January 26, 2010

Mathematician who wrote fundamental proof to be U of C prof

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Ngô Bao Châu, who helped unite two fields of mathematics, accepted a position at the University Monday, and will start next September.

Ngô’s proof of the famous Langlands’ lemma, earned praise from TIME magazine, which called the achievement one of the top 10 scientific discoveries of 2009.

“He has made transformational achievements,” said Peter Constantin, chair of the Mathematics Department, referring to the lemma. “His work was not just a curiosity of a small, singular difficult problem, but a bridge between two fields.”

Langlands’s theories drew connections between algebra and analysis. “Often in math, you have two ways of expressing the same thing,” Constantin said. “It creates a set of correspondences, like a dictionary.” This relationship allows information to be transported from one set of mathematical objects to another, but is hinged on what Langlands called “the fundamental lemma.”

Lemmas are usually smaller theorems mathematicians use as intermediate steps in their overall proof, but the Langlands lemma stumped mathematicians for 30 years. “In this case, the lemma turned out to be one of the hardest parts,” said mathematics professor Robert Kottwitz, who also worked on the problem.

The lemma was a core piece of mathematician Robert Langlands’s work, and many thought it could be solved relatively easily. “I thought at the time I should be able to prove it: It was an elementary-sounding lemma, so it should have an elementary proof,” said Langlands, a former professor at the Institute for Advanced Study in Princeton, NJ.

Langlands, Kottwitz, and others proved some specific cases of the lemma, but Ngô’s “beautiful” proof solved the general problem. “You have to prove two things are equal without ever knowing explicitly what they are,” Kottwitz said. “Professor Ngô found the right point of view that only looks natural with hindsight.”

Ngô, 37, was born in Hanoi, Vietnam, received his doctorate from the Université Paris-Sud, and currently teaches at the Institute for Advanced Study. Ngô said he considered it “a big privilege” to discuss his projects with Kottwitz and others at the University whose work he admired. “I’m still amazed by how generous [Kottwitz] was in sharing his knowledge with me,” Ngô said in an e-mail interview.

Since 2003, Ngô has visited Hyde Park frequently, giving seminar talks on his work and visiting Kottwitz. “What I like most in Hyde Park,” he said, “is the wonderful blend of people, totally dedicated to the pursuit of knowledge and scholarship.”

Langlands praised Ngô, and said he was excited about the math Ngô and Kottwitz would produce together. Ngô said he would talk to Kottwitz about a branch of analysis called the automorphic spectrum. “Despite the progress accomplished in the field recently, the automorphic spectrum somehow knows how to hide its ultimate truth very well,” he said.