MATRIX-SMRI Symposium: Nijenhuis Geometry and Integrable Systems

David Wood

  •  14 Feb 2022 - 18 Feb 2022
     7:00 am - 5:00 pm

Emma Carberry (University of Sydney)
Holger Dullin (University of Sydney)
Vladimir Matveev (Universität Jena)

Program Description:
Many integrable systems allow for separation of variables. The global theory of separation of variables on Riemannian manifolds has made recent progress that leads to the study of Nijenhuis geometry.
Nijenhuis geometry provides a link between separation of variables and projectively equivalent metrics. While Riemannian geometry and symplectic or Poisson geometry have been very well studied, global Nijenhuis geometry is relatively new and the workshop aims to exploit this theory and its connection to finite and infinite-dimensional integrable systems. Specifically two problems related to polynomial integrals of geodesic flows on the torus and the sphere will be studied.


Alexey Bolsinov works as a Reader in Mathematics at Loughborough University. His research results include the discovery of a new phenomenon in dynamical systems known as integrable chaos, theory of orbital classification for integrable two-degrees-of-freedom systems, loop molecule method in topology of integrable systems and new classes of holonomy groups and symmetric spaces in pseudo-Riemannian geometry. Under his supervision, 18 PhD students successfully completed their research projects, many of them continue their academic careers in USA, Russia, Brazil, Germany and China.

Vladimir Matveev is a Chair of Mathematics at the University of Jena. He has solved a number of major open problems in several areas of Differential Geometry and in the theory of Integrable Systems including two problems explicitly posed by Sophus Lie in 1882, the projective Lichnerowich conjecture and c-projective Yano-Obata conjecture. He constructed two new examples of natural integrable Hamiltonian systems on closed surfaces, Dullin-Matveev and Matveev-Shevchishin systems.

Program Structure: 
Please click on the image below.

Selected seminar recordings are available on the SMRI YouTube playlist.

Click here for the accompanying lectures

For more information on the online week 7 – 11 Feb, please see:

Please click on image to enlarge

In-person participant list:
Reinout Quispel (LaTrobe University)
Peter Van der Kamp (LaTrobe University)
Yuri Nikolayevsky (LaTrobe University)
Jonathan Kress (University of New South Wales)
Holger Dullin (University of Sydney)
Nathan Duignan (University of Sydney)
Sean Gasiorek (University of Sydney)


MATRIX Wine and Cheese Afternoon 15 February 2022
On the first Tuesday of each program, MATRIX provides a pre-dinner wine and cheese afternoon. Produce is locally-sourced to showcase delicacies from the region.