted to the following problem of fundamental importance throughout science and engineering: how to approximate, integrate, or optimize multivariate functions.

The breakthroughs demanded by high dimensional problems may be at hand. Good methods of approximation arise as solutions of optimization problems over certain function classes that are now well understood in small and modesty large dimensions.

In high dimensions, the appropriate models involve sparse representations, which give rise to issues in nonlinear approximation methods such as greedy approximation. High dimensional optimization problems become intractable to solve exactly, but substantial gains in efficiency can be made by allowing for a small probability of failure (probabilistic recovery guarantees), and by seeking approximate solutions (up to a pre-specified threshold) rather than exact solutions. The contemporary requirements of numerical analysis connect approximation, optimization, and... (more)

##### Organizing Committee

- Albert Cohen
- Ronald DeVore
- Robert Nowak
- Vladimir Temlyakov
- Rachel Ward