Nijenhuis Geometry: singularities and global issues

Joint seminar Department of Mathematics_Centro Internazionale per la Ricerca Matematica

27 September 2019
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Venue: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Sala Seminari "-1"
At: 09:30 a.m. 

Speakers:

  • Alexey Bolsinov (Loughborough)    
  • Andrey Konyaev (Moscow)    
  • Vladimir Matveev (Jena)    

Abstract:

The talk is devoted to Nijenhuis operators, i.e., fields of endomorphisms with vanishing Nijenhuis torsion. This is possibly the simplest geometric condition; for this reason it appears independently and many times in geometry, analysis and mathematical physics, in particular in the theory of projectively equivalent metrics and in the theory of integrable systems. The talk is based on a series of papers in progress aiming at re-directing the research agenda in this area to “next level topics": Singular points: what does it mean for a point to be generic or singular in the context of Nijenhuis geometry? What singularities are non-degenerate? What singularities are stable? How do Nijenhuis operators behave near non-degenerate and stable singular points?
Global properties: what restrictions on a Nijenhuis operator are imposed by compactness of the manifold? And conversely, what are topological obstructions on a manifold carrying a Nijenhuis operator with specific properties (e.g.with no singular points)? We demonstrate that this research program is realistic by proving a series of new, not at all obvious, results, and finish the talk with a list of open problems some of which are easy to formulate.

Contact person: Sonia Mazzucchi

The speakers are guests as part of the Research in Pairs program