Monte Carlo methods are one of the main tools used to study the properties of complex physical, chemical and biological systems. Since their introduction in the late 1940s, these methods have undergone a remarkable expansion and are now used in many other fields, including statistical inference, engineering, and computer science. However, the design and theoretical understanding of Monte Carlo methods is still a challenging topic, especially for those problems where rare events play the key role in determining algorithm performance. The aim of the workshop is to bring together specialists in the application areas who understand the specific challenges posed by realistic problems and have developed sophisticated tools to tackle these problems, and mathematicians developing methods for algorithm analysis, abstraction, and optimization.

Rapid growth in computational resources has heightened the expectation that scientific knowledge can indeed be a driver for societal well-being and betterment. At the same time, our ability to measure the natural and social world around has significantly increased, aided by technological development in sensors, the internet, and other modalities of communication. Science is thus faced, simultaneously, with a complex description of reality at an unprecedented resolution, and the possibility to describe this reality with mathematical models of increasing complexity. Probabilistic formulations of physical problems can be viewed as attempts to adapt rational procedures to this complexity, while tackling the conceptual challenges they inevitably present. As a testament to the significance of this confluence of mathematics, science, and technology, Uncertainty Quantification is arguably one of the fastest growing sub-disciplines in mechanics.

The communities of computational science,... (more)

Data-rich investigations need advanced tools for allowing data to inform and interact with models. Bayesian Nonparametrics is a rapidly growing subfield of statistics and machine learning that provides a framework for creating complex statistical models that are both expressive and tractable. Recent, successful applications of nonparametric Bayesian models across a variety of domains suggests that these models have the potential for wide use. The challenge of constructing and using models on very high dimensional or even infinite dimensional spaces creates many opportunities for fruitful interactions between mathematicians, statisticians and computer scientists. Areas of interest include prior construction, posterior inference, posterior asymptotics, algorithmic development, and practical applications.

Modern explorations in science, technology and medicine increasingly demand complex stochastic models. Computational and theoretical advances are needed in order to formulate, analyze, apply and interpret these models. Recent years have witnessed a remarkable interplay between computation and probability. On the one hand, probabilistic techniques have led to powerful computational methods such as Markov chain Monte Carlo algorithms, while on the other hand the calculation of probabilistic quantities such as modes and marginals of high-dimensional distributions and the analysis of data from random samples has posed several computational challenges.

The Fall 2012 Semester on "Computational Challenges in Probability" aims to bring together leading experts and young researchers who are advancing the use of probabilistic and computational methods to study complex models in a variety of fields. The goal is to identify common challenges, exchange existing tools, reveal new application areas... (more)

Many important advances in material and biomedical science will come from controlling the chemical properties and nanoscale morphology of polymer mixtures. Predicting the longtime continuum-level properties of such complex systems poses a canonical computational challenge due to the disparate length and time scales separating the molecular description from the macroscopic behavior, particularly the evolution of morphology. This workshop focuses on four overlapping approaches to bridging this gap: Accelerated Molecular Methods, Coarse-Graining of Molecular Dynamics, Computational Approaches to Self-Consistent Mean Field, and Coupled Molecular and Continuum-Variational models. The goal is to spur the development of hybrid computational methods with the capacity to identify and characterize the rare events and the driving forces which steer the systems towards equilibrium, and connect the burgeoning growth in parallel-computation techniques for particle-based systems with recently... (more)

Imagine spending eight-weeks on the beautiful Brown University campus in historic Providence, RI, working in a small team setting to solve mathematical research problems developed by faculty experts in their fields.

Imagine creating career-building connections between peers, near peers (graduate students and postdocs), and academic professionals.

Imagine spending your summer in a fun, memorable, and intellectually stimulating environment.

Now, imagine having this experience with support for travel within the U.S., room and board paid, plus a $3,000 stipend*.

The Summer@ICERM 2012 program is designed for a select group of 10-12 undergraduate scholars. Students in the 2012 program worked in small groups of two or three, supervised by a faculty advisor and aided by a teaching... (more)

FEEC is a recent advance in the mathematics of finite element methods that employs differential complexes to construct stable numerical schemes for several important types of application problems. It has aroused great interest because it both presents interesting mathematical problems and shows great potential for application in computational science and engineering. The concentrated sequence of lectures in this program will provide participants with an understanding of the mathematical tools required to fully grasp the concepts in FEEC. ICERM is pleased to host this NSF-CBMS Regional Research Conference.

Douglas Arnold will deliver 10 lectures, one in the morning and one in the afternoon of each day of the workshop. Richard Falk and Anil Hirani will both give one presentation.

Limited funding is available to support participants.

This workshop, sponsored by AIM, ICERM, and the NSF, will introduce undergraduate faculty to research opportunities in several fields of mathematics that will equip them with the tools to mentor students in undergraduate research in mathematics. Lectures at the workshop will provide background information and introduce open problems. The majority of the workshop will be spent working on problems, reporting on progress, and formulating plans for future work.

The workshop will be hosted at ICERM.

Preference will be given to faculty who teach and advise substantial numbers of minority students.

Mathematical topics at the workshop will include algebra, graph theory, and number theory.

For more information email workshops@aimath.org or go to http://aimath.org/ARCC/workshops/reuf4.html.

The theme of this workshop is the computation, modeling, and mathematical analysis of heterostructured nanocrystalline materials. This includes quantum dots, nanowires, graphene, and grain boundaries. These various phenomena will be discussed in the context of modeling and computation on different scales ranging from density functional theory to continuum mechanics. The workshop will also address various techniques that allow one to combine models on different scales to yield efficient computational methods.

This workshop will bring together dynamicists, number theorists, and algebraic geometers to study the geometry and arithmetic of dynamical moduli spaces. The set Rat_dⁿ of rational degree d self-maps of Pⁿ has a natural structure as an affine variety. The dynamical moduli space M_dⁿ is the quotient of Rat_dⁿ by the conjugation action of the group PGL_n+1. Problems to be investigated include the geometry of M_dⁿ, the distribution of special maps such as post-critically finite maps in M_dⁿ, dynamical modular curves associated to one-parameter families of maps with a marked point of period N, and degeneration of families of maps and the associated points on the boundary of moduli space. A tutorial session will be held the week before this workshop.