Last modified: Wednesday, March 30, 2011

## Michael J. Larsen

**Distinguished Professor**

**Distinguished Professor of Mathematics**

**Department of Mathematics**

**College of Arts and Sciences**

**University Graduate School**

**Indiana University Bloomington**

**Appointed to IU faculty, 1997**

**B.A., Harvard College, 1984**

**Ph.D., Princeton University, 1988**

Professor Michael Larsen's achievements in mathematics have been described as "remarkable" and "astonishing," and he has been labeled a "fountain of mathematical wisdom." Most notable about these accolades is that they come from winners of the Fields Medal, often described as the Nobel Prize for mathematics.

Considered one of the top mathematicians in the world working in the interface of arithmetic algebraic geometry, combinatorial group theory, combinatorics, and number theory, Larsen is recognized, in part, for his ability to work in diverse areas of mathematics. The editor of the *Indiana University Mathematics Journal* since 2001, Larsen also founded, in 2008, the Bloomington Math Circle, an after-school program for mathematically gifted elementary school students.

"Larsen is a remarkable mathematician—the kind we would all like to be," said 1990 Fields Medal winner Vaughn Jones, now a professor at the University of California Berkeley. "His breadth is astonishing, from number theory to topology to physics. He deserves to be a professor of the highest distinction wherever he chooses to work."

Since earning his Ph.D., Larsen has published in each year but one—1989. The next year, however, as a faculty member of the School of Mathematics at the Institute of Advanced Study at Princeton, Larsen and his colleague Richard Pink published the paper "Determining representations from invariant dimensions," which concerns finite simple groups. The mathematical world began to take notice.

Described as a "brilliant work" by Columbia University Professor A. J. de Jong, the paper's theorem recognizes the algebraic groups that arise from Galois representations, and it set Larsen on a long path of using group-theoretic methods to study Galois groups.

Classifying these building blocks of finite symmetries has been a preoccupation for twentieth-century mathematicians, and the proof alone, worked on by many people, occupies some 10,000 pages and consists largely of a massive induction where much of the attention is directed at the few exceptions.

"A direct conceptual analysis is unknown and remains one of the major problems of finite group theory," says Professor Ehud Hrushovski of Hebrew University's Institute of Mathematics. "The theorem of Larsen and Pink is the strongest venture in this direction to date. It is in my opinion one of the highlights of twentieth-century group theory."

But, as Vaughn Jones notes, the reach of Larsen's intellect stretches far beyond that contribution, with work in an array of subfields represented by more than 60 papers that have been cited by nearly 250 different authors, according to the American Mathematical Society.

"He is probably the best person in the world working in the interface of arithmetic algebraic geometry, combinatorial group theory, combinatorics, and number theory," says Peter Sarnak, a professor of mathematics at Princeton and the Institute for Advanced Study. "There are plenty of stars in each of these areas individually, but no one I can think of who is at Larsen's level, combining these domains to solve central and interesting problems. He has made Indiana University a center in number theory and arithmetic geometry."

And when it comes to the recognized tradeoffs between breadth versus depth, notes Henri Darmon, the James McGill Professor of Mathematics at McGill University, no such quandary exists. "Only the very strongest mathematicians can successfully achieve this," Darmon says. "One of the most appealing features of Michael's scientific style is his ability to straddle diverse areas of mathematics in original and unexpected ways."

The quality found in the range of Larsen's work is what sets him apart, notes Bjorn Poonen, a mathematics professor at Massachusetts Institute of Technology. "What distinguishes him from most other mathematicians is his ability to contribute to a wide variety of subfields within mathematics, and not just dabbling," Poonen says, "but making serious advances of interest to many researchers."