## Programs & Events

##### Probabilistic Scientific Computing: Statistical inference approaches to numerical analysis and algorithm design

Jun 5 - 9, 2017

There is an urgent and unmet need to formally analyze, design, develop and deploy advanced methods and algorithms that can scale in statistical and computational efficiency to the size of modern data sets and the complexity of contemporary mathematical models. Addressing this need will require a holistic approach involving new foundational theory, algorithms, and programming language design.

The emerging research theme of Probabilistic Scientific Computing (PSC) or Probabilistic Numerics lies at the nexus of these overlapping directions. It aims to improve statistical quantification of uncertainty, improve computational efficiency, and build more effective and scalable numerical methods for statistical models by leveraging the natural correspondence between computation and inference.

The primary goal of the workshop is to introduce recent results and new directions in probabilistic scientific computing to the US research communities in statistics and machine learning, in numerical... (more)

##### Organizing Committee

- Philipp Hennig
- George Karniadakis
- Michael Osborne
- Houman Owhadi
- Paris Perdikaris

##### Current Developments in Mathematical Fluid Dynamics: Regularity, Instabilities, and Turbulence

Jan 24 - 27, 2017

The purpose of the topical workshop is to gather leading experts, postdoctoral scholars, and graduate students, to present exciting new developments in the field of mathematical fluid dynamics. The focus of the meeting will be placed on current research on regularity, instabilities, and the onset of turbulence in fluid flow, from a theoretical and from a computational perspective. Despite their long and fruitful history, to date these topics continue to enchant and inspire mathematicians, physicists, and computational scientists: in part due to their ubiquitous applications in areas from aeronautical engineering to medicine, and in part because the basic mathematical questions are still open. Among these are global in time existence of solutions to the equations describing motion of inviscid and viscous fluids in three spatial dimensions, and the conjectured relation between the phenomenological theories of turbulence and the statistical properties of solutions to the underlying... (more)

##### Organizing Committee

- Peter Constantin
- Nataša Pavlovic
- Vlad Vicol

##### Predictive Policing

Aug 8 - 12, 2016

This workshop is a one-week program aimed at 20-25 researchers interested in the opportunity to shape the future of research on the mathematics of crime. Small teams will come together to work on real problems with real crime and policing data provided by the Providence Police Department. Five teams will be assembled, each with a technical advisor who will share their expertise and serve as an anchor point and leader for hands-on research that will take place over the course of the week. This will be a truly hands-on experience in which groups will spend time brainstorming mathematical methods and models to approach the problem at hand, analyzing data provided, and creating code to implement ideas as necessary. There will also be research presentations from the technical advisors throughout the week, as well as closing presentations by each team to present their ideas and progress at the end of the workshop. We fully anticipate that lasting collaborations will be formed, and that work... (more)

##### Organizing Committee

- Andrea Bertozzi
- Jeff Brantingham
- Martin Short

##### Cycles on Moduli Spaces, Geometric Invariant Theory, and Dynamics

Aug 1 - 5, 2016

A moduli space parameterizes geometric objects with alike structures and encodes in itself the geometry of all possible families of such objects. This workshop will focus on three aspects of moduli spaces: Cycles, Geometric Invariant Theory, and Dynamics. One of our main goals is to synthesize the recent progress on moduli of abelian differentials on algebraic curves motivated by dynamics and in the GIT constructions of related moduli spaces, with the view towards better understanding of geometric cycles on these moduli spaces.

In many cases, computer programming and experiments are important tools to discover new phenomena, both in dynamics and in the study of cycles on moduli spaces. Hence many talks will emphasize computational and experimental aspects of these fields and the workshop will feature a computational problem session whose goal is to disseminate computational techniques and problems to a wider body of researchers.

An integral part of the workshop is a series of three... (more)

##### Organizing Committee

- Ana-Maria Castravet
- Dawei Chen
- Maksym Fedorchuk
- Anton Zorich

##### 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

##### 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

##### 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. InformationÂ¬-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 informationÂ¬-security researchers and mathematicians. The main focus of this workshop will consist of researchers in information-security presenting the mathematical challenges they face in latticeÂ¬-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-Â¬security researchers will give talks about various topics and indicate interesting... (more)

##### Organizing Committee

- Nigel Boston
- Somesh Jha

##### 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

##### 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

##### Numerical Methods for Large-Scale Nonlinear Problems and Their Applications

Aug 31 - Sep 4, 2015

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)

##### Organizing Committee

- Tim Kelley
- Homer Walker
- Carol Woodward

##### Mathematics in Data Science

Jul 28 - 30, 2015

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.

##### Organizing Committee

- Philip Kegelmeyer
- Tamara Kolda
- Randall LeVeque
- Aleksandra (Saska) Mojsilovic
- Linda Ness
- Alyson Wilson

##### Computational and Analytical Aspects of Image Reconstruction

Jul 13 - 17, 2015

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)

##### Organizing Committee

- Gaik Ambartsoumian
- Vladimir Druskin
- Esther Klann
- Venkateswaran Krishnan
- Alfred Louis
- Eric Quinto