The Faculty of Mathematics and Natural Sciences: Search
Now showing items 11-20 of 41
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. ...
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, ...
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 ...