Semi-Algebraic Proofs, IPS Lower Bounds and the τ-Conjecture

Explore the intricacies of semi-algebraic proofs, IPS lower bounds, and the τ-Conjecture in this 29-minute conference talk presented at the Association for Computing Machinery (ACM). Delve into the question "Can a Natural Number be Negative?" as the speaker guides you through key concepts such as the Binary Value Principle and Proof Complexity. Gain insights into the motivations behind semi-algebraic proofs and their applications. Learn about the definition of Algebraic Circuits and how they relate to semi-algebraic proofs. Examine illustrations that clarify complex ideas and understand the significance of IPS Upper Bounds in this context. This talk provides a comprehensive overview of advanced topics in computational complexity theory, suitable for those with a background in theoretical computer science or mathematics.

Introduction
Binary Value Principle
Proof Complexity
Motivation
SemiAlgebraic Proof
Motivations
Definition of Algebraic Circuit
SemiAlgebraic Proofs
Illustration
IPS Upper Bound
Conclusion