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Proposals are sought for focused workshops to be held at AIM in Palo Alto.

Please see the proposal guide for details and an online application form.

AIM also seeks proposals for a new program called SQuaREs, which involves a small group of researchers working at AIM for one week. For more information visit the SQuaREs page.

For both programs the deadline for proposals is November 1, 2008.

The American Institute of Mathematics (AIM) celebrated its 100^th workshop on Monday, May 12, 2008 with the beginning of the workshop, Ferroelectric Phenomena in Soft Matter Systems. "We are excited to reach this milestone," said Director Brian Conrey. "During the past six years, AIM has developed a workshop style that has been successful at bringing together different groups of researchers to share ideas and new developments in their fields toward a common goal."

The goal of the 100^th workshop is to overcome present obstacles in the modeling and simulation of liquid crystal systems and other ferroelectric phenomena. Specifically, researchers hope to better understand the process of switching, both for a liquid-like ferroelectric model and a solid material with liquid features. The organizers have brought together a cross-disciplinary group of participants to tackle this issue. Experimental and theoretical physicists are working with analytical and computational mathematicians to explore new techniques for modeling these unusual but ubiquitous systems.

A new mathematical object was revealed on March 12, 2008, during a lecture at the American Institute of Mathematics (AIM). Two researchers from the University of Bristol exhibited the first example of a third degree transcendental L-function. These L-functions encode deep underlying connections between many different areas of mathematics.

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The news caused excitement at the AIM workshop attended by 25 of the world's leading analytic number theorists. The work is a joint project between graduate student Ce Bian and his adviser, Andrew Booker. Booker commented that, "This work was made possible by a combination of theoretical advances and the power of modern computers." During his lecture, Bian reported that it took approximately 10,000 hours of computer time to produce his initial results.

"This breakthrough opens a door to the study of higher degree L-functions," said Dennis Hejhal, Professor of Mathematics at the University of Minnesota and Uppsala University. "It's a big advance" added Harold Stark of the University of California, San Diego, who, 30 years ago was the first to accurately calculate second degree transcendental L-functions. "I thought we were years away from doing this. The geometry of what you have to do and the scale of the computation are orders of magnitude harder."

There are two types of L-functions: algebraic and transcendental, and these are classified according to their degree. The Riemann zeta-function is the grand-daddy of all L-functions. It holds the secret to how the prime numbers are distributed, and is a first degree algebraic L-function. The Riemann Hypothesis, announced in 1859 and today the most important of all unsolved math problems, is an example of something that should be true for every L-function. Michael Rubinstein from the University of Waterloo, a participant at the workshop, quickly tested and confirmed the Riemann Hypothesis for the first few zeroes of this newly minted L-function. Rubinstein, along with William Stein of the University of Washington, will direct a new initiative to systematically chart L-functions; this project has been recommended for funding by the National Science Foundation. "The techniques developed by Bian and Booker open up whole new possibilities for experimenting with these powerful and mysterious functions and are a key step towards making our group project a success." Rubinstein added.

"It's a big step toward our understanding the 'world of L,' which is where most of the secrets of number theory are kept." said Brian Conrey, Director of AIM.

Dorian Goldfeld, Professor of Mathematics at Columbia University summarized the excitement, saying "This discovery is analogous to finding planets in remote solar systems. We know they are out there, but the problem is to detect them and determine what they look like. It gives us a glimpse of new worlds."

AIM is pleased to announce that Travis Schedler is the recipient of the 2008 AIM Five-Year Fellowship. Travis will receive his PhD from the University of Chicago this year under the direction of Professor Victor Ginzburg. His area of specialization is noncommutative algebraic geometry. In his thesis, he defines and applies a new formalism of differential operators for associative algebras. In other work, he computes Hochschild and cyclic homology of algebras associated to quivers. He has already written or co-authored 11 papers, including one that has appeared in the Journal of the American Mathematical Society and another in the Duke Mathematical Journal.

Travis received his A.B. from Harvard (summa cum laude) in 2002 and spent a year of his graduate studies at the Ecole Normale Superieure as a visiting student.

The other finalists for the Fellowship were Lionel Levine of the University of California, Berkeley, and Sarah Koch of Cornell University.

AIM's "castle," modeled after the majestic Moorish Alhambra palace in Granada, Spain, plans to host the first of its focused research workshops in Fall, 2010.

The 167,000 sq.ft. facility will incorporate a large, open meeting area, seminar rooms, a dining hall, and accommodation for visitors to the Institute. In addition, it will house the AIM library comprising a comprehensive mathematical working library, AIM's unique reprint collection, as well as other special collections.

Participating in the groundbreaking ceremony were the Honorable Jerry McNerney, 11th Congressional District of California and Mayor Steve Tate of Morgan Hill. Also present was Mr Steve Sorenson, co-founder and President of the AIM Board of Trustees, and Professor Gerald Alexanderson of Santa Clara University and Chairman of the Board of Trustees.

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Mathematicians have mapped the inner workings of one of the most complicated structures ever studied: the object known as the exceptional Lie group E₈. This achievement is significant both as an advance in basic knowledge and because of the many connections between E₈ and other areas, including string theory and geometry. The magnitude of the calculation is staggering: the answer, if written out in tiny print, would cover an area the size of Manhattan. Mathematicians are known for their solitary work style, but the assault on E₈ is part of a large project bringing together 18 mathematicians from the U.S. and Europe for an intensive four-year collaboration.

"This is exciting," said Peter Sarnak, Eugene Higgins Professor of Mathematics at Princeton University (not affiliated with the project). "Understanding and classifying the representations of Lie Groups has been critical to understanding phenomena in many different areas of mathematics and science including algebra, geometry, number theory, Physics and Chemistry. This project will be valuable for future mathematicians and scientists."

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