3:30–4:30 pm
Eckhart Hall, Room 206
1118 E. 58th Street
Chicago, IL 60637
The contractibility of a loop in our universe becomes almost irrelevant if it takes longer than the age of the universe to contract it; in other words, the simple connectivity of our experience is ultimately a geometric, not a topological fact. In the 1990's, this and other considerations led Gromov to propose a program of quantitative topology: asking about the "size" or "complexity" of the objects (a homotopy between two maps; a filling of a nullcobordant manifold) whose existence is implied by the results of algebraic and geometric topology. I will discuss the questions and the motivations behind them, as well as some answers, most of them recent.