## Programs & Events

##### Nonlinear Algebra

Sep 5 - Dec 7, 2018

The theory, algorithms, and software of linear algebra are familiar tools across mathematics, the applied sciences, and engineering. This ubiquity of linear algebra masks a fairly recent growth of *nonlinear algebra* in mathematics and its applications to other disciplines. The proliferation of nonlinear algebra has been fueled by recent theoretical advances, efficient implementations of core algorithms, and an increased awareness of these tools.

The benefits of this nonlinear theory and its tools are manifold. Pushing computational boundaries has led to the development of new mathematical theories, such as homotopy methods for numerical algebraic geometry, tropical geometry and toric deformations, and sums of squares methods for polynomial optimization. This uncovered many concrete nonlinear mathematical objects and questions, many of which are ripe for computer experimentation. In turn, resulting mathematical breakthroughs often lead to more powerful and efficient algorithms... (more)

##### Organizing Committee

- Cynthia Vinzant
- Sandra Di Rocco
- Anton Leykin
- Dan Bates
- Jonathan Hauenstein
- Frank Sottile
- Mike Stillman

##### An ICERM Public Lecture: How to be Human in the Age of Algorithms

Sep 27, 2018

For decades, human activities and decisions have been supported by algorithms. They are the hidden rules and instructions that help our computers to process data and run complex calculations. But in recent years, algorithms have moved from a supporting to a starring role. As our machines have become more powerful, the algorithms have become more sophisticated - so much so that they are now in control of potentially life-changing decisions. In the courts, algorithms decide if jail time is warranted. In hospitals, they match organ donors to waiting patients. And on the streets, they steer driverless cars. In each of these scenarios, wrong decisions can lead to tragic outcomes.

In this talk, I'll explore our relationships with algorithms, the responsibilities we give them, and the impact they are having on our societies - including the good, the bad, and the downright ugly.

##### Real Algebraic Geometry and Optimization

Oct 15 - 19, 2018

This workshop will focus on techniques and structures in real algebraic geometry and optimization, including computational tools for semi-algebraic sets, semidefinite programming techniques for polynomial optimization, and applications of these tools to problems in computer vision. Real algebraic geometry provides powerful tools to analyze the behavior of optimization problems, the geometry of feasible sets, and to develop new relaxations for hard non-convex problems. On the other hand, numerical solvers for semidefinite programs have led to new fast algorithms in real algebraic geometry. Algebraic methods over the real numbers are essential for many real-world applications. This workshop aims to explore the cutting edge of techniques in real algebraic geometry and convex optimization as well as applications of these tools to problems in computer vision and other information sciences.

##### Organizing Committee

- Cynthia Vinzant
- Rekha Thomas
- Greg Blekherman
- Didier Henrion
- Pablo Parrilo

##### Celebrating 75 Years of Mathematics of Computation

Nov 1 - 3, 2018

This symposium will highlight the progress in the mathematics of computation over the last few decades. The invited lectures will present historical surveys of important areas or overviews of topics of high current interest. Together they will provide a panoramic view of the most significant achievements in the past quarter century in computational mathematics and also the most important current trends.

The year 2018 marks the 75th anniversary of the founding of Mathematics of Computation, one of the four primary research journals of the American Mathematical Society and the oldest research journal devoted to computational mathematics. This symposium will commemorate the event with invited lectures and poster presentations that reflect the spectrum of research covered by Mathematics of Computation at this juncture of its illustrious history.

The first day of the symposium (November 1) is devoted to the discrete topics and the other two days (November 2-3) are devoted to continuous... (more)

##### Organizing Committee

- Chi-Wang Shu
- Susanne Brenner
- Igor Shparlinski
- Daniel Szyld

##### An ICERM Public Lecture: Mathematics: Rhyme and Reason

Nov 8, 2018

A little more than three years ago, while attending the Conference for African American Researchers in the Mathematical Sciences at ICERM, I spontaneously announced to ICERM Associate Director Ulrica Wilson that I thought I would write a book about the heart of mathematics. Then I went ahead and did it. What was I thinking?! Publishing Mathematics: Rhyme and Reason is akin to undressing publicly. So, what ends up being exposed? Well, among other things, I place in plain view relationships with people in my mathematical upbringing, some of whom popped into my life for better and, at least once, for worse. One will also see my life-long attachment to the simple truths of mathematics. The book is a message to the kid I was, with the assumption that such kids still exist. I present a large collection of theorems and call them nursery rhymes in the book, though I didnâ€™t stumble across a few of them until I was well beyond nursery-rhyme age. I also write about whether or not I have ever... (more)

##### Blackwell-Tapia Conference 2018

Nov 9 - 10, 2018

The NSF Mathematical Sciences Institutes Diversity Committee hosts the 2018 Blackwell-Tapia Conference and Awards Ceremony. This is the ninth conference since 2000, held every other year, with the location rotating among NSF Mathematics Institutes. The conference and prize honors David Blackwell, the first African-American member of the National Academy of Science, and Richard Tapia, winner of the National Medal of Science in 2010, two seminal figures who inspired a generation of African-American, Native American and Latino/Latina students to pursue careers in mathematics.

The Blackwell-Tapia Prize recognizes a mathematician who has contributed significantly to research in his or her area of expertise, and who has served as a role model for mathematical scientists and students from underrepresented minority groups, or has contributed in other significant ways to addressing the problem of underrepresentation of minorities in math.

The

##### Organizing Committee

- Brendan Hassett
- Ulrica Wilson
- David Eisenbud
- Carlos Castillo-Chavez
- Robert Megginson
- Mariel Vazquez
- Robin Wilson
- Jacqueline Hughes-Oliver

##### 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

##### Scientific Machine Learning

Jan 28 - 30, 2019

The machine learning revolution is already having a significant impact across the social sciences and business but it is also beginning to change computational science and engineering in fundamental and very varied ways.

We are experiencing the rise of new and simpler data driven methods based on techniques from machine learning such as deep learning. This revolution allows for the development of radical new techniques to address problems known to be very challenging with traditional methods and suggests the potential dramatic enhancement of existing methods through data informed parameter selection, both in static and dynamic modes of operation. Techniques are emerging that allows us to produce realistic solutions from non-sterilized computational problems in diverse physical sciences.

However, the urgent and unmet need to formally analyze, design, develop and deploy these emerging methods and develop algorithms must be addressed. Many central problems, e.g. enforcement of physical... (more)

##### Organizing Committee

- George Karniadakis
- Jan Hesthaven

##### Abelian varieties over finite fields

Jan 31 - Feb 3, 2019

This will be a hands-on workshop focused on a specific computational problem: enumerating all isomorphism classes of abelian varieties of of dimension g over a finite field of cardinality q, for a suitable range of integers g and q. Isogeny classes of abelian varieties over finite fields have been previously classified by Weil polynomials and can be found in the L-functions and Modular Form Database. The goal of this workshop is to refine this to the level of isomorphism classes, and, whenever possible, to construct explicit representatives for each isomorphism class. By exploiting recent theoretical and computational advances and assembling an appropriate team of experts, we hope to make rapid and substantial progress during this short, focused workshop and to have results available in advance of the conference on the Arithmetic of Low-dimensional Abelian Varieties that will take place at ICERM in June.

**This is a closed workshop that will not be accepting applications.**

##### Organizing Committee

- John Voight
- Andrew Sutherland

##### 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 Fux 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

##### Image Description for Consumer and Overhead Imagery

Feb 25 - 26, 2019

Building systems that can understand visual concepts and describe them coherently in natural language is fundamental to artificial intelligence. Advances in machine learning have had profound impact on computer vision and natural language processing. There has been interesting progress in recent years at the intersection of these two fields, producing systems that describe (eg., caption) images and videos captured by personal cameras in ordinary scenes and street views. Much work remains in this and a host of related problems, including that of building natural language descriptions of commercial overhead imagery and videos, where automation is greatly needed: "If we were to attempt to manually exploit the commercial satellite imagery we expect to have over the next 20 years, we would need eight million imagery analysts" [Robert Cardillo, NGA Director, GEOINT Symposium 2017]. This workshop brings together researchers in machine learning, computer vision, natural language processing... (more)

##### Organizing Committee

- Triet Le
- David Jacobs
- Guillermo Sapiro
- Trevor Darrell
- Eric Xing