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Manchester Geometry Seminar - Alexei Bolsinov

Dates:13 October 2025
Times:15:00 - 16:00
What is it:Seminar
Organiser:Department of Mathematics
Who is it for:University staff, External researchers, Current University students
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  • Department of Mathematics

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  • In category "Seminar"
  • In group "(Maths) Geometry, topology and mathematical physics"
  • In group "(Maths) Maths seminar series"
  • By Department of Mathematics

Speaker: Alexei Bolsinov (Loughborough)

Title: Nijenhuis Geometry

Abstract:

A Nijenhuis structure on a smooth manifold is given by a field $L$ of endomorphisms with zero Nijenhuis torsion: $$ L^2u,v - LLu,v - Lu,Lv + lv=0. $$ The classical Haantjes theorem states that locally every Nijenhuis endomorphism with a simple real spectrum reduces, in a suitable coordinate system, to the diagonal form $L = diag ( f_1(u_1), \dots f_n(u_n))$. However, almost nothing is known about the global properties of Nijenhuis endomorphisms, nor about their behaviour at singular points where eigenvalues collide. The talk will be devoted to our recent attempts to clarify these issues. I will try to provide an overview of the results in this area obtained over the past 5-7 years. The most of them will be fairly elementary and understandable to anyone familiar with the basics of differential geometry.

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Frank Adams Room 1
Alan Turing Building
Manchester

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Theodore Voronov

theodore.voronov@manchester.ac.uk

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