This article is only in Czech.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 podzimním semestru 2023
 25. 9. 2023 (start at 10:00, lecture room M5 and MSTeams)
Ioannis Chrysikos On the geometry of torsionfree SO*(2n)Sp(1)structures and related bundle constructions
Abstract: In this talk, first we will focus on the 2nd order geometry of torsionfree SO*(2n)Sp(1)structures, where SO*(2n) is the quaternionic real form of SO(2n, C). This includes a curvature characterization of the so called ``quaternionic skewHermitian manifolds'' (torsionfree case), and other related results. We will also discuss the construction of SO*(2(n+1))structures on the Swann bundle over a quaternionic skewHermitian manifold (M^{4n}, Q, \omega) with $n>1$. Time permitting, we will describe conditions related to their 1storder integrability. This provides a generalization of the wellknown construction of (pseudo) hyperKähler structures on the Swann bundle over a (pseudo) quaternionic Kählerian manifold (M^{4n}, Q, g). The talk is based on a joint work with V. Cortés and J. Gregorovič.
Přednášky v jarním semestru 2023
 17. 4. 2023 (start at 10:00, lecture room M5 and MSTeams)
Igor Zelenko Morse inequalities for ordered eigenvalues of generic families of selfadjoint matrices
Abstract: The topic of the talk was originally motivated by the FloquetBloch theory of Schroedinger equations with periodic potential and other problems in Mathematical Physics and also related to the topology of vectorvalued quadratic maps, motivated by secondorder conditions in optimal control. The eigenvalue branches of families of selfadjoint matrices are not smooth at points corresponding to repeated eigenvalues (called diabolic points or Dirac points). Generalizing the notion of critical points as points for which the homotopical type of (local) sublevel set changes after the passage through the corresponding value, in the case of the generic family we give an effective criterion for a diabolic point to be critical for those branches and compute the contribution of each such critical point to the Morse polynomial of each branch, getting the appropriate Morse inequalities as a byproduct of the theory. These contributions are expressed in terms of the homologies of Grassmannians. The talk is based on the joint work with Gregory Berkolaiko.
 20. 3. 2023 (start at 10:00, lecture room M5 and MSTeams)
Jan Gregorovič First BGG operators on homogeneous conformal geometries
Abstract: I will talk about first BGG operators and their solutions on homogeneous conformal geometries. I will describe an invariant calculus that allows us to find solutions explicitly using only algebraic computations. I will discuss applications to holonomy reductions and conserved quantities of conformal circles.
 6. 3. 2023 (start at 10:00, lecture room M5)
Henrik Winther Minimal Projective Orbits of Semisimple Lie Groups
Abstract: Let \(G\) be a Lie group \(G\) with representation \( \rho\) on a real simple \(G\) module \( \mathbb{V} \). We will call the orbits of the induced action of \( \rho\) on the projectivization \( P\mathbb{V} \) the projective orbits, and projective orbits of lowest possible dimension will be called minimal. We show that when \(G\) is semisimple and noncompact, there exists a compact subgroup \(K\) \(\subset\) \(G\) such that the minimal orbits of \(G\) are in bijection with the minimal \(K\)orbits on a \(K\)invariant proper subspace \( \mathbb{W}\subset \mathbb{V} \). In the case that \(G\) is splitreal, \(K\) is the trivial subgroup and the minimal projective orbit is unique.
Přednášky v podzimním semestru 2022
 7. 11. 2022 (start at 10:00, lecture room M5 and MSTeams)
Jan Slovák Bundles of Weyl structures and invariant calculus for parabolic geometries
Abstract: For more than hundred years, various concepts were developed to understand the fields of geometric objects and invariant differential operators between them for conformal Riemannian and projective geometries. More recently, several general tools were presented for the entire class of parabolic geometries, i.e., the Cartan geometries modelled on homogeneous spaces G/P with P a parabolic subgroup in a semisimple Lie group G. Similarly to conformal Riemannian and projective structures, all these geometries determine a class of distinguished affine connections, which carry an affine structure modelled on differential 1forms Υ. They correspond to reductions of P to its reductive Levi factor, and they are called the Weyl structures similarly to the conformal case. The standard definition of differential invariants in this setting is as affine invariants of these connections, which do not depend on the choice within the class. In this article, we describe a universal calculus which provides an important first step to determine such invariants. We present a natural procedure how to construct all affine invariants of Weyl connections, which depend only tensorially on the deformations Υ.
 3. 10. 2022 (start at 10:00, lecture room M5 and MSTeams)
Sam Blitz Introduction to Conformal Hypersurface Geometry
Abstract: Hypersurfaces embedded in conformal manifolds appear naturally in string theory, and their geometry is an invaluable tool for studying interesting problems in differential geometry. While Weyl's classical invariant theory makes easy work of diffeomorphism invariants in Riemannian geometry, it is less obvious how to restrict these invariants to only those that respect an underlying conformal structure. This remains the case when studying embedded hypersurfaces. We are thus faced with the problem of how one might generate such invariants; in doing so, we are led to tractors, an invaluable tool for studying conformal geometry, amongst other things. By analogizing to the Riemannian setting, we can develop a hypersurface tractor calculus, enabling us to generate a (perhaps incomplete) set of conformal hypersurface invariants.
Přednášky v jarním semestru 2022
 9. 5. 2022 (start at 10:00, lecture room M5 and MSTeams)
Josef Šilhan Modified PattersonWalker construction
Abstract: The classical PattersonWalker (spit signature) metric is defined on the cotangent bundle of an affine manifold. A slight generalisation leads to a projectiveto 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 noncommutative generalization of the jet functor
 22. 11. 2021
Giovanni Russo Nearly Kahler sixmanifolds with twotorus symmetry
 25. 10. 2021
David Sykes On geometry of 2nondegenrate, hypersurfacetype CauchyRieman 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 CartanKähler 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 Nondegenerate Almost and ParaComplex 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 paraCR 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 subRiemannian geometry
Přednášky v podzimním semestru 2016
Přednášky v jarním semestru 2016
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 pseudoRiemannian manifolds
Přednášky v jarním semestru 2015
Přednášky v podzimním semestru 2014
 10. 11. 2014
Georgy Sharygin Local formulas for characteristic classes
 3. 11. 2014
Dmitri Alekseevski Homogeneous pseudoRiemannian 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 LichnerowiczObata sphere theorems on a quaternionic contact manifold of dimension bigger than seven"
 22. 9. 2014
Dimiter Vassilev LichnerowiczObata sublaplacian 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 ,12:0013:50, lecture room M4
25. 3. 2014, 10:0011:50, lecture room MS1 27. 3. 2014, 10:0011:50, lecture room M4 31. 3. 2014, 12:0013:50, 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 hyperKaehler geometry
 11. 11. 2013
Anton Galaev Holonomy groups of superconnections on supermanifolds
 4. 11. 2013
Giovanni Moreno Metasymplectic geometry of 3rd order MongeAmpére equations
 21. 10. 2013
Jan Gregorovič Generalized symmetries of homogeneous parabolic geometries
 7. 10. 2013
Ivan Kolář General connections and the FroehlicherNijenhuis bracket
 30. 9. 2013
Dmitri Alekseevsky Classification of cohomogeneikty one Kaehler GmanifoldsÂÂÂÂÂÂÂÂÂ of a compact semisimple groupÂÂÂÂÂÂÂÂÂ $G$ 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 PseudoRiemannian 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 nonnaturally reductive spaces
 29. 10. 2012
Andrea Santi On the automorphism group of extended Poincaré structures
 15. 10. 2012
Anton Galaev Algorithm for deRhamWu decomposition for Riemannian and Lorentzian manifolds
 1. 10. 2012
Jan Gregorovič Geometric structures invariant to symmetries
