Recently the common geometry of tensors arising in questions in computational complexity, statistical learning theory, signal processing, scientific data analysis have been looked at from a unified perspective. The underlying geometry and representation theory will be covered in this workshop with and eye towards problems such as the complexity of matrix multiplication, Valiant's approach to P=NP, measures of entanglement in quantum information theory, graphicalmodels in statistical learning theory, independent component analysis and other multilinear data analytic techniques.

This conference, jointly funded by MSRI and the Clay Mathematics Institute, will bring together researchers on many aspects of the arithmetic applications of modular (and automorphic) forms. This is currently a very broad and very active subject. Our intention is to encourage interaction between those working in different sub-disciplines. To this end it is hoped to limit lectures to 4 hours a
day, allowing plenty of time for informal interactions. On Tuesday, July 1, 2008 at 7pm there will be a dinner to honor Ken Ribet on his 60th birthday.

In recent years,a noteworthy and very fruitful interlacing of number theory and physics has emerged.As indicated in the September 2007 issue of the AMS Notices,for example,a new journal "Communications in Number Theory and Physics " has just been launched to follow significant interactions and dynamics between these two fields.Several books are now available,in addition to an array of conference and workshop activity,that accent this fortunate merger of "pure"mathematics and physical theory-with applications that range from field theory (conformal and topological),extended objects (strings and branes)cosmology and black hole physics, to Bose-Einstein condensation and the theory of relativistic gases.

The MSRI-UP is a comprehensive program for undergraduates that aims at increasing the number of students from underrepresented groups in mathematics graduate programs. MSRI-UP includes summer research opportunities, mentoring, workshops on the graduate school application process, and follow-up support.

This workshop will concentrate on recently discovered relationships between Seiberg-Witten theory and contact geometry on 3 dimensional manifolds. One consequence of these relationships is a proof of the Weinstein conjecture in dimension 3. Another is an isomorphism between the Seiberg-Witten Floer (co)homology and embedded contact homology, the latter a form of Floer homology that was defined by Michael Hutchings. The over arching plan is to introduce the salient features of both the contact geometry side of the story and the Seiberg-Witten side, and then discuss how they are related.

For over two decades, the teaching and learning of algebra has been a focus of mathematics education at the precollege level. This workshop will examine issues in algebra education at two critical points in the continuum from elementary school to undergraduate studies: at the transitions from arithmetic to algebra and from high school to university. In addition, the workshop will involve participants in discussions about various ways to structure an algebra curriculum across the entire K-12 curriculum.

Exterior Differential Systems and the Method of Equivalence surveys state of the art applications of these techniques and celebrates the contributions of Robby Gardner to our current understanding of Cartan’s powerful machinery.

We hope that you will join us for the Anniversary celebration at the end of January 2008. As befitting the broad mission of the Institute these will include not only mathematical exposition by some of the leaders who have been and are about to be involved with MSRI programs, but also an opening program of mathematics and music and some panels to reflect on the most important directions for future development.