College of Science

Math Department hosts geometry and topology conference

Geometry and topology faculty and students and faculty from around the southwestern United States converged on UT Arlington for the 49th Texas Geometry and Topology Conference on February 8-10.

The conference featured invited talks from speakers representing universities from around the United States as well as from Germany.

The UT Arlington Department of Mathematics and Texas Christian University were hosts for the event, held every fall and spring since its founding in 1989. The conference was supported by a grant from the National Science Foundation. Conference organizers from UT Arlington included Ruth Gornet, associate professor, who served as organizing committee chair; Barbara Shipman, associate professor; Dimitar Grantcharov, assistant professor; and Gaik Ambartsoumian, assistant professor.

"The conference was a great success," Shipman said. "About 50 people attended, including graduate students from UT Arlington and other places. The longer, one-hour talks allowed for more depth into the mathematical ideas, context, history, and applications, as well as interactions with the audience. It was a focused, dedicated group, and the topics of the presentations complemented each other very well. People were very engaged in the presentations, and they asked good questions that added insight to the discussions."

Topology is the study of geometric properties and spatial relations unaffected by the continuous change of shape or size of figures.

Shipman gave the final talk of the Saturday session, "New Perspectives on Classic Definitions," which highlighted active learning materials that ask and resolve fundamental questions about definitions.

"The talk brought out subtle yet startling points and new ways of thinking about classic definitions that mathematicians use and teach every day," Shipman said. "I very much enjoyed presenting the ideas to this audience of prominent mathematicians."

Joseph Wolf, mathematics professor at the University of California at Berkeley, gave the featured research talk on Friday evening, "Representations of nilpotent Lie groups". Wolf is an expert in Lie groups and homogeneous spaces, harmonic analysis, complex manifolds and Riemannian geometry. He has been nominated twice as a Miller Research Professor. He is an Alfred P. Sloan Research Fellow and a recipient of numerous international honorary

degree and prizes including the Médaille de l'Université de Liège, Profesor Honorario of Universidad Nacional de Córdoba, and the Alexander von Humboldt Prize. His 11 books have been translated into numerous languages worldwide. One, "Spaces of Constant Curvature", just had its sixth edition published by the American Mathematical Society.

Other invited speakers and their topics included Paul Bracken, UT Pan American, "A Geometric Approach to the Study of Nonlinear Partial Differential Equations"; Gueo Grantcharov, Florida International University, "On the HKT geometry"; Sean Paul, University of Wisconsin at Madison, "From Semi-Stable Pairs to K-energy maps of Algebraic Manifolds"; Daniel Ramras, New Mexico State University, "Stable representation theory and families of flat bundles"; Julie Rowlett, Max Planck Institute for Mathematics in Bonn, Germany, "Dynamics of the Geodesic Flow on Negatively Curved Complete Manifolds"; and Stephan Stolz, University of Notre Dame, "Field theories and cohomology".
Many participants submitted posters detailing their research, which were displayed throughout the conference.

The Texas Geometry and Topology Conference is dedicated to the enhancement of both the educational and the research atmosphere of the community of geometers and topologists in Texas and surrounding states. The conference has three specific goals: (1) bringing researchers of national and international stature to the region to discuss their research and to interact with mathematicians from Texas and surrounding states; (2) making it possible for the community of geometers and topologists from Texas and surrounding states to meet and share mathematics on a regular basis, which both stimulates individual research and generates productive cooperative efforts between schools; (3) encouraging the development of graduate students and young faculty in geometry and topology.

The original Texas Geometry and Topology Conference confined itself primarily to Texas universities and attracted about 40 participants. Attendance at subsequent conferences has grown steadily. In 1991, the scope of the conference was permanently expanded to include essentially all universities and colleges in Texas, Arkansas, Louisiana, New Mexico, and Oklahoma. Since 1994, fall conferences have been national events, attracting participants from around the country.

Posted February 27, 2013