Seminář z diferenciální geometrie PDF Tisk

Seminář se koná v učebně M5 (a/nebo online) Ústavu matematiky a statistiky, budova 08, areál Přírodovědecké fakulty, Kotlářská 2, Brno, vždy v 10:00.

Vedoucí semináře:

  • Prof. RNDr. Jan Slovák, DrSc.,
  • Prof. RNDr. Josef Janyška, DSc.,
  • Doc. Josef Šilhan, PhD. (programový vedoucí),



Přednášky v jarním semestru 2022

  • 9. 5. 2022 (start at 10:00, lecture room M5 and MSTeams)
    Josef Šilhan
    Modified Patterson-Walker construction

    Abstract:
    The classical Patterson-Walker (spit signature) metric is defined on the cotangent bundle of an affine manifold. A slight generalisation leads to a projective-to conformal version of this construction. There are several ways how to modify this construction and we shall discuss certain class of these modifications in details. In particular, we shall identify conformal symmetries 'upstairs' in terms of suitable projective data 'downstairs'. We shall also discuss almost Einstein scales in a similar way. (This is a joint work with M. Hammerl, K. Sagerschnig a V. Žádník.)

  • 3. 5. 2022 (start at 10:00, lecture room M3 and MSTeams)
    Gerd Schmalz
    CR manifolds with symmetries and the embeddabilty problem

    Abstract:
    It is a classical result by Jacobowitz that a hypersurface type CR manifold $M$ with complex structure $V$ can be locally realised as a hypersurface in complex space if and only if there exists a complex vector field $Z$ transversal to $V$ and such that $[Z,V]\subseteq V$. Hill and Nacinovich proved the following generalisation: If $(M,V)$ is a  CR manifold of type $(n,k)$ and there exists a solvable Lie algebra of complex vector fields of dimension $\ell\le k$ transversal to $V$ then $(M,V)$ can be embedded into a CR manifold $(M'V')$ of type $(n+\ell, k-\ell)$. In particular, if $k=\ell$ this is an embedding into complex space. I will present a generalisation for Hill and Nacinovich's theorem without the assumption of solvability of the Lie algebra. This is joint work with M. Cowling and A.Ottazzi (UNSW) and Masoud Ganji (UNE).
  • 14. 2. 2022
    Ondřej Hulík
    Generalized and Exceptional geometry and its relation to supergravity and M theory


Přednášky v podzimním semestru 2021

  • 29. 11. 2021
    Mauro Mantegazza
    Towards a non-commutative generalization of the jet functor

  • 22. 11. 2021
    Giovanni Russo
    Nearly Kahler six-manifolds with two-torus symmetry

  • 25. 10. 2021
    David Sykes
    On geometry of 2-nondegenrate, hypersurface-type Cauchy-Rieman structures encoded by dynamical Legendrian contact structures

  • 11. 10. 2021
    Henrik Winther
    Differential geometry of $SO*(2n)$-structures and $SO*(2n)Sp(1)$-structures


Přednášky v podzimním semestru 2017


  • 13. 11. 2017
    Radoslaw Kycia
    Topological modelling of nuclear pasta phases


  • 6. 11. 2017
    Jan Slovák
    Cartan-Kähler theory -- application to quaternionic contact structures


  • 30. 10. 2017
    Josef Šilhan
    Interesting connections in the projective class, and obstructions


Přednášky v jarním semestru 2017


  • 22. 5. 2017
    Henrik Winther
    Non-degenerate Almost- and Para-Complex structures, and their Symmetries


  • 24. 4. 2017
    Sumit Kaushik

    Curve Evolution under Extrinsic metrics for DTI processing

  • 10. 4. 2017
    Jan Gregorovič
    On standard models of CR and para--CR manifolds


  • 20. 3. 2017
    Vojtěch Žádník
    The curves, or from Frenet apparatus to Thomas tractors and back again


  • 6. 3. 2017
    Jan Slovák:
    Constant curvature models in sub-Riemannian geometry



Přednášky v podzimním semestru 2016


  • 12. 12. 2016
    Josef Šilhan
    Curves in conformal and projective geometries


  • 21. 11., 2016, the lecture room M5:
    10.00
    Miroslav Kureš
    TBA



  • 14. 11. 2016, the lecture room M5:
    10.00
    Phan Thanh Nam

    Recent progress on the ionization problem


  • 31. 10. 2016
    10.00 - 10.50
    Ivan Minchev
    On the generality of quaternionic contact structures

    11.00 - 11.50
    Gerd Schmalz
    Chern-Moser theory for para-CR-manifolds and degenerate multi-contact structures


  • 24. 10. 2016
    Ilya Kossovskiy

    The Associated Differential Equations Method in CR-geometry


  • 10. 10. 2016
    Arman Taghavi-Chabert


Přednášky v jarním semestru 2016

  • 13. 6. 2016
    Stefan Ivanov
    The quaternionic contact Yamabe problem


  • 9. 5. 2016
    Josef Šilhan
    Higher supersymmetries


  • 25. 4. 2016
    Diana Barseghyan
    (University of Ostrava)
    Spectral analysis of a class of Schroedinger operators exhibiting a
    parameter-dependent spectral transition



  • 11. 4. 2016
    Anton Galaev
    Special Kähler-Lorentz metrics



  • 14. 3. 2016
    Jan Slovák



  • 7. 3. 2016
    Vladimir Ezhov (Flinders University/ MPIM Bonn)
    New familiy of unbounded homogeneous tube domains
    in Cn


  • 29. 2. 2016
    Ioannis Chrysikos
    Spin and metaplectic structures on homogeneous spaces

  • 22. 2. 2016
    Matthias Hammerl (University of Greifswald):
    Holography of BGG-Solutions



Přednášky v podzimním semestru 2015



  • 7. 12. 2015
    Katja Sagerschnik
    Nurowski's conformal structures with almost Einstein scales



  • 30. 11. 2015
    Matthew Randall


  • 23. 11. 2015
    Vojtěch Žádník
    Report on Lie contact structures

  • 2.11.2015
    Gueo Grantcharov (the Florida International University, USA):
    On HKT geometry

  • 26.10.2015
    Matthew Burke
    Synthetic Lie Theory Part I: An Introduction to Synthetic Differential Geometry

    Parts II and III will be presented on the seminar on algebra on October 29 and Novenber 5 (1pm, seminar room)


  • 12.5.2015
    Anton Galaev
    Holonomy algebras of Einstein pseudo-Riemannian manifolds



Přednášky v jarním semestru 2015


  • 18.5.2015
    Yaroslav Bazaykin

    Numerical analysis of topological characteristics of three-dimensional geological models of oil and gas fields

    Zoran Škoda
    Hopf algebroids of differential operators


  • 11.5.2015
    Ioannis Chrysikos
    Killing spinors with torsion and applications



  • 27. 4. 2015
    Zdeněk Dušek
    How many are affine connections of special types


  • 20. 4. 2015
    Michal Marvan

    Integrable surfaces II


  • 13. 4. 2015
    Arman Taghavi-Chabert:
    Twistorial description of null foliations

  • 30.3.2015
    Dmitri Alekseevsky

    Conformally homogeneous manifolds


  • 2. 3. 2015
    Anton Galaev
    Classification of third-order symmetric Lorentzian manifolds


  • 9. 3. 2015
    Jan Slovák
    Linearized metrizability problem for Parabolic Geometries
    -- general procedure and examples



Přednášky v podzimním semestru 2014

  • 15.12. 2014
    Christian Gustad
    Regular and singular contact actions of Lie algebras

  • 8. 12. 2014
    Ioannis Chrysikos
    Killing and twistor spinors with torsion on compact naturally reductive spaces


  • 1. 12. 2014
    Jean-Philippe Michel
    Dirac operators and their symbols


  • 10. 11. 2014
    Georgy Sharygin
    Local formulas for characteristic classes



  • 3. 11. 2014
    Dmitri Alekseevski
    Homogeneous pseudo-Riemannian Einstein metrics associated with
    graded semisimple Lie algebras

  • 13. 10. 2014
    Ivan Kolář
    On the vertical Weil bundles


  • 6. 10. 2014
    Anton Galaev
    How to compute the holonomy algebra of a Lorentzian manifold


  • 24. 9. 2014
    Stefan Ivanov
    The Lichnerowicz-Obata sphere theorems on a quaternionic contact
    manifold of dimension bigger than seven"


  • 22. 9. 2014
    Dimiter Vassilev
    Lichnerowicz-Obata sub-laplacian eigenvalue theorem
    in CR geometry under a positive "Ricci" bound


Přednášky v jarním semestru 2014


  • 12. 5. 2014
    Dimiter Vassilev
    Quaternionic contact Liouville theorem and applications


  • 5. 5. 2014
    Ivan Kolář
    On general connections


  • 14. 4 .2013
    Dmitri Alekseevski


  • 7. 4. 2014
    Yaroslav Bazaykin
    Stability of integral persistence diagrams


  • 24. 3. 2014 ,12:00--13:50, lecture room M4
    25. 3. 2014, 10:00--11:50, lecture room MS1
    27. 3. 2014, 10:00--11:50, lecture room M4
    31. 3. 2014, 12:00--13:50, lecture room M4
    Evgeny Malkovich
    Construction of metrics with special holonomies via geometrical flows
    (series of lectures)


  • 10. 3. 2014
    Katja Sagerschnig
    Conformal structures in dimension four and generic rank two distributions in
    dimension five

  • 3. 3. 2014
    Anton Galaev
    Irreducible holonomy algebras of Riemannian supermanifolds




Přednášky v podzimním semestru 2013

  • 25. 11. 2013
    Jonathan Kress
    Recent progress in superintegrable systems

  • 18.11. 2013
    Ivan Minchev
    Quaternionic contact hypersurfaces in hyper-Kaehler geometry


  • 11. 11. 2013
    Anton Galaev
    Holonomy groups of superconnections on supermanifolds


  • 4. 11. 2013
    Giovanni Moreno
    Meta-symplectic geometry of 3rd order Monge-Ampére equations


  • 21. 10. 2013
    Jan Gregorovič
    Generalized symmetries of homogeneous parabolic geometries


  • 7. 10. 2013
    Ivan Kolář
    General connections and the Froehlicher-Nijenhuis bracket


  • 30. 9. 2013
    Dmitri Alekseevsky
    Classification of cohomogeneikty one Kaehler G-manifolds  of a compact semisimple group  $G$ in terms of painted Dynkin diagrams


Přednášky v jarním semestru 2013


  • 13. 5. 2013
    John Ryan
    Dirac type operators and conformal groups

  • 15. 4. 2013
    Christian Gustad

  • 8. 4. 2013
    Anton Galaev
    Pseudo-Riemannian manifolds with recurrent spinor fields

  • 25. 3. 2013
    Josef Šilhan
    On symmetries of the Laplacian

  • 18. 3. 2013
    Ivan Kolář
    On natural transformations of Weil bundles

  • 4. 3. 2013
    Rikard von Unge
    Generalized Kahler reduction

  • 25. 2. 2013
    Joseph Krasiľshchik
    On geometry of integrable systems and its cohomological background




Přednášky v podzimním semestru 2012

  • 10. 12. 2012
    Jan Slovák
    Conformal Fedosov manifolds

  • 26. 11. 2012
    Dmitri Alekseevsky
    TBA

  • 19. 11. 2012
    Ivan Kolář
    On the functorial prolongations of fiber bundles

  • 12. 11. 2012
    Ioannis Chrysikos
    The Dirac operator on non-naturally reductive spaces

  • 29. 10. 2012
    Andrea Santi
    On the automorphism group of extended Poincaré structures

  • 15. 10. 2012
    Anton Galaev
    Algorithm for deRham-Wu decomposition for Riemannian and
    Lorentzian manifolds


  • 1. 10. 2012
    Jan Gregorovič
    Geometric structures invariant to symmetries
Aktualizováno Úterý, 03 Květen 2022 09:39