Speakers:
André Joyal - Université du Québec à Montréal
Ieke Moerdijk - Universiteit Utrecht
Bertrand Toën - Université Paul Sabatier, Toulouse

http://www.crm.cat/ACQuasiCategories/

Expanders are highly-connected sparse graphs widely used in Computer Science, in areas ranging from parallel computation to complexity theory and cryptography. 2008 marks two important anniversaries in the development of the theory of expander graphs: the field was born 35 years ago, in 1973, when, following Pinsker’s observation that random regular graphs are expanders, Margulis gave the first explicit construction using Kazhdan’s Property T; fifteen years later, in 1988, Margulis, Lubotzky, Phillips and Sarnak constructed Ramanujan graphs (optimal expanders form spectral point of view) using deep results from the theory of automorphic forms. After a period of steady development, the theory of expander graphs has undergone explosive growth over the past several years: on the one hand, a number of long-standing problems have been resolved; on the other hand, several completely new and unexpected lines of development have emerged. Currently expanders are at the center of a great deal of research involving mutually beneficial interactions between computer science, number theory, combinatorics, group theory, and geometry. The workshop will bring together researchers from these fields to survey the progress made, outline the challenges ahead, and generate further collaborations.

http://www.ipam.ucla.edu/programs/eg2008/

Featured Topics: Pseudodifferential calculi, index theory and L²-cohomology on singular and non-compact spaces; scattering of waves by singularities.

http://www.hausdorff-center.uni-bonn.de/pde/

This workshop will focus on recent work by a number of distinguished researchers in Hodge theory and algebraic geometry. It is also an opportunity to recognize Mark Green’s contributions to Mathematics.

Dr. Green obtained his PhD from Princeton, where his thesis adviser was Phillip Griffiths. After teaching at Berkeley and MIT, he came to UCLA as an Assistant Professor in 1975. Dr. Green's research has taken him into several areas of mathematics--several complex variables, differential geometry, commutative algebra, Hodge theory and algebraic geometry. He received an Alfred P. Sloan fellowship and was an invited speaker at the International Congress of Mathematicians in Berlin.

Along with Eitan Tadmor, he was one of IPAM's Founding Co-Directors. He has been Director of IPAM since 2002 and is responsible for its remarkable success. It is fair to say that IPAM, under Mark's guidance, has positively and significantly influenced the path that research in mathematical science and its applications to technology has taken the past decade.

http://www.ipam.ucla.edu/programs/HT2008/

Nonequilibrium quantum field theory is needed to understand pressing topical phenomena in high-energy physics related to collisions of heavy nuclei ("Little Bangs'') and early universe cosmology ("Big Bang''). Out-of-equilibrium dynamics is an area which has seen substantially increased theoretical activity in recent years. High-energy particle physicists as well as cosmologists are starting to work with very similar techniques and sometimes even on the same underlying nonequilibrium phenomena. Very similar theoretical issues also arise in other areas, such as ultra-cold quantum gases.

The goal of this program is to bring together physicists working on different aspects and applications of nonequilibrium quantum field theory, in order to promote cross-fertilization between different areas and to stimulate theoretical advances which can help to address the challenges posed by present-day experiments.

http://www.kitp.ucsb.edu/activities/auto/?id=834

Many computer vision and image processing problems can be formulated as a discrete optimization problem. Among several available optimization schemes, combinatorial min-cut algorithms on graphs emerged as an increasingly useful tool for performing these optimizations. This success is mainly twofold. First, in some cases graph cuts produce globally optimal solutions. More generally, there are iterative graph-cut based techniques that produce provably good local optimizer that are also high-quality solutions in practice. Second, graph-cuts allow for a geometric interpretation. Provided some assumptions, a cut on a graph can be seen as a hypersurface in N-D space embedding the corresponding graph. This point of view has been very fruitful in computer vision for computing hypersurfaces. Besides, graph-cut approaches have been shown to be very fast in practice. Finally some links between graph-cuts, message passing and belief propagation have been recently shown.

The aim of the workshop is to put together mathematicians and computer scientists interested in graph cuts (or network flows) as a framework bridging the gap between important classes of discrete and continuous optimization problems. The workshop will cover both theoretical/mathematical aspects, as well as algorithms and applications in computer vision and image processing.

http://www.ipam.ucla.edu/programs/gc2008/

http://www.him.uni-bonn.de/semester-w-0708-workshops