3:30 pm - 4:30, Seminar Hall
Simplicial resolution a la Vassiliev and counting points
University of Chicago.
Given the current terrain of Algebraic Geometry, it is tempting to think of singular (Ã©tale?) cohomology as generalizing (categorifying) point counts. Vassiliev in some of his recent papers (and following on his work, Gorinov and Tommasi among others) developed a robust set of techniques to compute the cohomology of spaces of non-singular algebraic objects (for instance the space of degree-d smooth curves in the plane). We will see how each step in this framework can be seen as the analogue of a step if one were naively counting points of the same space over some finite field. In particular, the inclusion-exclusion method will show up as the spectral sequence of a filtration. No knowledge fancier than PoincarÃ© duality will be assumed.