Fellow: Awarded 2011
Field of Study: Mathematics
Competition: US & Canada
Bjorn Poonen received an A.B. in Mathematics and Physics from Harvard in 1989, and a Ph.D. in Mathematics under Kenneth A. Ribet at UC Berkeley in 1994. After postdoctoral positions at MSRI and Princeton University, he served on the faculty at Berkeley until 2008, when he moved to MIT, where he is now the Claude Shannon Professor of Mathematics. Poonen's research focuses on number theory and algebraic geometry; in particular, he is interested in developing methods for understanding the rational number solutions to multivariable polynomial equations, but also interested in proving that certain problems are undecidable. Occasionally he has done research in other areas, including combinatorics, probability, and theoretical computer science. Poonen is the founding managing editor of Algebra & Number Theory and serves on the editorial board of several other journals. He has received the Packard, Sloan, and Rosenbaum fellowships, as well as a Miller Professorship. Earlier, he was a four-time Putnam Competition winner, and the unique perfect scorer out of 385,000 participants in the 1985 American High School Mathematics Exam. At MIT, Poonen serves as co-chair of the mathematics graduate program with Professors Peter Shor and Gigliola Staffilani. Thirteen mathematicians have completed a Ph.D. thesis under his guidance.
Poonen will use the Guggenheim Fellowship to study Selmer groups of elliptic curves. Whereas the rational solutions to polynomial equations of degree 2 are completely understood, the next case, the case of elliptic curves (certain curves of degree 3), remains mysterious despite over a century of research. Selmer groups provide one of the only known approaches to understanding such curves, but they too hold many mysteries. Instead of studying one elliptic curve at a time, Poonen will study a family of such curves, and in particular will examine the statistical distribution of the Selmer group.
Profile photograph by Bryce Vickmark.