## Programs & Events

##### Nonlinear Algebra in Applications

Nov 12 - 16, 2018

Applications often pose many algorithmic, computational, and theoretical challenges, and overcoming these challenges has been a driving force behind many recent innovations in nonlinear algebra. This workshop will bring together mathematicians and practitioners with a focus on recently developed methods that have been motivated by solving problems arising in applications. Three key hallmarks of the methods presented are efficient computation of solutions, exploitation of structure, and reformulation of numerically unstable systems. Some of the topics planned for discussion include algebraic cryptanalysis and coding theory, chemical reaction networks, computational biology, computer-aided geometric design, applications of enumerative and tropical geometry, gauge and string theory in physics, and applications to statistics such as probabilistic graphical models and singular learning theory.

##### Organizing Committee

- Yang-Hui He
- Caroline Uhler
- Alicia Dickenstein
- Jonathan Hauenstein
- Elisa Gorla

##### Computer Vision

Feb 4 - May 10, 2019

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)

##### Organizing Committee

- Yali Amit
- Ronen Basri
- Alex Berg
- Tamara Berg
- Pedro Felzenszwalb
- Stuart Geman
- Basilis Gidas
- David Jacobs
- Benar Svaiter
- Olga Veksler

##### Theory and Practice in Machine Learning and Computer Vision

Feb 18 - 22, 2019

Recent advances in machine learning have had a profound impact on computer vision. Simultaneously, success in computer vision applications has rapidly increased our understanding of some machine learning techniques, especially their applicability. This workshop will bring together researchers who are building a stronger theoretical understanding of the foundations of machine learning with computer vision researchers who are advancing our understanding of machine learning in practice.

Much of the recent growth in the use of machine learning in computer vision has been spurred by advances in deep neural networks. At the same time, new advances in other areas of machine learning, including reinforcement learning, generative models, and optimization methods, hold great promise for future impact. These raise important fundamental questions, such as understanding what influences the ability of learning algorithms to generalize, understanding what causes optimization in learning to converge... (more)

##### Organizing Committee

- Ronen Basri
- Alex Berg
- David Jacobs

##### Computational Imaging

Mar 18 - 22, 2019

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)

##### Organizing Committee

- Pedro Felzenszwalb
- Basilis Gidas

##### Optimization Methods in Computer Vision and Image Processing

Apr 29 - May 3, 2019

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.

##### Organizing Committee

- Pedro Felzenszwalb
- Benar Svaiter
- Olga Veksler
- Yuri Boykov

##### Arithmetic of low-dimensional abelian varieties

Jun 3 - 7, 2019

In this workshop, we will explore a number of themes in the arithmetic of abelian varieties of low dimension (typically dimension 2â€“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)

##### Organizing Committee

- John Voight
- Andrew Sutherland
- Jennifer Balakrishnan
- Noam Elkies
- Brendan Hassett
- Bjorn Poonen

##### Encrypted Search

Jun 10 - 14, 2019

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.

##### Organizing Committee

- Charalampos Papamanthou
- Alexandra Boldyreva
- David Cash
- Seny Kamara
- Hugo Krawczyk
- Tarik Moataz

##### ICERM Research Experiences for Undergraduate Faculty (REUF)

Jun 17 - 21, 2019

This workshop, a formal collaboration between ICERM and the American Institute of Mathematics (AIM), is one in a series of annual REUF workshops. These workshops bring together leading research mathematicians and faculty based at primarily undergraduate institutions to investigate open questions in the mathematical sciences and to equip participants with tools to engage in research with undergraduate students. REUF also serves to jump-start faculty who want to re-engage in research or who are considering a change in their research area.

The goals of this workshop are to promote undergraduate research and to forge 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. Note that there are opportunities for participants to continue research activities beyond the workshop week, which will be discussed during the workshop.

Preference will... (more)

##### Illustrating Mathematics

Sep 4 - Dec 6, 2019

The Illustrating Mathematics program brings together mathematicians, makers, and artists who share a common interest in illustrating mathematical ideas via computational tools.

The goals of the program are to:

- introduce mathematicians to new computational illustration tools to guide and inform their research;
- spark collaborations among and between mathematicians, makers and artists;
- find ways to communicate research mathematics to as wide an audience as possible.

The program includes week-long workshops in Geometry and Topology, Algebra and Number Theory, and Dynamics and Probability, as well as master courses, seminars, and an art exhibition.

Mathematical topics include: moduli spaces of geometric structures, hyperbolic geometry, configuration spaces, sphere eversions, apollonian packings, kleinian groups, sandpiles and tropical geometry, analytic number theory, supercharacters, complex dynamics, billiards, random walks, and Schrammâ€“Loewner... (more)

##### Organizing Committee

- David Dumas
- Laura Taalman
- Henry Segerman
- Katherine Stange
- Richard Schwartz
- David Bachman
- Saul Schleimer
- Kelly Delp

##### Illustrating Geometry and Topology

Sep 16 - 20, 2019

This workshop will focus on the interaction between visualization, computer experiment, and theoretical advances in all areas of research in geometry and topology. Fruitful interactions of this type have a long history in the field, with physical models and computer images and animations providing both illustration of existing work and inspiration for new developments. Emerging visualization technologies, such as virtual reality, are poised to further increase the tools available for mathematical illustration and experimentation. By bringing together expert practitioners of mathematical visualization techniques and researchers interested in incorporating such tools into their research, the workshop will give participants a clear picture of the state of the art in this fast-moving field while also fostering new collaborations and innovations in illustrating geometry and topology.

##### Organizing Committee

- Ellen Eischen
- David Dumas
- Keenan Crane

##### Illustrating Number Theory and Algebra

Oct 21 - 25, 2019

The symbiotic relationship between the illustration of mathematics and mathematical research is now flowering in algebra and number theory. This workshop aims to both showcase and develop these connections, including the development of new visualization tools for algebra and number theory. Topics are wide-ranging, and include Apollonian circle packings and the illustration of the arithmetic of hyperbolic manifolds more generally, the visual exploration of the statistics of integer sequences, and the illustrative geometry of such objects as Gaussian periods and Fourier coefficients of modular forms. Other topics may include expander graphs, abelian sandpiles, and Diophantine approximation on varieties. We will also focus on diagrammatic algebras and categories such as Khovanov-Lauda-Rouquier algebras, Soergel bimodule categories, spider categories, and foam categories. The ability to visualize complicated relations diagrammatically has led to important advances in representation theory... (more)

##### Organizing Committee

- Katherine Stange
- Joel Kamnitzer
- Alex Kontorovich

##### Illustrating Dynamics and Probability

Nov 11 - 15, 2019

This workshop will focus on the theoretical insights developed via illustration, visualization, and computational experiment in dynamical systems and probability theory. Some topics from complex dynamics include: dynamical moduli spaces and their dynamically-defined subvarieties, degenerations of dynamical systems as one moves toward the boundary of moduli space, and the structure of algebraic data coming from a family of dynamical systems. In classical dynamical systems, some topics include: flows on hyperbolic spaces and Lorentz attractors, simple physical systems like billiards in two and three dimensional domains, and flows on moduli spaces. In probability theory, the workshop features: random walks and continuous time random processes like Brownian motion, SLE, and scaling limits of discrete systems.

##### Organizing Committee

- Sarah Koch
- Jayadev Athreya
- Alexander Holroyd