## Programs & Events

##### An ICERM Public Lecture: Discovering Black Holes and Gravitational Waves: Algorithms and Simulation

Feb 20, 2019

The equations of general relativity, Einstein's field equations, are among the most complicated partial differential equations in mathematical physics. These equations predict the existence of gravitational waves, which are propagating disturbances in spacetime itself. In 2016, the first direct observation of these waves from colliding black holes was reported on, a historic discovery that led to last years Nobel Prize. This discovery would not have been possible without intense interaction between physicists, mathematicians, and high-performance computing tools. Indeed, numerically solving Einstein's equations for the expected wave signal and the processing of gravitational-wave datasets was enabled by advances in algorithms, numerical methods, and access to large computing resources. In this talk, I will focus on the critical role all three played in making this historic discovery as well as summarizing current directions in computational relativity and gravitational-wave data... (more)

##### 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 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

- Andrew Sutherland
- John Voight

##### Scientific Machine Learning

Jan 28 - 30, 2019

**Note:** *At this time, ICERM is no longer accepting applications for this workshop as we are at capacity. Talks will be live streamed and recorded for viewing.*

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... (more)

##### Organizing Committee

- Jan Hesthaven
- George Karniadakis

##### Models and Machine Learning for Causal Inference and Decision Making in Health Research

Jan 14 - 18, 2019

Causal and mathematical models are widely used for decision making and policy evaluation at both the micro and macro levels. For example, causal models using large datasets are used to evaluate treatment efficacy in HIV; mathematical models are used to simulate the effects of prevention or policy measures to improve health outcomes or reduce the spread of infectious diseases. Entities such as the World Health Organization and UNAIDS rely on these models to set wide-ranging and high-impact policy related to treatment and prevention of infectious disease.

Causal models tend to rely on large-scale cohort data, while mathematical models in many ways represent evidence synthesis. Important methodologic issues in the development, application, and interpretation of these models include the role of untestable assumptions, transportability of findings to specific populations of interest, model calibration and validation, and uncertainty quantification. The datasets used to develop these... (more)

##### Organizing Committee

- Joseph Hogan

##### 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

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

##### 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

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

##### 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)

##### 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

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

##### 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

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

##### 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.

##### Core Computational Methods

Sep 17 - 21, 2018

This workshop will focus on core algorithms in the three crucial areas in nonlinear algebra: numerical algebraic geometry, symbolic computation, and combinatorial methods. There have been tremendous advances in algorithms in these areas. As applications become more sophisticated, and require more computing resources, the basic algorithms and implementations need to step up to match the demand from applications. This workshop will bring together experts to exchange ideas on new algorithms that are needed and on improvement of existing ones. It will incite collaboration on hybrid algorithms involving computational methods from the three areas. Examples of open problems to be addressed include: certification of numerical methods, and combining numerical, symbolic and combinatorial methods to allow a much larger reach for decomposition algorithms.

##### Organizing Committee

- JesÃºs De Loera
- Wolfram Decker
- Andrew Sommese
- Mike Stillman

##### Nonlinear Algebra Bootcamp

Sep 5 - 12, 2018

The primary goal of this opening workshop is to expose program participants to many of the methods and software packages relevant to this program. There will be introductory lectures and ample time for experimentation with methods and software under the tutelage of area experts and software developers.

##### Organizing Committee

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