Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

 Siegel der Universität Augsburg

 

Oberseminar Differentialgeometrie

 

Levin Maier
Universität Heidelberg
 
spricht am
 
Montag, 17. November 2025
 
um
 
16 Uhr s.t.
 
im
 
Raum 2004 (L1)
 
über das Thema:
 

»On the Contact Type Conjecture for Exact Magnetic Systems«

Abstract:
In this talk, I will present a broad class of exact magnetic systems—called magnetic systems of strong geodesic type—for which the contact type conjecture (posed by Contreras, Iturriaga, Paternain & Paternain in 1998) can be affirmatively resolved.

On any closed manifold, we construct an infinite-dimensional space of such systems. For each, there exists a null-homologous embedded periodic orbit on every energy level, with negative action below the strict Mañé critical value. This implies that the corresponding energy levels are not of contact type below this threshold, confirming the conjecture in this setting.

The structure of these systems also leads to rich multiplicity results, ensuring arbitrarily many embedded null-homologous periodic magnetic geodesics at each energy level.

I will also highlight explicit constructions:
– On any non-aspherical manifold, there exists a dense set of Riemannian metrics giving rise to infinitely many such magnetic systems.
– On any closed contact manifold satisfying the strong Weinstein conjecture, there exists an infinite-dimensional family of Riemannian metrics such that the induced magnetic system is of strong geodesic type.

This is joint work with L. Deschamps and T. Stalljohann


 

Hierzu ergeht herzliche Einladung.
Prof. Dr. Urs Frauenfelder
 

Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).


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