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Bonahon Named Simons Fellow

The mathematics department chair will study newly discovered connections between two fields of mathematics.

By Carl Marziali
July 8, 2014

With his Simons Fellowship, Bonahon will study new connections between two fields of mathematics: quantum topology and hyperbolic geometry.

With his Simons Fellowship, Bonahon will study new connections between two fields of mathematics: quantum topology and hyperbolic geometry.

A mathematician’s foundation will give a USC Dornsife math professor and 39 others the creative foundation they need: a year to think.

The Simons Foundation, established by noted mathematician, investor and 2014 USC honorary degree recipient James H. Simons, awards annual fellowships to leading researchers in mathematics, theoretical physics, neuroscience and other fields.

This year’s group of Simons Fellows includes Francis Bonahon, chair of mathematics and a member of the faculty since 1986.

Bonahon’s award will let him focus purely on research for the 2014-15 academic year. He will divide his time between USC and the Mathematical Sciences Research Institute in Berkeley, California, where he will be a Simons Visiting Professor.

“Having more time for research will be a big boost,” Bonahon said.

“The award to professor Francis Bonahon of a Simons Fellowship is further evidence of the high quality of mathematics at USC. One year ago, USC Professors Jason Fulman, Robert Guralnick and Ko Honda were Simons Fellows,” said Eric Friedlander, the department’s incoming chair.

“As one of the research stars of the department [as well as an excellent teacher and soon to be past-chair of the department], Professor Bonahon truly merits this highly competitive award.”

Bonahon will study newly discovered connections between two fields of mathematics: quantum topology and hyperbolic geometry.

The first is a discipline inspired by quantum physics for studying knots and links in various dimensions. Hyperbolic geometry is an equally strange world where streets never run straight or meet at right angles.

Neither field is exactly a household name, and Bonahon proudly admits that most pure math, like art, is done for its own sake. However, knot theory turns out to be a powerful model system for simplifying and understanding key geometric concepts in physics and chemistry, such as the orientation of certain molecules.

“Knot theory is to topology and geometry what the fruit fly is to the biologist,” he said.

And then there is the pure beauty of nonlinear geometry, as demonstrated on Bonahon’s website.

“One part that I enjoy is there are lots of pretty pictures,” he said.

Not surprisingly for a scholar of strange shapes and unimaginable dimensions, Bonahon served this year on the judging panel for the Wonderland Award, a popular USC competition to transform the life and writings of Lewis Carroll into new creative and scholarly work.

More information on this year’s Simons Fellows

More information on the fellowship program