## Programs & Events

##### Research Cluster: Geometric analysis methods for graph algorithms

Feb 3 - 28, 2014

This working group will develop new mathematics at the interface between graph structures and high dimensional data and geometric analysis. In the last ten years we have seen an explosion of work in both (a) compressive sensing (sparsity, L1-based methods) and in (b) machine learning involve graphical structures for large scale and high dimensional data. The focus is on both analysis and algorithm development. In the case of new algorithms - codes will be tested against state of art machine learning algorithms. In the case of analytical results - we will draw on expertise in diverse areas of mathematics including differential geometry, nonlinear PDE, optimization, and spectral analysis of graphs. Application areas represented include machine learning, social network data, modularity optimization, L1-compressive sensing methods, and image processing.

One area of focus is community detection in large networks. A current approach for community detection consists in minimizing the... (more)

##### Organizing Committee

- Andrea Bertozzi
- Thomas Laurent

##### Semidefinite Programming and Graph Algorithms

Feb 10 - 14, 2014

Semidefinite programming is playing an ever increasing role in many areas of computer science and mathematics, including complexity theory, approximation algorithms for hard graph problems, discrete geometry, machine learning, and extremal combinatorics.

This workshop will bring together researchers from these different fields. The goal is to explore connections, learn and share techniques, and build bridges.

##### Organizing Committee

- Monique Laurent
- David Phillips
- David Steurer
- Kilian Weinberger

##### Research Cluster: Graphs with incomplete information

Feb 17 - Mar 15, 2014

How can we handle graph problems when the graph is only known imperfectly?

In one setting, the input is a noisy version of some unknown ground truth graph, to which random edges have been added, destroying the structure : planarity, clustering, distances for example. In another setting, the graph itself can only be accessed via queries such as shortest path queries, distance queries, or cut queries, and must be inferred from the result to well-chosen queries ; this comes up in internet tomography. In a third setting, the graph evolves dynamically over time and solutions must adapt to edge additions and removals.

The cluster will gather researchers around a bi-weekly working group drawing on the skills of the participants in random graphs and discrete probability, optimization and linear, semi-definite or convex programming methods, structural graph properties, and randomized dynamic data structures.

##### Organizing Committee

- Claire Mathieu

##### Stochastic Graph Models

Mar 17 - 21, 2014

Random graphs, stochastic processes on graphs and algorithms for computations on these structures continue to play a dominant role in algorithmic research and discrete mathematics, with recent applications ranging from web search and recommendation engines to social networks and system biology.

This workshop will be an opportunity for researchers from diverse fields to get together and share problems and techniques for handling and analyzing graphs structures. The connections---mathematical, computational, and practical---that arise between these seemingly-diverse problems and approaches will be emphasized.

##### Organizing Committee

- Susanne Albers
- Ravi Kumar
- Michael Mitzenmacher
- Eli Upfal

##### Electrical Flows, Graph Laplacians, and Algorithms: Spectral Graph Theory and Beyond

Apr 7 - 11, 2014

Spectral graph theory, which studies how the eigenvalues and eigenvectors of the graph Laplacian (and other related matrices) interact with the combinatorial structure of a graph, is a classical tool in both the theory and practice of algorithm design. The success of this approach has been rooted in the efficiency with which eigenvalues and eigenvectors can be computed, and in the surprisingly large number of ways that a graph's properties are connected to the Laplacian's spectrum---particularly to the value of its second smallest eigenvalue, λ2.

However, while the eigenvalues and eigenvectors of the Laplacian capture a striking amount of the structure of the graph, they certainly do not capture all of it. Recent work in the field suggests that we have only scratched the surface of what can be done if we are willing to broaden our investigation to include more general linear-algebraic properties of the matrices we associate to graphs.

A particularly fruitful example of this... (more)

##### Organizing Committee

- Jonathan Kelner
- Ioannis Koutis
- Gary Miller

##### Research Cluster: Towards Efficient Algorithms Exploiting Graph Structure

Apr 24 - May 3, 2014

This working group will develop new theoretically grounded approaches to practical problems on graphs and networks using the arsenal of graph structure theory and algorithms (treewidth, minors, fixed-parameter tractability, approximation algorithms, etc.).

Our approach is to combine the expertise of a mix of junior and senior researchers from three disciplines: mathematics (graph theory), computer science (fixed-parameter and approximation algorithms), and applied network analysis (social networks, power grid, bioinformatics, etc.). During this research cluster, we will identify specific practically motivated problems, and tackle the key associated mathematical challenges, with a goal of ultimately encouraging broader adoption of graph-structure-based tools in the computational community. This goal is particularly important given the emergence of vast quantities of relational data (a.k.a. networks) and increased need for analysis via scalable algorithms.

We face several challenges in... (more)

##### Organizing Committee

- Erik Demaine
- Daniel Marx
- Blair Sullivan

##### Eigenvectors in graph theory and related problems in numerical linear algebra

May 5 - 9, 2014

The analysis of problems modeled by large graphs is greatly hampered by a lack of efficient computational tools. The purpose of the workshop is to explore possibilities for designing appropriate computational methods that draw on recent advances in numerical methods and scientific computation. Specifically, the questions of how to form the matrices representing graph Laplacians, and how to compute the leading eigenvectors of such matrices will be addressed. It seems likely that these problems will be amenable to algorithms based on randomized projections that dramatically reduce the effective dimensionality of the underlying problems. Such techniques has recently proven highly effective for the related problems of how to find approximate lists of nearest neighbors for clouds of points in high dimensional spaces, and for constructing approximate low-rank factorizations of large matrices. In both cases, a key observation is that the problem of distortions of distances that is inherent to... (more)

##### Organizing Committee

- Anna Gilbert
- Peter Jones
- Gunnar Martinsson
- Van Vu

##### Robust Discretization and Fast Solvers for Computable Multi-Physics Models

May 12 - 16, 2014

Most systems targeted by mathematical modeling in modern science and engineering are fundamentally multi-physical and multi-scale in nature. As such, they involve solving complex coupled, generally nonlinear, systems of partial differential equations (PDEs) built from subsystems of PDEs that mathematically model very different physical processes, often at very different scales.

Recent advances in high-performance computer hardware and advanced numerical algorithms have made it feasible to construct realistic mathematical models and to build corresponding numerical simulation software for these types of complex multi-physics/multi-scale problems. However, developing robust, efficient, and practical numerical algorithms for such simulation software that are capable of tackling these complex mathematical models is still extremely challenging in a number of fundamental ways. For example, we do not yet have robust methods that can handle strong coupling between different physics and/or... (more)

##### Organizing Committee

- Franco Brezzi
- Jan Hesthaven
- Michael Holst
- Jinchao Xu

##### Computational Nonlinear Algebra

Jun 2 - 6, 2014

Over the last two decades, algebraic and numerical techniques for nonlinear problems have begun a steady and relentless transition from mostly academic constructions, to widely used tools across the mathematical sciences, engineering and industrial applications. The workshop will bring together participants from many diverse fields including computer vision, cryptography, optimization and control, partial differential equations, robotics, and quantum computation, with the common interest in nonlinear algebraic computations. The main goal is to assess the state of the art, to stimulate further progress, and to accelerate developments by bringing together these diverse communities and have them share computational challenges and successes.

##### Organizing Committee

- Greg Blekherman
- Lek-Heng Lim
- Pablo Parrilo
- Andrew Sommese
- Rekha Thomas

##### Summer@ICERM 2014: Polygons and Polynomials

Jun 16 - Aug 8, 2014

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 2014 program is designed for a select group of 12-14 undergraduate scholars. Students work in groups of two or three, supervised by faculty advisors and aided by teaching assistants. The faculty advisors... (more)

##### Organizing Committee

- Michael Mossinghoff
- Sinai Robins

##### Careers in Academia

Jun 25 - 27, 2014

This workshop will focus on preparing each participant for a successful career as a mathematician at a college or university. Beginning with the hiring process, a thorough discussion of the various elements of the application packet will take place in the context of each participant's materials. Working individually with experienced faculty, participants will review and refine their cover letters, C.V., research, and teaching statements. This will be followed by activities related to the interview. The primary goals of the workshop are to develop an understanding of the hiring process from the institutions' perspective, to refine the application packet, to learn what to expect during the interview process (including the job talk), and to prepare for negotiating salary and start-up packages.

Additional time will be spent on aspects of the pre-tenure years including the development of a research program, writing grant proposals, and mentoring research students. The three-day workshop... (more)

##### Organizing Committee

- David Farmer
- Ruth Haas
- Loek Helminck
- Sally Koutsoliotas