Research and outreach are normally thought to divide mathematics in two. This separation is, however, completely artificial; it is impossible to “find” a mathematical idea without explaining it. Exploration and exposition are two sides of the same coin. One striking example of this is the epochal work of William Thurston; often his theorems were accompanied by pictures, and computer programs, illustrating the underlying ideas.

The goal of this conference is to bring together mathematicians from a range of fields, and practitioners from the digital arts (animation, 3D printing, laser cutting, CNC routing, virtual reality, computer games, etc). The attendees will share their expertise in mathematics and with the procedural tools used to illustrate mathematics. In addition to talks in the traditional style, we plan to hold several workshops to train attendees about a variety of digital media, in particular 3D printing.

The goal of this workshop is to bring computer science researchers in security/privacy/cryptography together with researchers in mathematics. We will use information security as a term encompassing security, privacy, and cryptography. Information¬-security researchers employ various branches of mathematics such as number theory, probability theory, optimization, and real analysis. Despite this there is currently very little collaboration between information¬-security researchers and mathematicians. The main focus of this workshop will consist of researchers in information-security presenting the mathematical challenges they face in lattice¬-based cryptography, privacy, and security economics, with an eye towards interesting the mathematicians present, drawing on their expertise, and developing collaborations.

The format of the workshop will be designed to foster such collaborations. Information-¬security researchers will give talks about various topics and indicate interesting... (more)

In the theory of error correcting codes, a sender (Alice) wants to send a message to a receiver (Bob), over a noisy channel. Strategies for Alice and Bob have been studied since the works of Shannon and Hamming from the late 1940's, from many different communities. Coding theory is a fundamental solution to challenges that arise in communication, storage, cryptography, and others; as the world changes, our challenges in these areas change, and the scenario changes for Alice and Bob. Fueled by these new scenarios, coding theory remains a rapidly advancing area of research.

One trend in many of these new scenarios in coding theory is the need for algorithmic solutions. For many problems in coding theory, it is possible to come up with nearly optimal solutions (information-theoretically speaking) which are likely very hard for Alice and Bob to actually implement. The goal of algorithmic coding theory is to design solutions which are not only combinatorially good, but are also... (more)

The recent proof of Thurston's virtual fibering conjecture brought together tools at the forefront of geometric group theory, dynamics, and hyperbolic geometry. We still lack, however, an effective or constructive understanding of three-dimensional hyperbolic geometry, and more generally, 3-manifold topology. For example, a closed hyperbolic 3-manifold admits a finite cover which fibers over the circle, but can one construct such a cover from a presentation of the fundamental group? Can one implement an algorithm -- perhaps with the help of preexisting software such as SnapPea -- to obtain such a cover?

While much work remains, both computation and theory have progressed. Fast algorithms have been developed for running computations in the mapping class group and other finitely generated groups, as well as for recognizing certain types 3-manifolds and knot and link complements up to homeomorphism. These have been supplemented by a new wave of constructive theorems which explicitly... (more)

Over the last 20 years or so, Newton-Krylov methods have developed to maturity, allowing effective fully-coupled treatment of a broad range of large-scale nonlinear problems. This development has set the stage for addressing more difficult problems with more challenging features. Additionally, applications for which state-of-the-art Newton-Krylov approaches are inapplicable have recently exposed several basic research questions. At the same time, there remain many problem-specific methods and legacy codes that are still useful and can be regarded as a resource for further development.

This workshop will include mathematicians and computer scientists who work on algorithm design, implementation, and analysis, together with disciplinary scientists and engineers who use the algorithms in applications and have a working knowledge of their capabilities, weaknesses, and limitations. The major foci of the workshop will be acceleration methods, in particular Anderson acceleration; methods for... (more)

The goal of this workshop is to bring together mathematicians and data scientists to participate in a discussion of current methods and outstanding problems in data science. The workshop is particularly aimed at mathematicians interested in pursuing research or a career in data science who wish to gain an understanding of this rapidly evolving field and the ways in which mathematics can contribute.

Researchers currently working in data science are also encouraged to attend, to share ideas about mathematical methodologies and challenges. A number of experienced data scientists with a variety of backgrounds from academics, national laboratories, and industry (including startups) will be invited. The program will include overview and technical talks, several panels consisting of practitioners with different experience levels, and one or more poster sessions.

The mathematical study of image reconstruction problems can have a huge impact on human life. More efficient mathematical algorithms for X-ray tomography and more accurate mathematical models in seismic or hybrid imaging can lead to better imaging devices in fields such as medicine and remote sensing. Developing the underlying mathematics, including the analysis of reconstruction stability, regularization, singularity characterization, and efficient algorithms, may lead to fewer false positives in fields such as medical, seismic and radar imaging.

This topical workshop will bring together international experts working in computational and analytical aspects of image reconstruction (including but not limited to electron-microscope tomography, hybrid imaging, radar and sonar, full waveform inversion of seismic imaging and X-ray CT) as well as postdoctoral fellows and graduate students. There will be multiple introductory-level talks for early-career researchers and non-specialists in... (more)

This workshop will bring together mathematicians working on combinatorial, geometric and topological properties of arrangements. In addition to fundamental open problems in the area, we will emphasize connections to tropical geometry, configuration spaces, and applications (coding theory, statistical economics, topological robotics), building bridges between those working on different aspects of the area. The main aim of the workshop is to discuss computational issues that arise in studying topological and combinatorial invariants of arrangements.

The workshop will be comprised of two main activities: A series of short courses by leading experts and research or expository talks. The short courses will be aimed at a broad audience; in particular they will be appropriate for advanced graduate students and early career mathematicians. In addition to theory, talks will highlight computational aspects of the problems, and the state of the art on the main open conjectures in the field. We... (more)

This workshop focuses on topics at the interface of classical mechanics, differential geometry, and computer experiments. The directions of current research to be explored at the workshop include the study of invariants and complete integrability of geometrically motivated differential equations (in particular, vehicle motion, tire track geometry, and smoke ring equations), sub-Riemannian geometry, geometric control, nonholonomic systems (such as e.g. bicycle stability and nonholonomic methods in billiard problems), computational methods in mechanics and dynamics (including geometric integrators, biological applications, etc.).

The goal of the workshop is to explore broad applications of the mechanical approach to geometry and geometric one to classical mechanics, to foster interaction between researchers in the above areas, with a view of finding new domains for applications of these fertile ideas.

Lattices are abstractly very simple objects, yet their concrete realizations contain beautifully intricate problems that are stubbornly difficult even in low dimensions. For example, our present day understandings of densest lattice packings and reduction theory are still plagued with large gaps.

In the 1970's and 1980's lattices entered the world of cryptography as tools used to break certain crypto systems, particularly those based on the subset sum problem, and since the 1990's they have become increasingly important in the building of other types of crypto systems (thanks to the difficulty in the underlying mathematics). Their significance has recently been bolstered by average-case complexity bounds and their present resistance to quantum computing attacks.

Currently the theory of lattices is a lively research topic among mathematicians, computer scientists, and experts in cybersecurity. However, to this date, there has been little to no interaction between these communities.... (more)

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)

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)