Chennai Mathematical Institute


3:30 pm - 4:30, Seminar Hall
Simplicial resolution a la Vassiliev and counting points

Ronno Das
University of Chicago.


Given the current terrain of Algebraic Geometry, it is tempting to think of singular (étale?) 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 Poincaré duality will be assumed.