Computer vision is an inter-disciplinary topic crossing boundaries between computer science, statistics, mathematics, engineering and cognitive science.

Research in computer vision involves the development and evaluation of computational methods for image analysis. This includes the design of new theoretical models and algorithms, and practical implementation of these algorithms using a variety of computer architectures and programming languages. The methods under consideration are often motivated by generative mathematical models of the world and the imaging process. Recent approaches also rely heavily on machine learning techniques and discriminative models such as deep neural networks.

Problems that will be considered in the program include image restoration, image segmentation, object recognition and 3D reconstruction. Current approaches to address these problems draw on a variety of mathematical and computational topics such as stochastic models, statistical methods,... (more)

Computational imaging involves the use of mathematical models and computational methods as part of imaging systems. Algorithms for image reconstruction have important applications, including in medical image analysis and imaging for the physical sciences. Classical approaches often involve solving large inverse problems using a variety of regularization methods and numerical algorithms.

Current research includes the development of new cameras and imaging methods, where the hardware system and the computational techniques used for image reconstruction are co-designed. New developments have been influenced by the introduction of novel techniques for compressed sensing and sparse reconstruction. The use of machine learning methods for designing a new generation of imaging systems has also been increasingly important.

Specific topics that will be discussed include: image reconstruction, computational photography, compressed sensing, machine learning methods, numerical optimization,... (more)

Optimization appears in many computer vision and image processing problems such as image restoration (denoising, inpainting, compressed sensing), multi-view reconstruction, shape from X, object detection, image segmentation, optical flow, matching, and network training. While there are formulations allowing for global optimal optimization, e.g. using convex objectives or exact combinatorial algorithms, many problems in computer vision and image processing require efficient approximation methods.

Optimization methods that are widely used range from graph-based techniques and convex relaxations to greedy approaches (e.g. gradient descent). Each method has different efficiency and optimality guarantees. The goal of this workshop is a broad discussion of mathematical models (objectives and constraints) and robust efficient optimization methods (exact or approximate, discrete or continuous) addressing existing issues and advancing the state of the art.

Data science in low-dimensional spaces is motivated by applications in mapping, navigation, geographic resource allocation, modeling of body shapes and chemical structures, and more. In addition to datasets that naturally reside in low-dimension spaces, dimension-reduction methods can often transform high dimensional data to lower-dimensional data while preserving properties of interest. Since many computational problems are intractable for high-dimensional data but potentially tractable for low-dimensional data, it is useful to establish the algorithmic foundations of data science on low-dimensional data, to understand the special properties of such data, and to identify computational methods that are highly effective when applied to such data.

This workshop will bring together researchers in academia and industry to explore algorithmic and data analysis technique specialized for low-dimensional data, and application areas in which such problems arise. The focus of this workshop is... (more)

In this workshop, we will explore a number of themes in the arithmetic of abelian varieties of low dimension (typically dimension 2–4), with a focus on computational aspects. Topics will include the study of torsion points, Galois representations, endomorphism rings, Sato-Tate distributions, Mumford-Tate groups, complex and p-adic analytic aspects, L-functions, rational points, and so on. We also seek to classify and tabulate these objects, in particular to understand explicitly the underlying moduli spaces (with specified polarization, endomorphism, and torsion structure), and to find examples of abelian varieties exhibiting special behavior. Finally, we will pursue connections with related areas, including the theory of modular forms, related algebraic varieties (e.g., K3 surfaces), and special values of L-functions.

Our goal is for the workshop to bring together researchers working on abelian varieties in a number of facets to establish collaborations, develop algorithms, and... (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 $3,570 stipend*.

The 2019 Summer@ICERM program at Brown University is an eight-week residential program designed for a select group of 18-22 undergraduate scholars.

The faculty advisers will present a variety of interdisciplinary research... (more)

The area of encrypted search focuses on the design and cryptanalysis of practical algorithms and systems that can search on end-to-end encrypted data. With encrypted search algorithms, data can remain encrypted even in use. As such, encrypted search algorithms have a wide array of applications including in data management, healthcare, cloud computing, mobile security, blockchains, and censorship- and surveillance-resistant systems.