Tong Liu awarded Sloan Fellowship
Purdue mathematics assistant professor Tong Liu has been awarded a 2012 Sloan Research Fellowship. Established in 1955 by the Alfred P. Sloan Foundation, the fellowships provide support and recognition to young scientists who are regular (tenure track) faculty members of a college or university in the U.S. or Canada. The $50,000 fellowship is awarded for a two-year period.
Liu earned his Ph.D. at the University of Michigan in 2005. Prior to joining the Purdue mathematics faculty in fall 2008, he was a Lecturer in Mathematics at the University of Pennsylvania for three years, and he held a six-month visiting appointment at the Université de Paris-Sud 11 in 2006. In spring 2011, Liu was a Member of the Institute for Advanced Study in Princeton.
Liu's research is in algebraic number theory, where his focus has been on representations of Galois groups. Fontaine's p-adic Hodge theory finds such representations in etale cohomology groups of algebraic varieties, and the study of these representations has born much fruit, for example in the work of Taylor and Wiles on the modularity of elliptic curves and their subsequent proof of Fermat's last theorem. Liu has obtained impressive results on constructing these representations starting from simple data such as a vector space, a so-called semilinear endomorphism, and a filtration. Partly with collaborators, he has settled important long-standing conjectures of Fontaine and Breuil, and made fundamental contributions to the more complicated theory over the p-adic integers. These, in turn, led him to new results on modularity.