Programs & Events
Ergodic, Algebraic and Combinatorial Methods in Dimension Theory
Feb 15 - 19, 2016
There are natural interactions between dimension theory, ergodic theory, additive combinatorics, metric number theory and analysis. Each of these fields provides different perspectives on, and complementary approaches to, the hierarchical structures which appear in fractal geometry.
The workshop will focus on recent advances at the interfaces of these fields, including:
- Classical fractals (self-similar and self-affine sets, random fractals)
- Dimension theory and additive combinatorics
- Diophantine approximation and equidistribution
- Schmidt games
- Rigidity phenomena
- Scenery flow methods
- Projection and slice theorems
Organizing Committee
- Michael Hochman
- Izabella Laba
- Pablo Shmerkin
- Barak Weiss
Public Lecture: The Beautiful Mathematically Ordered Colors of Birds
Feb 17, 2016
The blue and green colors we see in birds, and even some of the ultraviolet that we cannot see, are produced by the way in which light interacts with ordered structures in the tissues of the birds. This order in the structures can be measured using Fourier analysis, a powerful mathematical tool.
Like a prism that decomposes a beam of light into a rainbow of colors, Fourier analysis transforms the geometrical arrangements observed in electron microscope images of the tissues into a mathematical rainbow of basic components that quantify order. We will illustrate how Fourier analysis processes the images and helps decipher the colors of birds and other animals. We will use this application of Fourier analysis to present also some of its mathematical concepts and interest.
The talk will be accessible to all those who are curious about some of the physics behind the bright blue and green colors found in nature and how mathematics can be used to describe such coloration.
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Mar 7 - 11, 2016
A surprising discovery of 20th century mathematics is that many deterministic systems exhibit random behavior. One early example of a chaotic system was Lorenz equation used by meteorologist Edward Lorenz as a simplified model of atmospheric convection. One of the most common mechanisms of stochasticity is the Smale horseshoe appearing near a homoclinic intersection.
The Lorentz attractor and Smale horseshoe are typical examples of fractal invariant sets for dynamical systems. Fractal objects are ubiquitous in dynamics, including invariant sets, invariant measures, invariant foliations et cetera.
Thermodynamical formalism is a powerful tool for studying dimensions of fractal objects. It originated in statistical mechanics, but currently it has applications to many areas of mathematics including spectral theory, hyperbolic geometry and probability theory.
The goal of this conference is to bring together experts studying fractal objects in dynamics in order to review recent progress... (more)
Organizing Committee
- Lorenzo Diaz
- Dmitry Dolgopyat
- Maarit Jarvenpaa
- Jörg Schmeling
- Masato Tsujii
- Amie Wilkinson
Computation in Dynamics
Apr 4 - 8, 2016
Numerical computations have always played an important role in the development of the theory of Differential Equations and Dynamical Systems, more and more so as the availability and power of computers has increased dramatically over the last few decades. At the same time, the limitations of computer-assisted numerical calculations have also become increasingly apparent. Notwithstanding their enormous power, the intrinsic finite resolution of computers can lead to significant errors, especially as a result of a large number of calculations through which small errors can accumulate.
An important and growing approach to certain mathematical problems consists of developing rigorous numerical techniques in combination with more classical analytic methods in order to obtain rigorous qualitative and quantitative results. In some cases this leads to the proof of deep mathematical theorems and in other cases to quantitative, and thus more concrete and applicable, versions of abstract... (more)
Organizing Committee
- Denis Gaidashev
- Stefano Galatolo
- Stefano Luzzatto
- Warwick Tucker
- Michael Yampolsky
Public Lecture: Inverse Problems and Harry Potter's Cloak
Apr 20, 2016
Dr. Uhlmann will begin his talk by describing several inverse problems that arise in several contexts. For example, human vision: from the measurements of scattered light that reaches our retinas, our brains construct a detailed three-dimensional map of the world around us. Solving inverse problems is in fact how we obtain a large part of our information about the world we live in.
In the second part of his talk, Dr. Uhlmann will discuss invisibility, addressing the question, "can we make objects invisible?" This has been a subject of human fascination for millennia in Greek mythology, movies, science fiction, etc., including the legend of Perseus versus Medusa and the more recent Star Trek and Harry Potter stories. In the last 13 years or so there have been several scientific efforts to achieve invisibility. Dr. Uhlmann will describe a simple and powerful proposal, the so-called transformation optics and the progress that has been made in achieving invisibility.
Effective and Algorithmic Methods in Hyperbolic Geometry and Free Groups
May 16 - 20, 2016
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)
Organizing Committee
- Tarik Aougab
- Mladen Bestvina
- Jeffrey Brock
- Eriko Hironaka
- Johanna Mangahas
Algorithmic Coding Theory
Jun 13 - 17, 2016
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)
Organizing Committee
- Hamed Hassani
- Atri Rudra
- Mary Wootters
The SaTC Workshop on Privacy and Security at the University of Wisconsin
Jun 15 - 17, 2016
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)
Organizing Committee
- Nigel Boston
- Somesh Jha
Summer@ICERM 2016: Dynamics and Stochastics
Jun 20 - Aug 12, 2016
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 2016 Summer@ICERM program is designed for a select group of 14-16 undergraduate scholars. Students work in groups of two to four, supervised by faculty advisors and aided by teaching assistants. The faculty... (more)
Organizing Committee
- Margaret Beck
- Todd Kapitula
- Bjorn Sandstede
Illustrating Mathematics
Jun 27 - Jul 1, 2016
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.
Organizing Committee
- Kelly Delp
- Saul Schleimer
- Henry Segerman
- Laura Taalman
Stochastic numerical algorithms, multiscale modeling and high-dimensional data analytics
Jul 18 - 22, 2016
This workshop is concerned with sampling challenges, modeling and simulation for data-rich applications in high dimensions. It brings together mathematicians, statisticians and computational scientists to explore the interplay between computational applied mathematics and data science. On the agenda will be novel developments in the study of complex phenomena based on data-analytic techniques, such as efficient calculation of ergodic (long term) averages and statistical inference under a wide range of geometric, physical and analytical constraints.
In applied mathematics and computational science, in particular in molecular modeling, image analysis and geosciences, among others, many objects of interest are high-dimensional and stochastic, and a wide variety of techniques have been developed for sampling and approximating the quantities of interest. Similar issues arise in the area of data science and statistical modeling, where learning problems in the presence of high-dimensional... (more)
Organizing Committee
- Mark Girolami
- Susan Holmes
- Benedict Leimkuhler
- Mauro Maggioni
Research Experiences for Undergraduate Faculty (REUF) on the Mathematics of Data, at Duke University, Durham, NC
Jul 18 - 22, 2016
This workshop, sponsored by the National Science Foundation and the Departments of Mathematics and Statistical Science at Duke, is part of the REUF program that brings together leading research mathematicians with faculty at undergraduate institutions who are interested in involving their student in areas of active research. The Workshop is also a research renewal opportunity for faculty who want to re-engage in research or are considering a change of research.
REUF on the Mathematics of Data will focus on the recently developing fields that lie at the interface of pure mathematics and big data analytics; for example, manifold learning, topological data analysis, and wavelet theory. Faculty trained in topology, geometry, algebra, or analysis will work on problem that are phrased in the language of their fields but are accessible to dedicated undergraduates through the use of computers.
The majority of the workshop will be spent working in small research groups, reporting on progress,... (more)