Invariants in Low Dimensional Geometry conference

Cuny College Of Staten Island, Staten Island NY

Investigators

Abstract

A conference, "Invariants in Low Dimensional Geometry," will be held on August 10-14, 2015, at Gazi University in Ankara, Turkey. Geometric structures on 3-manifolds have been a central focus of topology since the seminal work of Thurston in the 1970s. Significant advances, such as Perelman's proof of Thurston's Geometrization Conjecture and the recent proof of the Virtual Fibering Conjecture, have generated enormous interest in geometric topology. Separately, a new research area called quantum topology was ushered in by discoveries in the 1980s of many new quantum topological invariants. The major aims of this conference, like the major research aims of geometric and quantum topology, are to advance our understanding of how geometric structures on surfaces and 3-manifolds, and the geometric, topological and quantum invariants are related to each other. Conference speakers from institutions from the United States, Turkey and other countries will describe the leading current developments and trends in the active mathematical fields surrounding geometric and quantum topology. Another important goal is to provide graduate students and young researchers with a coherent view of this wide-ranging and active research area. The week before the conference will be dedicated to introductory seminars and workshops for graduate students, recent Ph.D.'s and researchers who are new to this area. Research on various topics in geometric topology, geometry of surfaces and quantum topology has proceeded at a remarkable pace, in a multitude of directions, and using diverse methods of study and application. This conference will gather a group of the world's leading researchers in these fields, many of whom have pioneered these approaches. Topics will include: Quantum hyperbolic geometry, triangulations and angle structures on 3-manifolds, geometry of surfaces and mapping class groups, character varieties and arithmetic invariants, colored Jones polynomials and quantum invariants of 3-manifolds. Many important open problems in these fields relate these different points of view, and require techniques from distinct research areas. This conference will focus on new developments that highlight connections between these fields, and help create new avenues for collaboration. Conference website: http://www.math.csi.cuny.edu/abhijit/turkey2015