Title: Analyzing the simplex method by-the-book, or, what theory can learn from practice

Abstract: The simplex method is an algorithm for linear programming, and this algorithm is much faster than theory is able to explain. In this talk I will describe a new theoretical framework we introduced to address this question. Under this framework, we prove new strong running time guarantees, using mathematical assumptions taken from software user manuals. I will discuss which features of real-world software and LP's we have managed to theoretically capture for this purpose, and what will come next.