Fakultäten der Universität Bonn: Suche
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Periodicity in motivic homotopy theory and over BP*BP
(2018-07-03)
In classical homotopy theory, the Periodicity theorem by Devinatz-Hopkins-Smith gives a complete answer as to what types of periodicities can occur in stable homotopy theory. In motivic homotopy theory, there are additional ...
Elliptic multiple zeta values, modular graph functions and genus 1 superstring scattering amplitudes
(2018-03-05)
We study holomorphic and non-holomorphic elliptic analogues of multiple zeta values, namely elliptic multiple zeta values and modular graph functions. Both classes of functions have been discovered very recently, and are ...
Intrinsic Dimension Estimation using Simplex Volumes
(2018-01-18)
In this thesis, we introduce a novel approach for the estimation of the intrinsic dimension of high-dimensional datasets. For this purpose, the volumes of high-dimensional simplices, with vertex points sampled from local ...
Hodge theoretic aspects of Soergel bimodules and representation theory
(2018-01-19)
In the last years, methods coming from Hodge theory have proven to be fruitful in representation theory, most remarkably leading to a new algebraic proof of the Kazhdan-Lusztig conjectures based on the Hodge theory of ...
The L2-Torsion Polytope of Groups and the Integral Polytope Group
(2018-01-24)
This thesis contains three projects revolving around the L2-torsion polytope. First we show that the L2-torsion polytope of infinite elementary amenable groups vanishes. Then we establish a link between ...
On some variational problems in geometry
(2018-08-28)
In this thesis we consider several variational problems in geometry that have a connection to the spectrum of the Laplacian acting on functions. In the first part, we study a quantity called the analytic systole, which was ...
On the geometry of nodal sets and nodal domains
(2018-12-13)
In the present work, we study and prove results related to the nodal geometry of Laplacian eigenfunctions on closed Riemannian manifolds, as well as solutions to more general classes of elliptic partial differential ...
Scalable Algorithms for Parallel Tree-based Adaptive Mesh Refinement with General Element Types
(2018-12-12)
In this thesis, we develop, discuss and implement algorithms for scalable parallel tree-based adaptive mesh refinement (AMR) using space-filling curves (SFCs). We create an AMR software that works independently of the used ...
G-theory of group rings for finite groups
(2018-12-13)
In this thesis we investigate Quillen's G-theory of group rings mostly focusing on the case of finite groups. We study the Hambleton-Taylor-Williams decomposition conjecture for G-theory of the integral group rings. The ...
On discrete surfaces: Enumerative geometry, matrix models and universality classes via topological recursion
(2019-03-21)
The main objects under consideration in this thesis are called maps, a certain class of graphs embedded on surfaces. We approach our study of these objects from different perspectives, namely bijective combinatorics, matrix ...