|Topic:||Synthetic Differential Cohomology|
|Affiliation:||University of California, San Diego; Member, School of Mathematics|
|Date:||Wednesday, October 24|
|Time/Room:||6:00pm - 7:30pm/Dilworth Room|
Today the prevailing method in mathematics is 'analytic', in the sense that all mathematical objects are broken down into very small bits. For instance, a space or manifold is regarded as merely a set of points with structure. By contrast, in a 'synthetic' approach, we study objects via basic axiomatic properties, such as in Euclid's geometry. I will describe a synthetic approach to topological and smooth objects, due to Lawvere, and sketch how its 'stacky generalization', due to Schreiber, encodes notions like flat connections on principal bundles.