Hardness of Approximation: From the PCP Theorem to the 2-to-2 Games Theorem

Computer scientists firmly believe that no algorithm can efficiently compute optimal solutions to a class of problems called NP-hard problems. For many NP-hard problems, even computing an approximately optimal solution remains NP-hard. This phenomenon, known as the hardness of approximation, has numerous connections to proof checking, optimization, combinatorics, discrete Fourier analysis, and geometry.

The talk will provide an overview of these connections. It will address why graph coloring is a computationally hard problem, how it is possible to check a proof without even looking at it, why computer scientists love the majority vote, and whether a shape exists that looks spherical as well as cubical. It will explain how all this fits into a 30-year research program starting with the foundational Probabilistically Checkable Proofs (PCP) Theorem and leading to the recent 2-to-2 Games Theorem.

Bio: Subhash Khot is a professor of computer science at the Courant Institute of Mathematical Sciences at New York University. His prior affiliations include Princeton University (PhD), Institute for Advanced Study (member), Georgia Tech (assistant professor) and University of Chicago (visiting professor). His research centers on computational complexity and its connections to geometry and analysis. He is a recipient of the National Science Foundation’s Alan T. Waterman Award, the International Mathematical Union’s Nevanlinna Prize, the Simons Investigator Award, a MacArthur Fellowship, and is a Fellow of the Royal Society. 

Lunch for talk attendees will be available at 12:00pm. 
To request accommodations for a disability, please contact Emily Lawrence, emilyl@cs.princeton.edu, 609-258-4624 at least one week prior to the event.