Manchester Geometry Seminar - Alexei Bolsinov
| Dates: | 13 October 2025 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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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.
Travel and Contact Information
Find event
Frank Adams Room 1
Alan Turing Building
Manchester
