E-Dissertationen: Suche
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Probabilistic and differential geometric methods for relativistic and Euclidean Dirac and radiation fields
(2020-07-09)
The main objective of the thesis is to study relativistic and Euclidean Fermionic quantum fields from a geometrical and probabilistic point of view as opposed to the standard treatment which is more algebraic in nature.
Gradient Flows, Metastability and Interacting Particle Systems
(2020-06-19)
Many stochastic models exhibit a phenomenon called metastability. The first goal of this thesis is to study this phenomenon for certain classes of interacting particle systems. The second goal of this thesis is the following. ...
Representations of the Kottwitz gerbes
(2022-03-15)
Let F be a local or global field and let G be a linear algebraic group over F. We study Tannakian categories of representations of the Kottwitz gerbes Rep(Kt_F) and the functor G → B(F,G) defined by Kottwitz in [28]. In ...
A variational approach to Gibbs measures on function spaces
(2022-03-18)
We study develop a variational technique to study models from constructive quantum field theory. Our starting point is the interpretation of the Polchinski equation as the Hamilton-Jacobi-Bellman equation of a stochastic ...
Perturbative quantization of the two-dimensional supersymmetric sigma model
(2022-03-15)
The two-dimensional nonlinear sigma model is a classical field theory whose fields are maps from a Riemann surface Σ to a Riemannian manifold X, and whose classical solutions are minimal surfaces. In this thesis, we study ...
Dynamics for the Random Cluster Model
(2021-08-20)
The random cluster model is a statistical model on random graph structures. It can also be thought of as a unification of the percolation model, the Ising model and the q-state Potts models. To simulate such models, the ...
Diffusions on Wasserstein Spaces
(2020-05-05)
We construct a canonical diffusion process on the space of probability measures over a closed Riemannian manifold, with invariant measure the Dirichlet–Ferguson measure. Together with a brief survey of the relevant literature, ...
Long-timescale atomistic simulations
(2021-03-31)
The simulation and analysis of particle systems dynamics is an important subfield of computational materials science. It allows the investigation of many properties of interest, such as reaction mechanisms, diffusion rates, ...
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, ...