Crossings - Math Seminars: Aaron NABER

Technical seminar: Structure and Regularity of Nonlinear Harmonic Maps
Locandina Crossings

Giovedì 29 Febbraio 2024 alle ore 14:00, per il ciclo “Crossings - Math Seminars”, Aaron NABER (Northwestern University) terrà un intervento intitolato Structure and Regularity of Nonlinear Harmonic Maps.

Il seminario si svolgerà nell’Edificio U4-01 (Geologia, floor -1), Quadrilatero della scienza, Università di Milano-Bicocca.

Abstract: We will consider harmonic maps between Riemannian manifolds u:M->N .  The first part of the talk will discuss and explain the known regularity of such mappings, in particular joint work with Daniele Valtorta on the size and rectifiability of the singular sets.  The second part of the talk will focus on sequences of such mappings u_j:M->N, where it is known that blow-up can occur on a m-2 dimensional subset.  This blow-up is characterized by the so-called defect measure, which we will review and discuss.  In recent joint work with Valtorta we have proved the energy identity, a conjectured explicit description of the defect measure in terms of bubble energy counting.


An introductory seminar on the topic will be organized by Daniele Valtorta on Tuesday, 20th February 2024, at 14:00, in U5-3014. The target are PhD and Master students. We will discuss:

- What is a harmonic map?
- How many different types of harmonic maps are there?
- Pythagorean theorem on fractals: how to make snowflakes nicer

Venerdì 1° Marzo 2024 alle ore 17:00, Aaron NABER terrà un 2° intervento intitolato Ricci Curvature, Fundamental Group and the Milnor Conjecture.

Dettagli evento all’indirizzo: