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Space as the new frontier

2008 University Scholar Marc Culler

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Marc Culler
“Far-reaching results that, so far as we know some 20 years later, cannot be obtained in any other way,” department head David Marker says of Marc Culler’s work with colleague Peter Shalen.

Photo: Roberta Dupuis-Devlin

The University Scholars Program, now in its 24th year, honors faculty members for superior research and teaching, along with great promise for future achievement. The award provides $10,000 a year for three years.

Marc Culler is a mathematician with manifold talents: computer savvy, a top-notch sailor and a man who knows his, well, manifolds, specifically "3-manifolds."

"Topology is geometry without measurement," says Culler of the shapes which are studied to five dimensions — sometimes higher. 

"It involves properties of geometric spaces that aren't detected by making measurements on a small scale, but instead reflect the global structure of the space. 

“The surface of a sphere and the surface of a donut are topologically different — it is not possible to distort one to make the same as the other because their global topological structures are different. The difference cannot be distinguished by measuring any particular part of the surface," explains Culler, professor of mathematics, statistics and computer science.

However, in the case of the hyperbolic 3-manifolds he studies, topological differences can be detected by global geometric measurements, such as the total volume of the space.

Culler has worked with UIC colleague Peter Shalen since both were at Rice University. They scored a breakthrough by associating an algebraic object with the geometric structure of a hyperbolic 3-manifold, then using the algebraic object to study topological properties of the manifold.

"This is an amazingly powerful construction that enabled them to obtain far-reaching results that, so far as we know some 20 years later, cannot be obtained in any other way," says David Marker, professor and head of mathematics, statistics and computer science. 

Culler's groundbreaking work in this field and in geometric group theory has made him a central figure in these areas of mathematics.

A native Californian, Culler did his undergraduate work at University of California at Santa Barbara and his graduate work at Berkeley. 

He considered computer science and physics as majors, but ultimately chose math. 

"I got derailed because I found I didn't know enough math to understand what they were doing in physics class, so I decided I should learn more math," he says.

Culler became a wizard with computers, writing his own programs and becoming adept in the hardware end as well. 

He was tutored by one of the legendary masters: his father, Glen Culler, a former professor of electrical engineering at Santa Barbara and a pioneering figure in the development of the Internet.  For his achievements, Glen Culler was awarded the National Medal of Technology in 1999 by President Bill Clinton.

Growing up in coastal Santa Barbara also led Culler to an interest in boating.

He has a Rhodes 19, a 19-foot sailboat he launches from Montrose Harbor and races regularly with friends twice a week during the summer, sailing to the water intake crib a few miles out.


Other 2008 University Scholars:

Questions with no answers: Yoshitaka Ishii

Living by design: Marcia Lausen

Digging down in the data mines: Bing Liu

The uneasy role of public intellectual: Walter Benn Michaels

In the laboratory, a fight against breast cancer: Hayat Onyuksel

Good teaching for better learning: Maria Varelas

Basic science, with an eye on the clinical: Richard Ye

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