Math prof wins prestigious prize

Until earlier this month, Mathematics Professor David Harbater's colleagues said he looked like the cat that swallowed the canary. After the American Mathematical Society notified Harbater last semester that he won the Frank Nelson Cole Prize in Algebra -- awarded only once every five years, he then learned that he would have to wait more than two months until the official announcement to tell anyone. Harbater received his award Jan. 5, at the annual conference in San Francisco. French mathematician Michel Raynaud, who collaborated with Harbater since 1991, also received the award. Building on work he began after graduate school, Harbater proved the Abhyankar Conjecture, an analogue of the broader Inverse Galois Problem which has stumped mathematicians for almost 200 years. A 19th century French mathematician, Galois studied the correspondence between symmetry in shapes and symmetry in solutions to equations. If a shape is rotated, there are specific orders of rotation that will eventually put the shape at its initial position, Harbater said. This sequence of movements is called a group. Equations often have several solutions, just as a shape has many possible rotations, that are placed in a specific order. He said the rotation groups of a shape and the solutions of an equation share symmetry when they follow the same order of permutations to arrive at the original position or value. Galois asked in his Inverse Problem -- which Harbater and his colleagues have dubbed the "white whale" -- whether it is true that every symmetry group has a corresponding equation. Harbater said Abhyankar's Conjecture applies the question to graphs. Using a set collection of points, coefficients and type of graph, only certain symmetry groups will occur no matter how the data is manipulated. After first proving Abhyankar's Conjecture, which mathematicians have been trying to solve since 1957, Harbater and Raynaud then showed how to construct graphs from the given groups. While Harbater said he is excited about the award, he is already looking towards future projects. "It feels like I'm moving on to the next phase," Harbater said. "It gives me more confidence that it's possible to solve the white whale. The fact that I've gotten attention has meant that I've been able to be in more contact with people all over the world." Advances Harbater makes in his research also enhance his teaching, because it helps him convey to students that math is an ongoing process, instead of information set in "stone tablets," he said. Students say that the time Harbater spends on his research has not interfered with his teaching. "He is the best math professor I've had at Penn," Engineering sophomore Deniz Cultu said. "He seemed to always have time for us."

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