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April 25, 2017

Conference on Low-Dimensional Topology and Geometry

Kirkland Hall on a warm spring day. (Vanderbilt University/Jenny Mandeville)

The Department of Mathematics hosted the Conference on Low-Dimensional Topology and Geometry from May 15 to 19, 2017. Held in conjunction with the 32nd Annual Shanks Lecture, the conference focused on the close interrelationships between geometry and topology in low dimensions, such as in the study of surfaces and three-dimensional manifolds (3-manifolds). Emphasis was on the powerful negative curvature and combinatorial techniques that are driving much of the current research in this area.

The inherent connection between geometry and topology pervaded William Thurston’s revolutionary work in the 1980s that refocused the field of 3-manifold topology around a handful of bold geometric conjectures. By drawing on the work of many mathematicians and incorporating wide-ranging ideas from ergodic theory, combinatorial geometry, hyperbolic geometry, and group theory, this new paradigm in 3-manifold topology has recently culminated in the proof of Thurston’s virtual fibering conjecture.

The Vanderbilt conference revisited some of the ideas that emerged from these developments and examined the tools and techniques that are now being refined and applied to broader contexts. Topics included hyperbolic 3-manifolds, moduli spaces of Riemann surfaces, the geometry and topology of curves on surfaces, surface bundles, Gromov-hyperbolic simplicial complexes, CAT(0) cube complexes, and many others.

This year’s featured Shanks Lecturer was Professor Ian Agol of the University of California, Berkeley. The title of his lecture was “Flow and Yamada Polynomials of Cubic Graphs.” Agol received the 2016 Breakthrough Prize in Mathematics for his contributions to low-dimensional topology and geometric group theory, including work on the solutions of the tameness, virtual Haken, and virtual fibering conjectures. Agol is also the recipient of the 2013 Oswald Veblen Prize in Geometry and the 2009 Clay Research Award.

The prestigious Shanks Lecture Series is organized annually by the Department of Mathematics of Vanderbilt University, honoring Baylis and Olivia Shanks. The late Professor Baylis Shanks was chairman of the Department from 1955 through 1969. A list of previous Shanks Conferences and Lecturers can be found here.

More information on the Conference on Low-Dimensional Topology and Geometry is available on the conference web site.