American Institute of Mathematics 360 Portage Ave Palo Alto, CA 94306-2244 Contact Information Directions to AIM

AIM announces a new online tool for creating and maintaining list of unsolved mathematics problems. This tool has the potential to change mathematics research by bringing a wider range of people and expertise in contact with research questions. The initial problem lists are being released on the same day as a worldwide celebration of the 150th anniversary of the most important problem in mathematics: the Riemann Hypothesis. Read more....

Go to the Problem List site, or the RH Day schedule.

Mathematicians from North America, Europe, Australia, and South America have resolved the first one trillion cases of an ancient mathematics problem. The advance was made possible by a clever technique for multiplying large numbers. The numbers involved are so enormous that if their digits were written out by hand they would stretch to the moon and back. The biggest challenge was that these numbers could not even fit into the main memory of the available computers, so the researchers had to make extensive use of the computers' hard drives.
Read more... Versión en español

The seven NSF Mathematical Sciences Research Institutes announce the creation of 45 new two-year positions for young, highly-trained mathematical scientists across the country. In addition to furthering research in all areas of the mathematical sciences, these positions will allow recent PhDs to teach at community colleges and other higher-education institutions or to participate in projects tied to business and industry. This new initiative is a result of a partnership among the National Science Foundation-supported mathematics institutes. Read more...

AIM is pleased to announce that Melanie Matchett Wood and Kirsten Graham Wickelgren have been named the 2009 AIM Five-Year Fellows.

Read the full story.

Update, January 26: Soundararajan has proven the original version of the QUE conjecture, completing the missing step in Lindenstrauss' program for noncompact arithmetic surfaces. His paper is available on the ArXiv.

October 10, 2008: In a seminar co-organized by Stanford University and the American Institute of Mathematics, Soundararajan announced that he and Roman Holowinsky have proven a significant version of the quantum unique ergodicity (QUE) conjecture. "This is one of the best theorems of the year," said Peter Sarnak, a mathematician from Princeton who along with Zeev Rudnick from the University of Tel Aviv formulated the conjecture fifteen years ago in an effort to understand the connections between classical and quantum physics. "I was aware that Soundararajan and Holowinsky were both attacking QUE using different techniques and was astounded to find that their methods miraculously combined to completely solve the problem," said Sarnak. Both approaches come from number theory, an area of pure mathematics which recently has been found to have surprising connections to physics.

The motivation behind the problem is to understand how waves are influenced by the geometry of their enclosure. Imagine sound waves in a concert hall. In a well-designed concert hall you can hear every note from every seat. The sound waves spread out uniformly and evenly. At the opposite extreme are "whispering galleries" where sound concentrates in a small area.

The mathematical world is populated by all kinds of shapes, some of which are easy to picture, like spheres and donuts, and others which are constructed from abstract mathematics. All of these shapes have waves associated with them. Soundararajan and Holowinsky showed that for certain shapes that come from number theory, the waves always spread out evenly. For these shapes there are no "whispering galleries."		Uniformly distributed points in a fundamental domain for SL(2,Z). Image courtesy of Fredrik Stromberg

Read more..., including articles by Peter Sarnak and Zeev Rudnick.