THE ENERGY OF VECTOR BUNDLES

Speaker(s)

FABIO EUGENIO GIOVANNI CIPRIANI

Affiliation

Politecnico di Milano, Italy

Language of the talk

English

Date

May 28, 2025, 5:15 p.m.

Information about the event

IMPAN 405 & ZOOM

Title in Polish

THE ENERGY OF VECTOR BUNDLES

Seminar

North Atlantic Noncommutative Geometry Seminar

---

Using ideas of (noncommutative) potential theory, we introduce the concept of energy E(V) of a vector bundle V over a Riemannian manifold and, more generally, over a Dirichlet space. We show that, in low dimension, E(V) measures the non-triviality of V, and that it is sub-additive on the semigroup of classes of vector bundles. Finally, we derive equations satisfied by the harmonic symmetries and projections representing critical points of the energy E(V). 

---