Topology concerns the study of shapes. From the beginning, its problems have been intertwined with the search for algorithms - procedures to compute quantities or solve problems. In fact, topological questions drove some of the developments in the theory of algorithms. An example is the search for an algorithm to determine whether a closed loop of string is knotted. This problem was studied for 40 years, and finally solved by W. Haken around 1960. The speaker will discuss some attempts to solve this problem, the ultimate successful strategy, and some recent connections to computational complexity, the study of the running time of algorithms.
Joel Hass is a Professor of Mathematics at UC Davis. He received his PhD from the University of California at Berkeley in 1981. His research is in geometry, topology, and computation. He has been a member of the Mathematical Sciences Research Institute at Berkeley, the Institute for Advanced Study at Princeton, and the Hebrew University of Jerusalem. He is a co-author, with Colin Adams and Abigail Thompson of the humorous and popular supplements to calculus "How to Ace Calculus" and "How to Ace the Rest of Calculus".