Fakultäten der Universität Bonn: Suche
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Trace-class properties of semi-groups associated with operator valued differential operators and their Witten index
(2021-06-23)
We consider the operator D = ∂ + A(X) in L2(ℝ, H), where ∂ is the closure of the derivative along ℝ in L2(ℝ, H), the operator A(X) is the ...
Symplectic Automorphic Forms and Kloosterman Sums
(2021-10-12)
In this thesis, we study automorphic forms on the rank 2 symplectic group Sp(4), in the context of analytic number theory. While much of the abstract theory is described in Langlands’ theory, one needs more explicit formulae ...
Extremes of the discrete Gaussian free field in dimension two
(2021-03-26)
In recent years, there have been many advances towards an understanding of the extreme value theory of log-correlated random fields. Log-correlated random fields are conjectured to compose a universality class for the ......
Natural maps in higher Teichmüller theory
(2021-09-17)
In this thesis we consider harmonic maps and barycentric maps in the context of higher Teichmüller theory. We are particularly interested in how these maps can be used to study Hitchin representations. The main results of ...
On the membrane model and the discrete Bilaplacian
(2021-04-26)
This thesis is concerned with the membrane model, an example of a discrete random interface model. This model arises, for example, when studying thermal fluctuations in biomembranes. Mathematically, it is given as a Gibbs ...
Symplectic non-squeezing theorem and Hamiltonian partial differential equations
(2021-12-01)
The thesis is concerned with providing a first natural generalization of M. Gromov's non-squeezing symplectic result in infinite dimensional case and applying it within the context of Hamiltonian partial differential ...
Homological Stability, Characteristic Classes and the Minimal Genus Problem
(2021-04-07)
The purpose of this thesis is to study the (co-)homological properties of the classifying space of subsurface bundles in a trivial background bundle with fiber a manifold M. We will investigate homological stability ...
External Spanier-Whitehead duality for C-spectra and applications to C-homology theories
(2021-07-19)
The thesis constructs a Spanier-Whitehead type duality functor relating finite C-spectra to finite Cop-spectra, where C is a topological index category. We prove that every C-homology theory is given by taking the homotopy ...
Approximation Algorithms for the Traveling Salesman Problem
(2021-05-11)
The traveling salesman problem (TSP) is probably one of the best-studied problems in discrete optimization. Given a complete weighted graph with n vertices, the task is to find a tour of minimal length that visits every ...