Fakultäten der RUB » Fakultät für Mathematik » Lehrstühle » Arbeitsgruppe Transformationsgruppen

Mittwoch,17. Juli, 10.15 in IA 1/109

Titel des Vortrages
The restricted Weyl group action on the set of orbits of a minimal parabolic subgroup for k-spherical varieties.

Abstract:
For a spherical variety of a reductive group G over algebraically closed field (i.e. for such variety that a Borel subgroup B has an open orbit) F.Knop in 95 has introduced an action of the Weyl group on the set of B-orbits. This action is closely related with an action of the so called little Weyl group. In my talk I shall speak about generalizations of these results to algebraically non-closed fields obtained with F.Knop. Let k be an algebraically non-closed field and X be a spherical k-variety with respect to the action of a reductive group G i.e. such that the minimal parabolic subgroup P acts with an open orbit. Under these assumptions the set of the P-orbits defined over k with non-empty set of k-points is finite and we construct an action of a restricted Weyl group on the set of orbits of maximal rank by relating it with a geometry of cotangent bundle. For the case of a real field we prove the existence of such action for the whole set of P-orbits containing R-points.

## Prof. Junjiro Noguchi (Universität Tokyo)

Donnerstag, 6. Juni 2019, 10.15 Uhr in IA 1/63

Titel des Vortrages
Value Distribution Theory and torsion points on semi-abelian varieties

## Prof. Hiroo Tokunaga (Tokyo Metropolitan University)

Mittwoch, 29.Mai 2019, 14.15 Uhr in IA 1/177

Titel des Vortrages
On the topology of cubic-line, quartic-line arrangements

## Dr. Leonid Ryvkin (IMJ-PRG)

Mittwoch, 8.Mai 2019, 14.15 Uhr in IA 1/177

Titel des Vortrages
An introduction to singular foliations

Abstract:
After a brief recap on regular foliations and the Frobenius theorem, we introduce singular foliations as partitions of a manifold into leaves. We explain how this description can be transformed into an infinitesimal one and discuss the additional information encoded by this infinitesimal description.

## Alexander Caviedes-Castro (Universität zu Köln)

Donnerstag, 21. Februar 2019, 11:00 Uhr in IA 1/109

Titel des Vortrages
Symplectic capacities and Cayley graphs

Abstract:
The Gromov non-squeezing theorem in symplectic geometry states that is not possible to embed symplectically a ball into a cylinder of smaller radius, although this can be done with a volume preserving embedding. Hence, the biggest radius of a ball that can be symplectically embedded into a symplectic manifold can be used as a way to measure the "symplectic size'' of the manifold. We call the square of this radius times the number π the Gromov width of the symplectic manifold. The Gromov width as a symplectic invariant is extended through the notion of "Symplectic Capacity". In this talk I will explain how to estimate bounds for symplectic capacities of homogeneous spaces of compact Lie groups in terms of the combinatorics of Cayley graphs associated to them.

## Dr. Kay Paulus (Erlangen)

Freitag, 8. Februar 2019, 10:15Uhr in IA 1/109

Titel des Vortrages
Construction of multiplicity-free quasi-Hamiltonian manifolds

Abstract:
This talk describes how the combinatorial theory of spherical varieties can be used to construct new examples of (quasi-) Hamiltonian spaces. We start with an introducation to spherical varieties and their combinatorics. The second part of the talk will be about the classification of a family of smooth affine spherical varieties of rank one and the classification of so-called quasi-Hamiltonian model spaces, multiplicity free quasi-Hamiltonian manifolds with surjective moment map.

## Dr. Valdemar Tsanov (RUB)

Dienstag, 22. Januar 2019, 12:15 Uhr in NA 2/64

Titel des Vortrages
On low degree generators of invariant rings

Abstract:
Let $V$ be a representation space of a complex reductive group $G$. We study the invariant ring $\mathbb{C}[V]^G$ and more specifically the generators of low degree. I will describe a criterion for existence of invariants of certain degrees. For irreducible representations, I will also derive a lower bound on the degrees of invariants, based on the geometry of the unique closed projective $G$-orbit, more specifically - its secant varieties.

## Elizaveta Vishnyakova, Universidade Federal de Minas Gerais (Brazil)

Dienstag, 15. Januar 2019, 12:15Uhr in NA 2/64

Titel des Vortrages
Invariant subalgebras in a skew-group ring and their modules

Abstract:
I. Gelfand and M. Zeitlin constructed a basis in finite dimensional gln(C)-modules together with explicit formulas for gln(C)-action. These formulas for gln(C)-action are called classical Gelfand-Zeitlin formulas. It was noticed by I. Gelfand and M. Graev that the classical Gelfand-Zeitlin formulas may be used to obtain a family of infinite dimensional gln(C)-modules. More general theory of the so-called Gelfand-Zetlin modules is developed by Yu. Drozd, S. Ovsienko and V. Futorny. The main difficulty here was to construct and classify so-called singular Gelfand-Zeitlin modules. That is Gelfand-Zeitlin modules where the (rational) coefficients of the classical Gelfand-Zeitlin formulas have potential singularities. A significant step in this direction was done in 2017-2018 by L. Ramirez, P. Zadunaisky and by N. Early, V. Mazorchuk, E.V. We will discuss our most recent paper with V. Mazorchuk that is devoted to a generalization of this construction to any invariant subalgebras in a skew-group ring.

## Prof. Dr. Jörg Winkelmann (Bochum)

Dienstag, 13. November 2018, 12:15Uhr in NA 2/64

Titel des Vortrages
Tame discrete sets in complex Lie groups

## Prof. Dr. Dr. h .c. mult. Alan T. Huckleberry (Bochum)

Mittwoch, 7. November 2018, 10:15 in IA 1/181

Titel des Vortrages
Moving cycles, ample normal bundles and pseudoconcave neighborhoods

Abstract:
For the talk a cycle is just a compact complex submanifold $C$ of a complex manifold $Z$. In the first part of the talk we will sketch some classical results which relate the three topics in the title. Here, moving $C$ means moving it in a holomorphically parameterized family $C_t$ in $Z$. This should in principle be related to the ampleness of the normal bundle of $C$, and this ampleness, when expressed in terms curvature, should be related to $C$ possessing a neighborhood basis with a certain degree of pseudoconcavity. The second part of the talk will be devoted to the special case where $(G,K)$ is a symmetric pair, $Z$ is a $G$-flag manifold and $C$ is a closed $K$-orbit in $Z$. In particular, we will outline certain recent results (see arXiv 1711.09333 and 1807.07311).

## Narasimha Chary Bonala (Bonn)

Freitag, 5. Oktober 2018, 11:00 in NA 1/64

Titel des Vortrages
On Bott-Samelson varieties

Abstract:
Let G be a simple algebraic group over the field of complex numbers and B be a Borel subgroup of G. Let X(w) be a Schubert variety in the flag variety G/B corresponding to an element w of the Weyl group of G, and let Z(w) be the Bott–Samelson variety, a natural desingularization of X(w). In this talk we discuss the automorphism group of Z(w) and the classification of "reduced expressions of w" such that Z(w) is Fano.

## Christian Miebach (Calais)

Freitag, 20. Juli 2018, 10:15 in NA 2/64

Titel des Vortrages
Hamiltonian actions of unipotent groups on compact Kähler manifolds.

Abstract:
In 2007 Doran and Kirwan published a paper discussing Geometric Invariant Theory of actions of unipotent group on projective varieties. In my talk I will explain a joint work with Daniel Greb where we obtained related results for meromorphic actions of unipotent complex Lie groups on compact K\"ahler manifolds using moment map techniques.

## Lucas Fresse (Nancy)

Mittwoch, 18. Juli 2018, 14-16 in NA 2/24

Titel des Vortrages
A version of Matsuki duality for generalized flags.

Abstract:
An (infinite-dimensional) ind-group is the direct limit of a chain of (complex, finite dimensional) algebraic groups. We consider a classical ind-group G, obtained as the limit of a chain of classical groups of a given type. Dimitrov and Penkov introduced a flag model ("generalized flags") for classifying the Borel subgroups of G. Contrary to the finite-dimensional case, all Borel subgroups of G are not conjugate. This yields several ind-varieties of generalized flags of the form G/B. In the finite-dimensional case, Matsuki duality relates two families of orbits on a flag variety: orbits of a symmetric subgroup and orbits of the corresponding real form. In this talk, we show that Matsuki duality extends to the case of ind-varieties of the form G/B.

## Karl Oeljeklaus (Marseille)

Dienstag 17. Juli 2018, 12:15, NA 4/24 (Teil 1)
15.15, NA 4/24 (Teil 2)

Titel des Vortrages, der gleichzeitig im Rahmen des Floer Kolloquiums gehalten wird:
Schottky group action on complex manifolds, Teil 1 und 2.

Abstract:
In this talk we consider Schottky group actions on complex manifolds. As an abstract group a Schottky group is isomorphic to a non-abelian free group F, and a Schottky group action on the complex manifold X yields an invariant connected open subset U of X on which the action of F is free and properly discontinuous. Our motivation for the study of Schottky group actions comes from the fact that the quotient manifolds U/F have interesting properties.
In the main case when the initial complex manifold is homogeneous-rational of dimension grater than one, i.e. a flag manifold, the quotients are non-Kähler compact complex manifolds. We investigate their analytic and geometric invariants such as the Kodaira and algebraic dimension, the Picard group and the deformation theory, thus extending results due to Lárusson and to Seade-Verjovsky. We recover examples of equivariant compactifications of Schottky quotients of SL(2,C). This is a joint work with Christian Miebach (Calais).

Dienstag 26. Juni 2018, 12:15, NA 4/24

Titel des Vortrages:
On complexity of algebraic varieties over algebraically non-closed fields.

Abstract:
In 1986 E.B.Vinberg introduced the notion of complexity for the action of a reductive group G on an algebraic variety over an algebraically closed field, which is equal to codimension of a generic orbit of a Borel subgroup in the algebraic variety. Vinberg has proved that the complexity does not increase after passing to the B-invariant subset of algebraic variety. In particular, this means that in a spherical variety, i.e. the variety with an open B-orbit, there is only a finite number of B-orbits.
In my talk I shall speak about generalization of this result to algebraic non-closed fields which is a joint work with F. Knop.

## Florian Scholz (Bochum)

Dienstag, 19. Juni 2018, 12:15, NA 4/24 Titel des Vortrages:
Die k/12-Formel

Dienstag 5. Juni 2018, 12:15, NA 4/24

Titel des Vortrages:
The Levi-Problem for pseudoconvex homogeneous manifolds

## Tobias Schemken (Bochum)

Dienstag 29. Mai 2018, 12:15, NA 4/24

Titel des Vortrages:
Jacobi Varietät und Spur-Abbildung

## Hannah Bergner (Freiburg)

Dienstag 15. Mai 2018, 12:15, NA 4/24

Titel des Vortrages:
On varieties with locally free logarithmic tangent sheaf

Abstract:
Let (X,D) be a pair consisting of a normal complex variety and a divisor D. In the talk, I will explain connections between the geometry of (X,D) and properties of the logarithmic vector fields on X, or dually the logarithmic 1-forms. If X is smooth and D is snc, then the logarithmic tangent sheaf is locally free. More generally, this holds true if X is toric. In the talk, I will explain a theorem about the local converse of this statement, i.e. in which cases local freeness of the the logarithmic tangent sheaf implies that X has to be locally toric.

## Leonid Ryvkin (RUB)

Freitag 4. Mai 2018, 10:15, NA 5/24

Titel des Vortrages:
Conserved quantities in multisymplectic geometry

Abstract:
We investigate the different notions of "conservation" of a differential form by a vector field in regard to their relation to homotopic structures on multisymplectic manifolds. We show that conserved quantities are a subalgebra of the observable Lie infinity-algebra and prove the Noether theorem in this context.

## Andrea Iannuzzi (Rom)

Dienstag 10. April 2018, 12:15, NA 4/24

Titel des Vortrages:
The adapted hyper-Kähler structure on the tangent bundle of a Hermitian symmetric space.

Abstract:
Let (I_0, w_0) denote the invariant Kähler structure of a compact Hermitian symmetric space X = G/K. The holomorphic cotangent bundle T*X (a tubular neighbourhood of the zero section, in the non-compact case) carries a unique G-invariant hyper-Kähler structure compatible with (I_0, w_0) and the canonical holomorphic symplectic form of T*X. Such a structure has been investigated, among others, by Eguchi-Hanson, Calabi, Biquard, Gauduchon, Feix, Kaledin.
On the other hand, the tangent bundle TX is isomorphic to T*X and carries a canonical complex structure J_ad, the so called adapted complex structure, introduced by Lempert-Szöke and Guillemin-Stenzel in 1991.
One can show that TX (the crown domain, in the non-compact case) admits a unique G-invariant hyper-Kähler structure compatible with (I_0, w_0) and J_ad. The two hyper-Kähler structures are related by a G-equivariant fiber preserving diffeomorphism of TX which was introduced by Dancer and Szöke.
The aim of the talk is to introduce the adapted hyper-Kähler structure and explain an advantage of such a point of view. Namely, it is possible to obtain an explicit realization of all the quantities involved by means of Lie theoretical tools and moment map techniques.
This is part of a joint project with Laura Geatti.

## Judith Brinkschulte (Leipzig)

Mittwoch 31. Januar 2018, 12:15, NA 5/24

Titel des Vortrages:
The normal bundle of Levi-flat real hypersurfaces.

Abstract :
There has been quite some interest in the classification of compact Levi-flat real hypersurfaces in complex manifolds, motivated by the different nature of classical examples on the one hand and basic problems in dynamical systems on the other hand. I will discuss the following recent result: Let X be a complex manifold of dimension > 2. Then there does not exist a smooth compact Levi-flat real hypersurface in X such that the nromal bundle to the Levi foliation admits a Hermitian metric with positive curvature along the leaves.

## PD Dr. Stéphanie Cupit-Foutou (RUB)

Mittwoch 17. Januar 2018, 12:15, NA 5/24

Titel des Vortrages:
On momentum-polytopes of spherical varieties.

## Hendrik Herrmann (Universität Köln)

Mittwoch 6. Dezember 2017, 12:00, NA 5/24

Titel des Vortrages:
An equivariant embedding theorem for CR manifolds with circle action

## Dr. Tomasz Maciazek (Polen)

Mittwoch 29. November 2017, 12:00, NA 5/24

Titel des Vortrages:
Momentum polytope at the highest weight

## Prof. Dimitri Akhiezer (Moskau/Rusßland)

Mittwoch 22. November 2017, 12:15, NA 5/24

Titel des Vortrages:
On common zeros of eigenfunctions of the Laplace operator

## Christian Schuster (RUB)

Mittwoch 15. November 2017, 12:00, NA 5/24

Titel des Vortrages:
The Kobayashi pseudometric on subvarieties of abelian varieties

## Chrstian Zöller (RUB)

Mittwoch 25. Oktober 2017, 12:00, NA 5/24

Titel des Vortrages:
The local structure theorem for projective representations

## Jorret Bley (RUB)

Mittwoch 18. Oktober 2017, 12:00, NA 5/24

Titel des Vortrages:
Invariance of moment image of fibers of open proper maps

## Prof Jón Magnússon (University of Iceland)

Montag 25. September 2017, 10:14, NA 4/24

Titel des Vortrages:
Intersection theory for analytic cycles

Abstract :
A description of intersection theory for analytic cycles on complex manifolds will be given. Then a generalisation of this theory will be discussed, where complex manifolds are replaced by so-called "nearly smooth complex spaces". These spaces are locally the image of a complex manifold by a finite and proper map.

## Prof. Dr. Dmitry Timashev (Moskau)

Mittwoch 26. Juli 2017, 10:15 Uhr, NA 2/24

Titel des Vortrages:
Real orbits on complex spherical homogeneous spaces: the split case

## Prof. Dr. Dmitry Timashev (Moskau)

Dienstag 25. Juli 2017, 10:15 Uhr, NA 1/64

Titel des Vortrages:
Classifying real orbits on complex symmetric spaces via Galois cohomology

## Elizaveta Vishnyakova (Belo Horizonte)

Dienstag 18. Juli 2017, 10:15 Uhr, NA 1/64

Titel des Vortrages:

Abstract :
Vector bundles and double vector bundles, or $2$-fold vector bundles, arise naturally for instance as base spaces for algebraic structures such as Lie algebroids, Courant algebroids and double Lie algebroids. It is known that all these structures possess a unified description using the language of super\-geometry and graded manifolds of degree $\leq 2$. Indeed, a link has been established between the super and classical pictures by the geometrization process, leading to an equivalence of the category of graded manifolds of degree $\leq 2$ and the category of (double) vector bundles with additional structures..

## Andriy Regeta (Grenoble)

Mittwoch 28.Juni 2017, 10:15 Uhr, NA 2/24

Titel des Vortrages:
Automorphism groups of affine toric varieties and affine surfaces

Abstract:
We are going to discuss the following problem: to which extent the group of automorphisms of an affine algebraic variety determines the variety? In general the answer is negative. On the other hand, H. Kraft proved that the group of automorphisms of the affine n-space seen as an ind-group determines the affine n-space in the category of connected affine varieties. In this talk we are going to discuss a similar result for affine toric varieties. In case of dimension two, we characterise a big class of affine surfaces by their automorphism groups viewed as abstract groups.

## Bart van Steirteghem (Erlangen-Nürnberg/New York)

Dienstag 27.Juni 2017, 10:15 Uhr, NA 3/64

Titel des Vortrages:
Momentum polytopes of multiplicity free Hamiltonian manifolds

Abstract:
Generalizing T. Delzant's classification of toric symplectic manifolds, F. Knop has shown that multiplicity free Hamiltonian manifolds are classified by their momentum polytope and generic isotropy group. In this talk I will explain how the theory of (smooth affine) spherical varieties can be used to give a combinatorial characterization of the momentum polytopes of these manifolds. This is joint work with G. Pezzini.

## Chin-Yu Hsiao (Taipeh)

Mittwoch 21. Juni 2017, 10:15 Uhr, NA 2/24

Titel des Vortrages:
G-invariant Szego kernel asymptotics and CR reduction

Abstract :
Let X be a compact connected orientable CR manifold with non-degenerate Levi curvature. Assume that X admits a connected compact Lie group action G. Under certain natural assumptions about the group action G, we show that the G-invariant Szego kernel for (0,q) forms is a complex Fourier integral operator, smoothing away the reduced space Y and there is a precise description of the singularity near Y. We apply our result to the case when X admits a transversal CR circle action and deduce an asymptotic expansion for the m-th Fourier component of the G-invariant Szego kernel for (0,q)-forms as m goes to infinity. As an application, we show that if m large enough, quantization commutes with reduction. This is a joint work with Rung-Tzung Huang.

## Chin-Yu Hsiao (Taipeh)

Dienstag 20. Juni 2017, 10:15 Uhr, NA 3/64

Titel des Vortrages:
Bergman kernel asymptotics in complex geometry

Abstract:
In a work jointly with Marinescu at 2014, we obtained a full asymptotic expansion of the spectral function corresponding to the lower part of the spectrum of the Kodaira Laplacian on high tensor powers of a holomorphic line bundle. From this result, we could deduce some classical results in complex geometry ( Demailly's Morse inequalities, Bergman kernel asymptotics for ample line bundles). In this talk, I will explain how to obtain these classical results from our result. I will also mention our result about Bergman kernel asymptotics for semi-positive line bundles.

## Maxime Pelletier (Lyon)

Mittwoch 14. Juni 2017, 10:15 Uhr, NA 2/24

Titel des Vortrages:
Some geometric methods to get results on coefficients from representation theory.

Abstract :
The branching coefficients appear in representation theory when one looks at the following situation: let G and H be two complex reductive groups such that H is a subgroup of G, and consider an irreducible representation of G. Then this is also a representation of H and as such it decomposes into a direct sum of irreducible ones. The multiplicities of the irreducible representations of H in this decomposition are called the branching coefficients. They have a geometric interpretation when the groups G and H are connected: they correspond to dimensions of spaces of invariant sections of line bundles over flag varieties.
This talk will then be mainly focused on a specific example of branching coefficients (even if most of the techniques apply to other ones): the Kronecker coefficients, which are indexed by triples of partitions of the same integer. A notion of "stable triple" can then be defined relatively to these coefficients, and we will see that their geometric interpretation allows to obtain a new proof of a characterisation of stability proven by S. Sam and A. Snowden. Finally we will discuss about some ways to produce such stable triples.

## Ramiro Lafuente (Münster)

Mittwoch 7.Juni 2017, 10:15 Uhr, NA 2/24

Titel des Vortrages:
Moment maps and homogeneous Riemannian manifolds

Abstract:
The idea of the talk is to explain how the moment map of a real reductive Lie group representation appears naturally in the study of the geometry of homogeneous Riemannian manifolds. After explaining how the properties of the moment map inspire and yield results in the Riemannian setting, if time permit we will also discuss ongoing projects and open questions.

## Prof. Mikhail Borovoi (Tel-Aviv/Bielefeld)

Mittwoch, 31. Mai 2017, 10:15 Uhr, NA 2/24

Titel des Vortrages:
Cayley groups

Abstract:
I will start the talk with the classical "Cayley transform" for the special orthogonal group SO(n) defined by Arthur Cayley in 1846. A connected linear algebraic group G over the field of complex numbers C is called a *Cayley group* if it admits a *Cayley map*, that is, a G-equivariant birational isomorphism between the group variety G and its Lie algebra Lie(G). For example, SO(n) is a Cayley group. A linear algebraic group G is called *stably Cayley* if G x S is Cayley for some C-torus S. I will consider semisimple algebraic groups, in particular, simple algebraic groups. I will describe classification of Cayley simple groups and of stably Cayley semisimple groups. (Based on joint works with Boris Kunyavskii and others.)
Let $X$ be a complex smooth projective algebraic variety. The algebra of global differential operators $D_X$ is rather badly understood, except in the case of curves, toric varieties, and flag varieties. In this talk, we will investigate these algebras in the case of some wonderful varieties of small rank. More precisely, if $X$ is a wonderful $G$-variety, two questions naturally arise, namely the study of the infinitesimal action of the Lie algebra of $G$, and when ${\cal L}$ is an invertible sheaf on $X$, the study of the algebra of twisted global differential operators $D_{X,{\cal L}}$ on the cohomology groups $H^i(X,{\cal L})$. We will give an answer to these questions in some particular cases, keeping in mind that wonderful varieties can be seen as generalizations of flag varieties.