Programs & Events
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
Information-Based Complexity and Stochastic Computation
Sep 15 - 19, 2014
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)
Organizing Committee
- Frances Kuo
- Erich Novak
- Klaus Ritter
- Grzegorz Wasilkowski
- Henryk Wozniakowski
High-dimensional Approximation
Sep 8 - Dec 5, 2014
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)
Organizing Committee
- Dmitriy Bilyk
- William Chen
- Frances Kuo
- Michael Lacey
- Vladimir Temlyakov
- Rachel Ward
- Henryk Wozniakowski
Integrability and Cluster Algebras: Geometry and Combinatorics
Aug 25 - 29, 2014
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.
Organizing Committee
- Vladimir Fock
- Max Glick
- Olga Kravchenko
- Sophie Morier-Genoud
- Valentin Ovsienko
- Richard Schwartz
IdeaLab 2014: Program for Early Career Researchers
Aug 11 - 15, 2014
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)
Organizing Committee
- Ricardo Cortez
- Mark Levi
- Michael Minion
- Richard Montgomery
Combinatorial Link Homology Theories, Braids, and Contact Geometry
Aug 4 - 8, 2014
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
- Combinatorial knot Floer homology, with applications to contact geometry,
- Braid foliations and the Jones conjecture,
- Nielsen-Thurston theory, and
- Garside theory and a linear order on the braid group,
As the main goal of the workshop is to facilitate interaction... (more)
Organizing Committee
- John Baldwin
- Julia E Grigsby
- Joshua Greene
- Keiko Kawamuro
- Dan Margalit
Challenges in 21st Century Experimental Mathematical Computation
Jul 21 - 25, 2014
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)
Organizing Committee
- David Bailey
- Jonathan Borwein
- Olga Caprotti
- Ursula Martin
- Bruno Salvy
- Michela Taufer