P vs NP and Complexity Lower Bounds

Date: 29 September - 3 October 2025

Location: Mathematical Institute, University of Oxford

The P vs NP problem remains one of the deepest and most consequential open questions in mathematics and theoretical computer science. To mark the 25th anniversary of the Millennium Prize Problems, this workshop will bring together researchers to reflect on progress, challenges, and evolving perspectives in computational complexity. The event will explore major breakthroughs in complexity theory, highlighting circuit lower bounds, meta-complexity, algebraic and geometric complexity theory, hardness of approximation, proof complexity, and beyond. With a focus on both technical advancements and broader insights into the nature of mathematical difficulty, the workshop will provide a forum for cutting-edge research and lively discussion on the future directions of one of the most celebrated problems in mathematics.

Speakers: Shuichi Hirahara (NII), Christian Ikenmeyer (Warwick), Russell Impagliazzo (UCSD), Valentine Kabanets (Simon Fraser), Nutan Limaye (ITU Copenhagen), Ryan O’Donnell (Carnegie Mellon), Igor Oliveira (Warwick), Toni Pitassi (Toronto), Benjamin Rossman (Duke), Shubhangi Saraf (Toronto), Iddo Tzameret (Imperial), Ryan Williams (MIT), Henry Yuen (Columbia)

Registration:  Participation in the workshop is by invitation, but a limited number of additional places is available.  To register for the Clay Research Conference or to register interest in a workshop, please email Naomi Kraker, providing the name of your institution and stating which workshop you wish to attend. Students please also provide a letter of reference from your supervisor.

HOTEL SCAM ALERT:  Some speakers may be contacted via email or telephone by Travellerpoint.org or similar.  Please be advised that we use no external organizing service.  All emails regarding the workshop will be sent by CMI or a workshop organizer.