Phd
Research Associate (f/m/d)
The principal aim of this project is to use methods from Algebraic Combinatorics to solve combinatorial problems related to coding and design theory. This mostly involves the theory of association schemes and related topics, such as orthogonal polynomials and the theory of linear programming.
Contact: Prof. Dr. Kai-Uwe Schmidt. Use ID: Kennziffer5648
Research Positions
Bielefeld
1. We investigate zeta functions associated with various lattice enumeration problems and connect these to Ehrhart polynomials of polytopes and Hecke algebras of p-adic Lie groups. We seek for a combinatorial interpretation of the image of the generating series of the symplectic Hecke operators under the Satake isomorphism.
2. We investigate Euler factors of Dirichlet series counting various kinds of similar submodules. We focus on establishing connections with rationality results from p-adic integration theory for p-adic Lie groups one the one side and on the investigation of the analytic properties in analogy with the Riemann hypothesis on the other side.
Research Position
Bielefeld
Foundations of tensor-triangular geometry will be developed within Project C6. The project will deal with problems of classification of localising and thick subcategories of various triangulated categories arising from representation theory of associative algebras (strict polynomial functors, tame hereditary algebras) and algebraic geometry (perfect complexes of coherent sheaves on an algebraic stack).
Contact: Prof. Dr. Henning Krause, Prof. Dr. Eike Lau. Use ID: Wiss22854
Research Position
Bielefeld
Project C7 lies at the juncture of algebraic geometry and representation theory of finite-dimensional algebras. Its goal is to study algebraic schemes defined over a field of positive characteristic (or a Dedekind ring), which are derived splinters. The purely geometric (cohomological) splinter property of a scheme shares similarities with the existence of full exceptional collections in the corresponding derived category of coherent sheaves, the construction of which is going to be achieved using the technique of highest weight categories and polynomial representations of linear algebraic groups over Z.
Research Position
Bielefeld
Project C8 combines methods of complex geometry and arithmetic algebraic geometry to study algebraic varieties with special cohomological structure, in particular K3 surfaces and specializations of hyper-Kähler varieties to positive characteristic.
Contact: Prof. Dr. Charles Vial, Prof. Dr. Eike Lau. Use ID: Wiss22859
Research Position
Bielefeld
Euler products are the incarnation of local-global principles. They often arise as leading constants of an asymptotic formula describing a counting problem in algebra or number theory, and they encode the underlying integral structures. Prototypes are the conjectures of Manin and Malle. The Euler products and their associated zeta functions investigated in this project come from a variety of mathematical fields including graph theory, algebraic geometry, representation theory and algebraic number theory.
Contact: Prof. Dr. Christopher Voll. Use ID: Wiss22861
Research Position
Bielefeld
Project C1 combines algebraic cycle theory and moduli theory in the context of hyper-Kähler geometry. The two guiding goals are, on the one hand, to understand the hidden structure of the intersection theory of hyper-Kähler varieties and, on the other hand, to understand, via the theory of modular forms, the birational complexity of their moduli spaces. Key examples of such hyper-Kähler varieties arise as moduli spaces of stable objects in appropriate triangulated 2-Calabi--Yau categories.
Contact: Prof. Dr. Charles Vial. Use ID: Wiss22870
Research Position
Bielefeld
Matroids are combinatorial abstractions of linear independence in vector spaces. One aspect of this project concerns the interplay of matroids and algebra in the context of free hyperplane arrangements. The concept of a matroid has been extended to that of a Coxeter matroid and, recently, to that of a q-analog of a matroid. Another aspect of the project concerns generalized representations of q-analogs of matroids on the one hand and the investigation of a notion of a q-analog of a Coxeter matroid on the other hand.
Research Associate (f/m/d)
Possible research directions of the advertised PhD position concern tilting theory in hereditary categories defined over finite fields or the field of real numbers as well as the theory of Hall algebras of non-commutative hereditary curves and their relation with quantized enveloping algebras. Potential candidates are expected to have a strong background in homological algebra and representation theory of finite dimensional algebras and possess basic knowledge of algebraic geometry.
Contact: Prof. Dr. Igor Burban. Use ID: Kennziffer5643
Research Associate (f/m/d)
One possible research direction of the advertised PhD position concerns the study of blocks of categories of Harish-Chandra modules for reductive groups defined over arbitrary fields invloving the technique of D-modules including a description of indecomposable objects in representation tame cases. Another possible direction involves the theory of tame matrix problems over arbitrary fields and their applications, inlcuding the theory of tame non-commutative nodal curves. Potential candidates should have strong background in representation theory, homological algebra or/and algebraic geometry.
Contact: Prof. Dr. Igor Burban, Prof. Dr. Fabian Januszewski. Use ID: Kennziffer5644
Research Position
Bielefeld
The PhD project is will focus on metric distortion in affine twin buildings. The goal is to settle an accessible special case of a general conjecture about the distortion of arithmetic groups in their ambient Lie groups. The PhD project is suitable for someone with a background in group theory, geometry, topology, or the theory of buildings.
Contact: Prof. Dr. Kai-Uwe Bux. Use ID: Wiss22848
Postdoc
Research Position (Postdoc)
Bielefeld
This position is associated to two different projects. For both projects knowledge on Coxeter groups is expected. In the first project we want to study designs in permutation groups, focusing on (finite) Coxeter groups. In the second project methods from combinatorial and geometric group theory will be applied to extended Coxeter and related groups. Further we aim also to study extended Coxeter groups, which are not simply laced, which will lead to a general combinatorial descriptions of hereditary categories.
Contact: PD Dr. Barbara Baumeister. Use ID: Wiss22867
Research Position (Postdoc)
Bielefeld
Research in asymptotic algebra, related to Projects A1, A4, and A6.
Contact: Prof. Dr. Christopher Voll. Use ID: Wiss22876
Postdoctoral Researcher (f/m/d)
Malle's conjecture for local and global fields in characteristic $p$ Determine the asymptotical behavior of the counting function of local and global fields in characteristic $p$ with a given $p$-group as Galois group. Potential candidates should have a background in number theory and/or in neighbor areas.
Contact: Prof. Dr. Jürgen Klüners. Use ID: Kennziffer5647
Research Position (Postdoc) in Arithmetic Geometry
Bielefeld
Contact: Prof. Dr. Eike Lau. Use ID: Wiss22770
Research Positions (Postdoc) in Algebraic Geometry
Bielefeld
These are two PostDoc positions for which expertise in any areas pertaining to Algebraic Geometry will be considered.
Contact: Prof. Dr. Charles Vial. Use ID: Wiss22837
Research Position (Postdoc) in Arithmetic Geometry/Representation Theory
Bielefeld
Foundations of tensor-triangular geometry will be developed within Project C6. The project will deal with problems of classification of localising and thick subcategories of various triangulated categories arising from representation theory of associative algebras (strict polynomial functors, tame hereditary algebras) and algebraic geometry (perfect complexes of coherent sheaves on an algebraic stack).
Contact: Prof. Dr. Henning Krause, Prof. Dr. Eike Lau. Use ID: Wiss22850
Research Position (Postdoc) in Algebraic Geometry/Arithmetic Geometry/Representation Theory
Bielefeld
Project C7 lies at the juncture of algebraic geometry and representation theory of finite-dimensional algebras. Its goal is to study algebraic schemes defined over a field of positive characteristic (or a Dedekind ring), which are derived splinters. The purely geometric (cohomological) splinter property of a scheme shares similarities with the existence of full exceptional collections in the corresponding derived category of coherent sheaves, the construction of which is going to be achieved using the technique of highest weight categories and polynomial representations of linear algebraic groups over Z.
Research Position (Postdoc) in Algebraic Geometry/Arithmetic Geometry
Bielefeld
Project C8 combines methods of complex geometry and arithmetic algebraic geometry to study algebraic varieties with special cohomological structure, in particular K3 surfaces and specializations of hyper-Kähler varieties to positive characteristic.
Contact: Prof. Dr. Charles Vial, Prof. Dr. Eike Lau. Use ID: Wiss22858
Research Position (Postdoc)
Bielefeld
This is a PostDoc position for which expertise in number theory / automorphic forms will be considered.
Contact: Prof. Dr. Claudia Alfes-Neumann. Use ID: Wiss22765
Postdoctoral Researcher (f/m/d)