# On the anisotropy theorem of Papadakis and Petrotou

Speaker:

Elizabeth XiaoSpeaker Affiliation:

UBCDecember 6, 2022

ESB 4127

Vancouver, BC

CanadaAbstract:

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.

Event Topic:

### Event Details

December 6, 2022

4:00pm

**ESB 4127**

Vancouver, BC, CA