Fakultäten der Universität Bonn: Suche
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Vertex Algebras and Factorization Algebras
(2021-07-19)
This thesis is about the relationship between vertex algebras and Costello-Gwilliam factorization algebras, two mathematical approaches to chiral conformal field theory. Many vertex algebras have already been constructed. ......
Embeddings of groups rings and L2-invariants
(2021-06-02)
The strong Atiyah conjecture for a group G, which restricts the possible values taken by L2-Betti numbers of G-CW-complexes, implies far-reaching structural statements about a canonical *-regular ring RℚG, ...
Hyperbolic and dispersive singular stochastic PDEs
(2021-07-19)
The purpose of this thesis is to analyse nonlinear Schrödinger and wave equations which have been perturbed by a singular stochastic potential. The tools are, on the one hand, paracontrolled calculus, and, on the other ...
On steady Kähler-Ricci solitons
(2021-08-26)
In this thesis we study the existence and uniqueness of steady Kähler-Ricci solitons. We consider two classes of manifolds on which we obtain new examples of steady solitons by using different methods for each class. In ...
On the theory of higher Segal spaces
(2020-10-21)
This thesis contains three chapters, each dealing with one particular aspect of the theory of higher Segal spaces introduced by Dyckerhoff and Kapranov:
(1) By exhibiting the simplex category as an ∞-categorical ...
(1) By exhibiting the simplex category as an ∞-categorical ...
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 ...
Uniform Boundedness of Pole Order of General Eisenstein Series
(2020-08-24)
This work consists of two parts. In the first part we give a general introduction to the chapter 7 of [L1], and settle down some bases needed for the second chapter in which we prove that the order of the poles of a residual ...
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 ......
An Easton-like Theorem for all Cardinals in ZF
(2020-07-01)
We show that in Zermelo-Fraenkel Set Theory without the Axiom of Choice (ZF), a surjectively modified Continuum Function θ(κ) can take almost arbitrary values on all cardinals. This is in sharp contrast ......