This Week at AIM: September 17-21, 2018
The topic of this week’s workshop is the mathematics of Boltzmann machines. Since their debut in the context of deep learning, Boltzmann machines have been studied intensively, with significant leaps over the past six years. Read more…
Call for Proposals: Due November 1
Applications are now being accepted for AIM Workshops and SQuaREs to be held during the 2019-20 academic year. The deadline for submission is November 1, 2018. Decisions will be announced by mid-January. Proposals must be submitted using the on-line forms:
AIM Announces the First Alexanderson Award
The American Institute of Mathematics (AIM) is pleased to announce the first annual Alexanderson Award. The 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 the first award are Alexei Borodin, Ivan Corwin, and Patrik Ferrari for their article Free energy fluctuations for directed polymers in random media in 1+1 dimensions, Communications in Pure and Applied Mathematics, 67 (2014), 1129-1214. This work began during the October 2011 AIM workshop “The Kardar-Parisi-Zhang equation and universality class”. Read more…
- Boltzmann machines
September 17-21, 2018
- Discrete geometry and automorphic forms
September 24-28, 2018
- Categorified Hecke algebras, link homology, and Hilbert schemes
October 1-5, 2018
- Modeling the eye as a window on the body
October 15-19, 2018
- Sarnak’s conjecture
December 10-14, 2018
- All Upcoming Workshops
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.