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Geometric Topology Workshop at Calvin
June 21, 2007

An upcoming workshop at Calvin College, supported by a grant from the National Science Foundation and by the Calvin College Department of Mathematics and Statistics, will take on some rarefied topics.

The 24th annual Workshop in Geometric Topology will be held at Calvin on June 28-30 and is being organized by Calvin's Gerard Venema with the help of colleagues at the University of Wisconsin-Milwaukee, Oregon State, Colorado College and Brigham Young University.

Another particularly timely application of geometric topology is to assist in the placement of sensors that are used to secure our borders.

The featured speaker is Ian Agol of the University of Illinois at Chicago and the University of California at Berkeley. He will give a series of one-hour talks on the topology of 3-manifolds.

Seminars will be on such areas as finiteness of arithmetic hyperbolic reflection groups, the Singer conjecture for Coxeter groups, Fox re-embedding and Bing submanifolds, volumes of hyperbolic 3-manifolds and strategies for characterizing tame ends of manifolds.

While it might be a foreign language for many, Venema says the discipline of geometric topology has seen an explosion of new applications the past few years.

"Some of these applications involve the use of geometric topology in molecular biology and polymer chemistry," he says. "Small structures at the level of molecules turn out to be twisted and knotted in ways that were never imagined in the past and geometric topology is the tool that allows us to understand this kind of knotting and what effects it has on chemical and biological properties."

Another area of application of topology is to robotics. In fact two Calvin students are spending their summer working on applications of that kind (supervised by Calvin's Jim Turner and supported by an NSF grant on which Turner and Venema are the principal investigators on the project).

Another particularly timely application of geometric topology, says Venema, is to assist in the placement of sensors that are used to secure our borders.

The upcoming workshop will give the almost 50 attendees a chance to not only dive deeply into three days of study in such areas, but also the chance to catch up with old friends.

"This event is called a workshop because it is a little different from a standard academic research conference," he says. "It is organized by a group of us who are doing mathematical research at places that are not known as centers of such research. While Calvin provides a great deal of support for faculty members who do research, it is still challenging for a Calvin faculty member to maintain an ongoing program of research that competes with those of mathematicians at major research universities. In particular, at a place like Calvin we do not have the opportunity to participate in regular research seminars in which researchers pass through and talk about the latest research results that have not yet been published."

The Workshops in Geometric Topology, he says, attempt to address this challenge by bringing in one speaker who gives a substantial introduction to an area of research.

"We try to find speakers who are doing some of the most exciting and influential work in the field and have them talk about their latest results," Venema says.

Students, including Calvin students Venema says, benefit from the annual event as well. This year, for example, nearly one-third of the registered participants are students, including Calvin's Laura Feys who will go to Notre Dame in the fall for graduate school and last summer worked with Venema on an NSF-funded research project. Two other Calvin students will attend the workshop: Justin Kenderes and Timothy Ferdinands. And there are two additional Calvin graduates on the list of attendees: John Engbers (a current graduate student) and Bob Daverman.

"Laura Feys is doing a substantial part of the organization," says Venema, "especially the registration of participants. It is unusual for an undergraduate to be capable of assuming so much responsibility, and we are very grateful for her work."

That partnering with students is a hallmark of the Calvin mathematics department, Venema says, adding that doing mathematics at a Christian college is particularly meaningful for Calvin professors and their students.

"The discipline of mathematics is unique," he says, "in that it is both one of the liberal arts and one of the sciences. God has created us with an ability to recognize, understand, and appreciate certain kinds of abstract patterns. Most mathematicians, geometric topologists, in particular, are motivated by a desire to understand and explore mathematical relationships. For them the study of mathematics is part of our cultural mandate to explore and understand the world in which we live."

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