Thomas Berger - US grants

9355680 Berger This is a three-year project, funded at $767,024, is designed to provide teacher enhancement and leadership skills for 30 middle school and 30 high school mathematics teachers in using NSF- supported standards-based mathematics materials in Minneapolis urban classrooms and in neighboring districts. The project is housed at the University of Minnesota-Twin Cities, with a subcontract in range of innovative materials with specific instruction preparation provided as the district completes instructional materials selection. The high school component will focus on the Interactive Mathematics Project, and the middle school component will participate with materials form several projects. Each year, a three-week summer program on content, instructional techniques, and classroom assessment. The summer program includes participant work with students two mornings each week. Academic year follow-up includes focused project staff visitations and support along with 6.5 days of sessions, organized in time blocks appropriate to teacher needs, each year. Cost sharing commitments of $249,359 include support form district, grantee institution, and other federal programs.

Mathematics departments in the nations's doctoral institutions represent a powerful resource for fulfilling important national needs. From improving quantitative literacy to training scientists and engineers, from connecting universities and industries to educating the next generation of mathematics teachers, these departments have the potential to make a real difference in areas that extend well beyond their own majors and boundaries. Universities have become vitally engaged in efforts to assess their role, exploring new thinking about scholarship, reform in curriculum and teaching and the relationship between undergraduate teaching, graduate training and research. Since nearly every student who enrolls in a university takes a mathematics course at some point, mathematics is strategically positioned--even obligated--to affect the role of the university and improve in teaching, learning and scholarship. This project will identify critical issues related to quality mathematical experiences for undergraduate students in doctoral institutions, set strategies for implementation of the recommendations of recent reform reports and develop a continuing agenda enabling mathematics departments to assure quality undergraduate and graduate programs at doctoral institutions. The project will highlight activities that work in departments across the country, engage both faculty and administrators in dialogues about programs and resource needs, and give departments the information and means necessary to replicate or adapt successful programs.

Eruptions generated by sunspots --- large concentrations of magnetic field on the visible surface of the Sun --- can have a number of dire impacts on Earth-based technological systems, crippling satellites and power grids, among many other things. With enough advance notice, the effects of these events can be mitigated, but predicting them is a real challenge. In current operational practice, this is accomplished by human forecasters examining images of the Sun, classifying each sunspot according to a taxonomy developed in the 1960s, and then using look-up tables of historical probabilities to say whether or not it will erupt in the next 24 hours. Recently, there has been a burst of work on machine-learning methods to automate this task. To date, the "features" used in these approaches have been predominately physics-based: the gradient of the magnetic field, for instance, or the sum of its strength over high-flux regions. The main objective of this 3-year research project is to leverage algorithms based on the fundamental mathematics of shape --- topology and geometry --- to improve the performance of these methods. The specific plan is to use these powerful techniques to extend the relevant feature set to include characteristics of the magnetic field that are based purely on the geometry and topology of 2D magnetogram images. Although this approach ignores the 3D structure of the full electromagnetic fields, it can enhance the predictive skill of machine learning systems. Preliminary results show clear topological changes emerging in magnetograms of a 2017 sunspot more than 24 hours before it flared, as well as clear improvements in the accuracy scores of a neural-net based flare prediction method that employs these shape-based features. Better predictions of solar flares could allow operators of power grids, airlines, communications satellites, and other critical infrastructure systems to mitigate the effects of these potentially destructive events. The broader impacts of this project also include the development of the STEM workforce through the training of graduate students at the University of Colorado at Boulder, as well as education and outreach, including community lectures, development of large-scale, online courses and public lecture series. The interdisciplinary nature of the project will deepen the contact between the fields of space weather, applied mathematics, and computer science, bringing researchers, students, and post-docs from both fields into productive new collaborations. The collaboration with the Space Weather Technology, Research, and Education Center at the University of Colorado offers unique opportunities to factor in real-world forecasting constraints and set the stage for transitioning the results to operational status.

For the first time, this 3-year research project would provide systematic quantitative measures of the shape of 2D magnetic structures in the Sun?s photosphere for the purposes of solar flare prediction. In a sense, this amounts to a mathematical systemization of the venerable McIntosh and Hale classification systems. This approach differs from current studies in the solar physics community that model the magnetic field-line structure: it uses topology to address the structure of two-dimensional sets. The analysis is restricted to photospheric magnetic field structures; the goal is to extract a formal characterization of shape that can be leveraged by machine learning to improve flare prediction. The considered addition of geometry into these methods by the project team is essential if they are to capture the full richness and physical relevance of the structures important in the evolution of a sunspot. This research project will point the way forward to a more robust set of features for machine-learning-based eruption prediction architectures. The research and EPO agenda of this project supports the Strategic Goals of the AGS Division in discovery, learning, diversity, and interdisciplinary research.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.