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)

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)

Information-based complexity (IBC) deals with the computational complexity of continuous problems for which available information is partial, priced and noisy. IBC provides a methodological background for proving the curse of dimensionality as well as provides various ways of vanquishing this curse.

Stochastic computation deals with computational problems that arise in probabilistic models or can be efficiently solved by randomized algorithms. Using IBC background, the complexity of stochastic ordinary (SDE) and partial differential (SPDE) equations have been studied.

Topics covered in the workshop will include: adaptive and nonlinear approximation for SPDEs, infinite-dimensional problems, inverse and ill- posed problems, quasi-Monte Carlo methods, PDEs with random coefficients, sparse/Smolyak grids, stochastic multi-level algorithms, SDEs and SPDEs with nonstandard coefficients, tractability of multivariate problems.

This workshop will bring together researchers from these... (more)

The fundamental problem of approximation theory is to resolve a possibly complicated function, called the target function, by simpler, easier to compute functions called approximants. Increasing the resolution of the target function can generally only be achieved by increasing the complexity of the approximants. The understanding of this trade-off between resolution and complexity is the main goal of approximation theory, a classical subject that goes back to the early results on Taylor's and Fourier's expansions of a function.

Modern problems in approximation, driven by applications in biology, medicine, and engineering, are being formulated in very high dimensions, which brings to the fore new phenomena. One aspect of the high-dimensional regime is a focus on sparse signals, motivated by the fact that many real world signals can be well approximated by sparse ones. The goal of compressed sensing is to reconstruct such signals from their incomplete linear information. Another aspect... (more)

This workshop focuses on certain kinds of discrete dynamical systems that are integrable and have interpretations in terms of cluster algebras. Some such systems, like the pentagram map and the octahedral recurrence, are motivated by concrete algebraic constructions (taking determinants) or geometric constructions based on specific configurations of points and lines in the projective plane. The systems of interest in this workshop have connections to Poisson and symplectic geometry, classical integrable PDE such as the KdV and Boussinesq equations and also to cluster algebras. The aim of the workshop is to explore geometric, algebraic, and computational facets of these systems, with a view towards uncovering new phenomena and unifying the work to date.

Interested in discussing cutting edge research ideas with both peers and leaders in their field?

Interested in broadening your professional network across the mathematical sciences?

Interested in the opportunity to present your ideas and hear about funding opportunities from program officers?

Idea-Lab invites 20 early career researchers (postdoctoral candidates and assistant professors) to ICERM for a week during the summer. The program will start with brief participant presentations on their research interests in order to build a common understanding of the breadth and depth of expertise. Throughout the week, organizers or visiting researchers will give comprehensive overviews of their research topics. Organizers will create smaller teams of participants who will discuss, in depth, these research questions, obstacles, and... (more)

This workshop will focus on recent advances in combinatorial link homology theories (e.g., Heegaard-Floer homology and Khovanov homology), especially as they apply to questions about braids and, more generally, mapping class groups of surfaces. There will be short mini-courses on

1. Combinatorial knot Floer homology, with applications to contact geometry,
2. Braid foliations and the Jones conjecture,
3. Nielsen-Thurston theory, and
4. Garside theory and a linear order on the braid group,

along with a number of research and expository talks. The talks will emphasize the role that computation and experiment have thus far played in stating key conjectures and establishing key results. The workshop will culminate in a computational problem session, in which participants will discuss promising directions for future exploration and indicate which computations may be most useful in that exploration.

As the main goal of the workshop is to facilitate interaction... (more)

Over the past 25 years, experimental mathematics has developed as an important additional arrow in the mathematical quiver. Many mathematical scientists now use powerful symbolic, numeric and graphic (sometimes abbreviated "SNAG") computing environments in their research, in a remarkable departure from tradition. While these tools collectively are quite effective, challenges remain in numerous areas, including: (a) rapid, high-precision computation of special functions and their derivatives; (b) user-customizable symbolic computing; (c) graphical computing; (d) data-intensive computing; and (e) large-scale computing on parallel and GPU architectures (including algorithm and software design for such systems).

This workshop will convene mathematical and computer scientists who create or exploit these tools, together with computational tool developers and commercial vendors of mathematical software, to exchange approaches and extend the state of the art in the field, both in the design... (more)

GirlsGetMath is a weeklong mathematics summer day-program for 9th and 10th grade high school girls in the Providence, RI area.

GirlsGetMath occurs in an encouraging environment that builds young women's confidence in math and science.

GirlsGetMath expands participants' understanding and knowledge of mathematics through computations and experimentations.

GirlsGetMath provides expert mathematical training and mentoring.

GirlsGetMath@ICERM 2014 is the first of what will become a replicable national model of mathematical outreach for high school girls, with an emphasis on mathematical experimentation.

This five-day non-residential mathematics program is open to high school girls from the greater Providence, RI area who will have just completed either grade 9 or grade 10 by July 2014.

GirlsGetMath@ICERM will... (more)

The American Institute of Mathematics (AIM), co-sponsored by ICERM, invites applications for the Research Experiences for Undergraduate Faculty (REUF) workshop to be held at AIM in Palo Alto, CA.

This workshop, sponsored by AIM, ICERM, and the National Science Foundation, is one in a series of annual REUF workshops that bring together leading research mathematicians with faculty at undergraduate institutions who are interested in involving their students in areas of active research. The workshop can also serve as a research renewal opportunity for faculty who want to re--engage in research or are considering a change of research area.

The goals of the workshop are to promote undergraduate research in undergraduate institutions, and to forge lasting research collaborations among the participating faculty. The majority of the workshop will be spent working on problems in small research groups, reporting on progress, and formulating plans for future work. In addition to the workshop... (more)

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)

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)