Explore the fascinating world of proof complexity in this comprehensive computer science seminar. Delve into the definition of proof systems, polynomial bounded proof systems, and specific proof systems. Examine induction, truth tables, and the Pigeonhole Principle. Investigate lower bounds and standard proof systems, including their rules and proof completeness. Gain insights into open problems in the field as presented by Toniann Pitassi, a visiting professor from the University of Toronto. Enhance your understanding of discrete mathematics and theoretical computer science through this in-depth lecture from the Institute for Advanced Study.