**Joint CSE and TOPS Talk**

May 13, 2016, 2:30pm

**PCAR 290**

**Alexander Razborov,** *University of Chicago*

*Abstract:* Semi-algebraic and algebraic proof systems make a very important part of the modern proof complexity. They explore the possibility of proving meaningful statements using algebra and geometry instead of or in addition to logic and manipulate with polynomial equations or inequalities rather than with logical formulas. Many of these systems are based on the powerful Nullstellensatz/Positivstellensatz theorems, while others are underlined by more ad hoc principles. This area is extremely well connected to other branches of theory of computing and mathematics, notably to approximation algorithms in combinatorial optimization, and it is growing fast.

The talk will consist of two parts. First, we will give a general overview of the area and explain some of the connections mentioned above. In the second, more technical, part we will talk about a recent paper on the width of semi-algebraic proofs in dynamical proof systems like Cutting Planes or Lovasz-Schrijver.