This Week at AIM: October 14-18, 2019
This week’s workshop Deep learning and partial differential equations is devoted to the interplay between the two subjects. Read more…
- Deep learning and partial differential equations
October 14-18, 2019
- Rigidity and flexibility of microstructures
November 4-8, 2019
- Geometric realizations of Jacquet-Langlands correspondences
November 11-15, 2019
- Interactive assessments in open source textbooks
December 9-13, 2019
- K-stability and related topics
January 6-10, 2020
- All Upcoming Workshops
- Deep learning and partial differential equations
Presentation of the 2019 Alexanderson Award
The American Institute of Mathematics has awarded the second annual Alexanderson Award. This award is given in honor of Gerald Alexanderson, Professor of Mathematics at Santa Clara University and founding chair of AIM’s Board of Trustees. The Alexanderson Award recognizes outstanding research articles arising from AIM research activities that have been published within the past three years.
Receiving this year’s award are Paul Bruillard, Siu-Hung Ng, Eric C. Rowell, and Zhenghan Wang for their paper “Rank-finiteness for modular categories” published in the Journal of the American Mathematics Society in 2016. The award was presented at the Alexanderson Award Ceremony and Lecture on the evening of October 4, 2019, in the Recital Hall of Santa Clara University. The lecture was given by Jordan Ellenberg, engaging author of the book How Not to Be Wrong.
Exploring the Mathematical Universe
A team of more than 80 mathematicians from 12 countries is charting the terrain of rich, new mathematical worlds, and sharing their discoveries on the Web. The “L-functions and Modular Forms Database (www.LMFDB.org)” started more than 5 years ago with funding to AIM from the National Science Foundation. The project has just announced its official release, providing a new and powerful tool for students and researchers in several areas of mathematics. Read more…
It is human nature to try to classify things–that is, to sort them into organized types. Many of the central problems in mathematics are problems of classification of various types of related mathematical objects. The classification of finite groups, for example, was a landmark accomplishment of the last century, and the classification of manifolds continues to challenge topologists.
The AIM SQuaRE “The global dynamics of Thurston’s pullback map” with participants, William Floyd, Gregory Kelsey, Sarah Koch, Russell Lodge, Walter Parry, and Kevin Pilgrim, sought to classify the particular dynamical systems known as nearly Euclidean maps. The late mathematician William Thurston studied—among many other things—dynamical systems resulting from repeated iteration of a mapping from the two-dimensional sphere to itself. Applying a mapping over and over again, and watching what happens to a point, can produce fantastic and beautiful patterns that are intriguing to mathematicians. He focused on some particularly nice ones, the Euclidean Thurston maps, which are fully understood and classified using the tools and concepts of linear algebra. But much less well-understood is the much larger family of nearly Euclidean Thurston (NET) maps—the very simplest generalizations of the Euclidean ones. These are the dynamical systems studied by this SQuaRE.
It turned out that the tools they used borrowed from an amazing range of areas of mathematics. Moreover, it also turned out that the classification of NET maps could be made practical in the sense that computer algorithms could be developed and used to systematically list and study examples. The elaborate web site produced by the participants shows the effectiveness of the algorithms that they developed for answering many basic questions. Read more…
Math Teachers’ Circle Network Named as Partner in 100Kin10
NEW YORK, Feb. 17, 2016 — 100Kin10, a national network coordinating and accelerating efforts to bring 100,000 new excellent science, technology, engineering, and math (STEM) teachers into schools by 2021, announced today that the Math Teachers’ Circle Network has been accepted as a partner. The Math Teachers’ Circle (MTC) Network is one of 49 new partners to join a network of now over 280 of the country’s top businesses, nonprofits, foundations and academic institutions to help achieve the goal of 100,000 excellent STEM teachers.
Established at AIM in 2006, Math Teachers’ Circles bring teachers together with mathematicians in a professional environment for mathematical problem solving. The goals are to engage teachers in thinking deeply about mathematics and to build a community of mathematics professionals dedicated to improving education for all students. The MTC Network helps start new MTCs across the U.S. and provides organizational resources to support their activities. As part of 100Kin10, the Math Teachers’ Circle Network has committed to reach 6,000 teachers and their 600,000 students by growing its national network from 80 to 300 Math Teachers’ Circles by 2020. Read more…
Math in the Quest for Sustainable Agriculture
Just sixty miles from AIM is the Pajaro Valley, one of the richest agricultural regions of the world, an ideal location for fresh berries, vegetables, and flowers. But the valley’s water source is a confined aquifer that is slowly being depleted. With California now in the third year of a serious drought, the problem is even more acute. There is hope, however, that the overdraft can be remedied and the water usage brought back into balance by using a combination of strategies. Mathematically, the problem can be modeled as a large constrained optimization problem, which is exactly what an AIM workshop began working on a little over two years ago.