Uses of randomness in complexity theory and algorithms; Efficient algorithms for finding approximate solutions to NP-hard problems (or proving that they don't exist); Cryptography.
Sanjeev Arora is the Charles C. Fitzmorris Professor in Computer Science. He joined Princeton in 1994 after earning his doctorate from the University of California, Berkeley. He was a visiting professor at the Weizmann Institute in 2007, a visiting researcher at Microsoft in 2006-07, and a visiting associate professor at Berkeley during 2001-02. Professor Arora’s honors include the D.R. Fulkerson Prize in Discrete Mathematics (awarded by the American Mathematical Society and Math Optimization Society) in 2012, the ACM-Infosys Foundation Award in the Computing Sciences in the same year, the Best paper award from IEEE Foundations of Computer Science in 2010, and the EATCS-SIGACT Gödel Prize (cowinner), also in 2010. He was appointed a Simons Foundation investigator in 2012, and was elected an ACM fellow in 2009. Professor Arora was the founding director and lead PI at the Center for Computational Intractability in 2008, a project funded partly by an NSF Expeditions in Computing grant.