On the anisotropy theorem of Papadakis and Petrotou

Abstract:

Papadakis and Petrotou showed that anisotropy of a quadratic form implies the Hard Lefschetz theorem for simplicial spheres in characteristic 2. In this talk, I will explain how we used an integration map to define a mixed volume on spheres, which is linear over a connected sum decomposition. Using this decomposition, we explicitly describe the quadratic form and prove an additional combinatorial conjecture of Papadakis and Petrotou. This is joint work with Kalle Karu.

Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.

Join Zoom Meeting: https://washington.zoom.us/j/91547335974
Meeting ID: 915 4733 5974