From finite elements to toric varieties. Why a numerical analyst should care about algebraic geometry

June 3, 2019
Versione stampabile

Venue: Seminar Room “-1” – Department of Mathematics – Via Sommarive, 14 Povo - Trento
Time: 12.00 a.m.

  • Ludovico Bruni Bruno - PhD in Mathematics

Abstract:

When we deal with algebraic varieties we describe them by their coordinate rings, which naturally provide them with the Zariski topology. However, when we need to draw an algebraic variety with chalk and blackboard, we fall into the structure of Euclidean topology.
In this talk, we explain how some concepts of classical topology and differential geometry, such as complexes and differential forms, apply to toric varieties. In particular, we start from famous numerical variational crimes to see the importance of understanding the real underlying topology and motivate a description of such algebraic varieties in terms of the MacPherson's theorem, which relates the theory of fans to the classical Euclidean topology, and provide then a parallelism between classical homology and the homology of the variety associated with a complete fan.

The seminar corresponds to one first year PhD exam

Supervisor: Luis E. Solá Conde