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Theory of persistence modules is a rapidly developing field lying on the borderline between algebra, geometry and topology. It provides a very useful viewpoint at Morse theory, and at the same time is one of the cornerstones of topological data analysis. In the course I'll review foundations of this theory and focus on its applications to symplectic topology. In parts, the course is based on a recent work with Egor Shelukhin arXiv:1412.8277

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Documents 37Jxx | enregistrements trouvés : 23

Persistence modules and Hamiltonian diffeomorphisms - Part 1 Polterovich, Leonid | CIRM H Nouveau

Séminaire Bourbaki. Vol. 2000/2001 :exposés 880-893 | Société Mathématique de France 1998 Nouveau

Persistence modules and Hamiltonian diffeomorphisms - Part 2 Polterovich, Leonid | CIRM H Nouveau

Persistence modules and Hamiltonian diffeomorphisms - Part 3 Polterovich, Leonid | CIRM H Nouveau

Persistence modules and Hamiltonian diffeomorphisms - Part 4 Polterovich, Leonid | CIRM H Nouveau

Multiphase averaging for classical systems : with applications to adiabatic theorems Lochak, P. ; Meunier, C. ; Dumas, H. S. | Springer-Verlag 1988 Nouveau

Applications of Lie groups to differential equations Olver, Peter J. | Springer 1993 Nouveau

Cohomological analysis of partial differential equations and secondary calculus Vinogradov, A. M. | American Mathematical Society 2001 Nouveau

Classical many-body problems amenable to exact treatments :(solvable and/or integrable and/or linearizable...) in one-, two- and three- dimensional space Calogero, Francesco | Springer 2001 Nouveau

Dynamical systems X :general theory of vortices Kozlov, V. V. | Springer 2003 Nouveau

Bifurcations in hamiltonian systems :computing singularities by Gröbner bases Broer, Henk ; Hoveijn, Igor ; Lunter, Gerton ; Vegter, Gert | Springer 2003 Nouveau

Topics in dynamics and ergodic theory Bezuglyi, Sergey ; Kolyada, Sergiy | Cambridge University Press 2003 Nouveau

Integrable hamiltonian systems :geometry, topology, classification Bolsinov, Alexey V. ; Fomenko, Anatoly T. | Chapman & Hall/CRC 2004 Nouveau

The principle of least action in geometry and dynamics Siburg, Karl F. | Springer 2004 Nouveau

Local and semi-local bifurcations in hamiltonian dynamical systems :results and examples Hanßmann, H. | Springer 2007 Nouveau

Simulating hamiltonian dynamics Leimkuhler, Benedict ; Reich, Sebastian | Cambridge University Press 2004 Nouveau

Introduction to the Perturbation Theory of Hamiltonian Systems Treschev, Dmitry ; Zubelevich, Oleg | Springer 2010 Nouveau

Nonlinear dynamical systems of mathematical physics:spectral and symplectic integrability analysis Blackmore, Denis ; Prykarpatsky, Anatoliy K. ; Samoylenko, Valeriy Hr. | World Scientific 2011 Nouveau

Complex Hamiltonian dynamics Bountis, Tassos ; Skokos, Haris ; Flach, Sergej | Springer 2012 Nouveau

Ordinary differential equations:qualitative theory Barreira, Luis ; Valls, Claudia | American Mathematical Society 2012 Nouveau

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Séminaire Bourbaki. Vol. 2000/2001 :
exposés 880-893 | Société Mathématique de France 1998 Nouveau

Multiphase averaging for classical systems :
with applications to adiabatic theorems Lochak, P. ; Meunier, C. ; Dumas, H. S. | Springer-Verlag 1988 Nouveau

Classical many-body problems amenable to exact treatments :
(solvable and/or integrable and/or linearizable...) in one-, two- and three- dimensional space Calogero, Francesco | Springer 2001 Nouveau

Dynamical systems X :
general theory of vortices Kozlov, V. V. | Springer 2003 Nouveau

Bifurcations in hamiltonian systems :
computing singularities by Gröbner bases Broer, Henk ; Hoveijn, Igor ; Lunter, Gerton ; Vegter, Gert | Springer 2003 Nouveau

Integrable hamiltonian systems :
geometry, topology, classification Bolsinov, Alexey V. ; Fomenko, Anatoly T. | Chapman & Hall/CRC 2004 Nouveau

Local and semi-local bifurcations in hamiltonian dynamical systems :
results and examples Hanßmann, H. | Springer 2007 Nouveau

Nonlinear dynamical systems of mathematical physics:
spectral and symplectic integrability analysis Blackmore, Denis ; Prykarpatsky, Anatoliy K. ; Samoylenko, Valeriy Hr. | World Scientific 2011 Nouveau

Ordinary differential equations:
qualitative theory Barreira, Luis ; Valls, Claudia | American Mathematical Society 2012 Nouveau