May 2021 Newsletter

GROW 2021 Application Open

The Graduate Research Opportunities for Women (GROW) 2021 conference will be hosted by the University of Illinois at Chicago October 15-17, 2021. GROW aims to increase the representation of women in U.S. math graduate programs and to encourage undergraduate women to pursue careers in mathematics. It has been held annually since 2015, and has been hosted at Northwestern University (2015-17), at the University of Michigan (2018), at the University of Illinois at Urbana-Champaign (2019), and (virtually) at the University of Chicago (2020). GROW has recently been recognized by the AMS through its Mathematics Programs that Make a Difference Award.

The conference brings together undergraduates from across the country for plenary research talks, panel discussions on topics such as graduate school admissions, mathematics research, and careers in the mathematical sciences, a conference banquet with a talk by a well-known speaker, and and numerous activities intended to facilitate informal interactions among participants, graduates students, and faculty.

The application for undergraduates interested in attending is now open.

Apply to Host GROW in 2022 and beyond

Administration of the GROW conference series is now being conducted through a partnership of the GROW Steering Committee (consisting of Kevin Corlette, Bryna Kra, Julius Ross, Brooke Shipley, and Jeremy Tyson) with IMSI. We invite applications to host the GROW conference in 2022 and/or 2023. Applications that commit to hosting GROW for two consecutive years are welcome. Organizing committees based in U.S. mathematics departments with doctoral degree-granting programs are eligible to apply. The host institution is expected to organize a GROW conference similar to previous in-person versions of GROW. For more information, please see the Call for Applications; applications are due by July 1, 2021.

Upcoming Activities

May 2021

May 10-14: Verification, Validation, and Uncertainty Quantification Across Disciplines

May 17-21: Decision Making in Health and Medical Care: Modeling and Optimization

May 24-28: Quantum Information for Mathematics, Economics, and Statistics

Summer 2021

June 1-25: Introduction to Mean Field Games and Applications

This program provides mathematical background for the long program in Fall 2021 on Distributed Solutions to Complex Societal Problems. Problems to be addressed in the long program include modeling of phenomena such as the macroeconomy, conflict, financial regulation, crowd movement, big data, and advertising, as well as engineering problems involving decentralized intelligence, machine learning, and telecommunications. A mathematical framework well-suited to the study of such phenomena is Mean Field Games. The intended audience consists of advanced graduate students, postdocs, and researchers interested in the general topic who have some knowledge of probability, stochastic analysis, and partial differential equations.

This program will take place online. Some financial support is available for participants who need it.

June 28-July 23: Introduction to Decision Making and Uncertainty

How do we make decisions in the face of risk? The need to make decisions in the presence of uncertainty cuts across a wide range of issues in science and human behavior. The underlying problems require both sophisticated modeling and advanced mathematical and statistical approaches and techniques.

This program will serve as an introduction to the long program on Decision Making and Uncertainty scheduled for Spring 2022. It aims to introduce participants to a variety of modeling questions and methods of current interest in this area. The intended audience is researchers interested in mathematical modeling and methods applicable to decision making under uncertainty in economics, finance, business, and other areas. Advanced Ph.D. students, postdocs, and junior faculty are especially encouraged to apply. Basic knowledge in probability, stochastics, and statistics is required.

This program will take place online. Some financial support is available for participants who need it.

August 30-September 3: Eliciting Structure in Genomics Data: Bridging the Gap between Theory, Algorithms, Implementations, and Applications

IMSI Seeks Program and Workshop Proposals

IMSI is seeking proposals for long programs for the academic year 2023-24 and for workshops and other activities for the winter of 2023 and beyond. Long programs are intended to bring together interdisciplinary groups of researchers to explore questions related to IMSI's themes. They generally last 3 months and take place during the autumn or spring quarter. Workshops are intended to be interdisciplinary and focused on a societally-relevant topic for which mathematicians and statisticians can partner with other sciences to make important contributions. For all activities, organizing committees are expected to attract a diverse group of participants, where diversity is measured across a number of dimensions, including gender, race, ethnicity, career stage, employment sector, and research area. The deadline for this round of proposals is September 1, 2021.

General expectations for proposals are discussed on IMSI's Proposing Activity web page. If you have an idea for a program or workshop, please contact Kevin Corlette ([email protected]) to initiate a dialogue.

paraDIGMS Spring Conference

The paraDIGMS Spring Conference took place April 23-26, 2021. The conference was part of the paraDIGMS initiative of the AMS, which aims to to create channels of communication, spaces for reflection, opportunities to collaborate, and a greater sense of collective responsibility for the well-being of the profession at the graduate level. The specific goal of the conference was to foster a community of practice for graduate education in the mathematical sciences, with the goal of making the profession stronger and more equitable. The conference included plenary lectures by Erica J. Graham, Shirley Malcom, and Kassou Okoudjou and Francis Su. In addition, there were panel discussions on helping students transition to research, models for orienting and acculturating students into the practice and culture of the mathematical sciences, and the experiences and perspectives of graduate student labor union organizers. Finally, there were reading groups to discuss the recent report of the Task Force on Understanding and Documenting the Historical Role of the AMS in Racial Discrimination, and lightning talks by participants on initiatives in individual departments.

IMSI Data Science Workshops in April

IMSI hosted two virtual workshops on data science in April.

The Multifaceted Complexity of Machine Learning took place April 12-16, 2021 with the goal of exploring multiple interrelated notions of complexity that arise in relation to machine learning tasks. The talks at the workshop included the following:

• Peter Bartlett discussed the phenomenon of Benign Overfitting, where deep learning algorithms are able to learn the training data to high accuracy without sacrificing predictive accuracy, even in cases where the training data contains significant amounts of noise.
• Moritz Hardt discussed Performative Prediction, where a prediction made by a statistical model triggers an action that changes the distribution of the outcome variable which the model is trying to predict.
• Samory Kpotufe discussed Some Recent Insights on Transfer Learning, which involves transferring learning based on training on data drawn from one population to related but distinct populations.
• Kamalika Chaudhuri explored The Mysteries of Adversarial Robustness to understand why small, often imperceptible, changes in inputs can lead to misclassification by machine learning algorithms.

Topological Data Analysis took place April 26-30, 2021, and brought together 9 invited talks, 18 contributed talks, and 42 poster presentations. Topological data analysis studies the "shape" of point clouds, which are finite sets of points in a Euclidean space, typically of large dimension. An initial attempt to describe the shape of a point cloud might involve deciding whether the point cloud can be reasonably described as breaking up into distinct clumps of points. Of course, when looked at through a magnifying class, each point in the point cloud is its own distinct clump, so one has to zoom out to some degree and decide that, if two points are within some distance d of each other, then they should be regarded as being in the same clump. For very small positive values of d, the clumps will still be individual points, but they will begin to coalesce into larger clumps as d gets bigger. If one considers all positive values of d, each clump will appear starting with some value d₀, and will persist until it is (possibly) absorbed into a larger clump for some value d₁>d₀. Some clumps will only persist over a relatively short interval [d₀,d₁], which generally suggests that these clumps are relatively unimportant features of the point cloud; in many cases, this will be true of the individual points themselves, which will disappear into larger clumps relatively quickly. Other clumps will have a much larger interval of persistence, suggesting that they are pointing to more essential features of the data.

A more sophisticated set of questions begins to appear if one suspects that the point cloud represents a sample from a submanifold M of the Euclidean space which contains the cloud. In that case, it become natural to ask what one can reasonably infer about the submanifold from the data in the point cloud. A natural invariant to try to capture is the homology of the submanifold. The homology H^k(M) for each nonnegative integer k measures the number of k-dimensional holes in M, and in the case k=0 captures our previous discussion about the number of clumps in a space. To define persistence of homology classes for point clouds, we build a topological space associated to the point cloud for every d>0 as follows: if the distance between two points is less than d, we connect them by a line segment; if three points are all connected to each other, then we fill in the three edges connecting them with a triangle; if four points are all connected to each other, we fill in the edges with a solid tetrahedron. This process continues for larger and large numbers of points, forming a space called the Vietoris-Rips complex of the point cloud for the value d. The Vietoris-Rips complex for d₀ is naturally included in the Vietoris-Rips complex for any larger value d₁, inducing a map of the homology of the first to that of the second. Thus, one can talk about homology classes in degree k appearing at a given value of d₀ and (possibly) disappearing at a larger value d₁. Again, the classes with large intervals of persistence can often reasonably be inferred to represent important features of the data. This perspective opens the door for the use of persistent homology as a tool to gain insight into complex data sets.

Persistent homology was a recurrent theme during the conference. A number of talks and posters addressed theoretical developments related to persistent homology, while others addressed applications such as mapping 3-dimensional shape variation onto genotypic and phenotypic variation, predicting survival outcomes from medical images, geometric and topological fingerprints for periodic crystals, website optimization, detection of deep fakes, the dimension of neuroscience data, and the structure of protein space.

News from the NSF

Juan Meza, the Director of the Division of Mathematical Sciences (DMS) at the NSF, recently sent principal investigators with DMS awards in the final year an email describing an opportunity to request supplements to help address the needs of PIs, postdocs, and students who have been most critically impacted by the pandemic. Supplements will be considered that provide near-term relief for those disproportionately impacted by the pandemic, including students, postdocs, and faculty at career transitions, with the goal of maintaining a robust scientific workforce. Supplements are intended for those awards with insufficient remaining funds to address these impacts through rebudgeting. Supplement proposals should be submitted by May 21st to the same program that supported the existing award. Questions may be directed to the cognizant program director for the award.

Juan Meza's term as Director of DMS is approaching an end. An ad for the position has been posted at https://www.usajobs.gov/GetJob/ViewDetails/600624900. Please bring this to the attention of anyone whom you think would be a good candidate.

Copyright © 2021. All rights reserved.
IMSI acknowledges support from the National Science Foundation
(Grant No. DMS-1929348)

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