Williams received his Doctor of Philosophy in computer science in 2007 from Carnegie Mellon University under the supervision of Manuel Blum. From 2010 to 2012, he was a member of the Theory Group of International Business Machines Corporation Almaden Center. Since Fall 2011, he is a professor at Stanford University.
Complexity theorist Scott Aaronson has called the result "one of the most spectacular of the decade". Williams is also an expert on the computational complexity of k-anonymity.
He won the Ron V. Book best student paper award at the Institute of Electrical and Electronics Engineers Conference on Computational Complexity in 2005 and 2007, and at the best student paper award at the International Colloquium on Automata, Languages and Programming in 2004 from the European Association for Theoretical Computer Science. Williams’s result that the complexity class NEXP is not contained in ACC0 received the best paper award at the Conference on Computational Complexity in 2011.
From 2010 to 2012, he was a member of the Theory Group of International Business Machines Corporation Almaden Center. Williams has been a member of the programme committee for the Symposium on Theory of Computing in 2011 and various other conferences.
