February 6, 2012
to February 10, 2012
Organizers: Emmanuel Breuillard* (Universite Paris-Sud, Orsay), Alexander Gamburd (CUNY Graduate Center), Jordan Ellenberg (University of Wisconsin - Madison), Emmanuel Kowalski (ETH Zurich), Hee Oh (Brown University)
The workshop will focus on recent developments concerning various quantitative aspects of "thin groups". These are discrete subgroups of semisimple Lie groups which are both « big » (i.e. Zariski dense) and « small » (i.e. of infinite co-volume). This dual nature leads to many intricate questions. Over the past few years, many new ideas and techniques, arising in particular from arithmetic combinatorics, have been involved in the study of such groups, leading for instance to far-reaching generalizations of the strong approximation theorem in which congruence quotients are shown to exhibit a spectral gap (super-strong approximation).
Simultaneously and sometimes surprisingly, the study of thin groups turns out to be of fundamental importance in a variety of subjects, including equidistribution of homogeneous flows and lattice points counting problems, dynamics on Teichmuller space, the Bourgain-Gamburd-Sarnak sieve in orbit, and arithmetic or geometric properties of certain types of monodromy groups and coverings. The workshop will gather a variety of experts from group theory, number theory, ergodic theory and harmonic analysis to present the accomplishments to date to a broad audience and discuss directions for further study.
October 25, 2010
to October 29, 2010
Organizers: Mike Hill (University of Virginia), Michael Hopkins (Harvard University), and Douglas C. Ravanel* (University of Rochester)
This workshop will focus on the ideas surrounding the recent solution to the Arf-Kervaire invariant problem in stable homotopy theory by Mike Hill, Mike Hopkins and Doug Ravenel. There will be talks on relevant aspects of equivariant stable homotopy theory, including the norm functor and the slice tower. The pertinent parts of chromatic homotopy theory will be covered including formal groups and formal $A$-modules, the Hopkins-Miller theorem, finite subgroups of Morava stabilizer groups and Ravenel's 1978 solution to the analogous problem at primes bigger than 3. There will also be several talks by the organizers giving a detailed account of the proof of the main theorem. Finally there will be a discussion of the questions raised by the unexpected statement of the theorem.
September 14, 2009
to September 18, 2009
Organizers: Mihalis Dafermos (University of Cambridge) and Igor Rodnianski* (Princeton)
The mathematical study of the dynamics of the Einstein equations forms a central part of both partial differential equations and geometry, and is intimately related to our current physical understanding of gravitational collapse.
June 9, 2008
to June 13, 2008
Organizers: Helmut Hofer, Michael Hutchings, Peter Kronheimer, Tom Mrowka and Cliff Taubes
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.
April 16, 2007
to April 20, 2007
Organizers: Alessio Corti, Jean-Pierre Demailly, János Kollár, Shigefumi Mori
The workshop will concentrate on the recent advances on canonical and minimal models of algebraic varieties. We plan to study the proofs, survey applications and related results and chart future directions for research.Two algebraic varieties are said to be ...
December 9, 2004
to December 13, 2004
Organizers: Gunnar Carlsson, Susan Holmes, Persi Diaconis
Complex data sets lying in high-dimensional spaces are by now a commonplace occurrence in many parts of science. There are many sources for this kind of data, including biology (genetic networks, phylogenetic trees, food webs, protein folding data, and neural ...
December 6, 1999
to December 10, 1999
Organizers: Brian Conrad, Jean-Marc Fontaine, Barry Mazur, Ken Ribet (chair), Richard Taylor
