The doctoral researcher will work at the interface of arrangements of hyperplanes, aperiodic tilings, and the classification of B-free lattice systems. One focus lies on high-dimensional tilings with a focus on aperiodicity and their Heesch numbers. Further questions pertain to infinite simplicial arrangements and their periodic structures. Another focus can be the algebraic and spectral structures of B-free lattice systems.
The position is particularly suited to candidates with a background in algebra, combinatorics or tilings, preferably with experience in some computer algebra system or programming language.
This project lies in geometric approximate group theory - the recent extension of geometric group theory that generalizes concepts and theorems from groups to approximate groups. It studies existence or non-existence of approximate lattices in totally disconnected, locally compact groups (almost) acting on trees that are known to not have any lattices.
More information will follow soon.
More information will follow soon.
More information will follow soon.
The PhD project is about invariants of triangulated categories that appear in commutative algebra and representation theory, like the derived category or the stable module category, and how they interact with properties of the rings or algebras. The invariants are generation time, which generalizes, among other things, projective dimension, and the lattice of thick subcategories.
The postdoctoral researcher will work at the interface of non-Archimedean geometry, tropical geometry, intersection theory, and matroid theory. The main focus will be the development of non-Archimedean volume polynomials and intersection-theoretic invariants associated with metrised vector bundles, with applications to the geometry and Hodge theory of valuated matroids. Toric varieties and toric schemes will provide an important testing ground for these ideas.
The position is particularly suited to candidates with a strong background in non-Archimedean or tropical geometry, intersection theory, or matroid theory.
In project A4, we investigate Kac–Moody groups from various perspectives. One aspect of interest is groups of integer points in affine Kac–Moody groups, i.e., groups like $\mathrm{SL}_n( \mathbf{Z}[t,t^{-1}] )$. We will be investigating finiteness properties of these groups (finite generation, finite presentability, and higher finiteness properties).
Project B4 is concerned with filling functions and isoperimetric inequalities for arithmetic groups in positive characteristic and consequently with measures of distortion for subspaces of Euclidean buildings. It turns out that filling functions are related to questions about "how much of a flat is close to infinity". Hence, this project connects geometry, spectral theory and tools from probability.
The postdoctoral researcher will work at the interface of logarithmic and tropical geometry, combinatorics, locally symmetric varieties, and automorphic forms. The main focus will be the construction and study of logarithmic compactifications of locally symmetric varieties, together with the development of logarithmic tautological rings generated by special cycles, characteristic classes of automorphic vector bundles, and boundary classes. A further direction concerns the combinatorial structures underlying these compactifications and their cohomology, including connections to complexes of regular matroids.
The position is particularly suited to candidates with a strong background in logarithmic or tropical geometry, combinatorial algebraic geometry, the geometry of locally symmetric varieties, or automorphic forms.