Ryan Williams works in the design and analysis of efficient algorithms and computational complexity theory. One of his major interests is to understand how the art of finding good algorithms for solving problems relates to the art of proving lower bounds, which are limitations on solving problems via good algorithms. Deep relationships between the existence of mildly efficient algorithms for simple problems in circuit analysis, and strong limitations on what problems circuits can solve, are presently being uncovered by Williams and others. Williams is also interested in theoretical topics that help give scientific explanations for computational phenomena, such as the unreasonable effectiveness of satisfiability solvers in practice.
- Lower Bounds in Computational Complexity, Fall 2018. Visiting Scientist, Program Organizer and Workshop Organizer.
- Fine-Grained Complexity and Algorithm Design, Fall 2015. Visiting Scientist, Program Organizer and Workshop Organizer.
- Algorithms and Complexity in Algebraic Geometry, Fall 2014. Visiting Scientist.