3-Manifolds, Artin Groups, and Cubical Geometry

Research Foundation Of The City University Of New York (Lehman), Bronx NY

Investigators

Abstract

NSF/CBMS REGIONAL CONFERENCE IN THE MATHEMATICAL SCIENCES 3-MANIFOLDS, ARTIN GROUPS, AND CUBICAL GEOMETRY JUNE 13-17, 2011 CITY UNIVERSITY of NEW YORK GRADUATE CENTER Principal Lecturer: Daniel T. Wise Full Professor Department of Mathematics and Statistics McGill University The lectures of Professor Wise will treat a body of interrelated techniques and theorems in geometric group theory that are aimed at resolving certain long-standing open problems on groups arising in combinatorial group theory and 3-manifold topology. This work has matured during the past few years to a powerful and coherent theory that will reorient much of the research in this area. Recent achievements include a proof of Baumslag's 1967 conjecture that one-relator group with torsion are residually finite, a proof that Haken hyperbolic 3-manifolds are virtually fibered (unexpectedly confirming a conjecture of Thurston's from the 1980's), and the stunning realization that a large swath of the finitely presented groups arising in geometric group theory are actually virtually subgroups of right-angled Artin groups. It is now time to take stock of the developments here, and educate the next generation of researchers entering this area. Indeed, this subject has proven to be extremely fertile terrain and new researchers are certain to take things to the next level, both in simplifying and extending the reach of some of the proofs, and in striving for novel applications in neighboring fields. This conference will address a broad collection of students and young researchers, including both those with interest in 3-manifold topology and geometric group theory. Having the conference at the City University of New York Graduate Center will also contribute to the diversity of the participants. CUNY is the largest urban university in the United States and the Graduate Center is its central Ph.D. granting institution. A majority of CUNY students are self-identified as African-American or Hispanic and approximately 60% are female.