The Faculty of Mathematics and Natural Sciences: Search
Now showing items 1-10 of 22
Gluing of metric measure spaces and the heat equation with homogeneous Dirichlet boundary values
(2020-07-09)
The first part of this thesis deals with gluing together several copies of an open subset of a metric measure space along the complement. This construction results in a metric measure space. We identify the Cheeger energy ......
Stochastic and deterministic models for the evolution of heterogeneous populations: Multiscale approximation and applications to melanoma T-cell therapy
(2020-07-24)
Stochastic modelling at the interface of mathematics and life sciences has gained great attention over the last decades. The study of many complex biological systems requires models taking random effects into account. Both ...
Faster Circuits for And-Or Paths and Binary Addition
(2020-07-24)
We consider the problem of constructing fast circuits both for binary addition and And-Or paths. And-Or paths are Boolean functions of the form t0 ∧ ( t1 ∨ ( t2 ∧ ( t3 ......
In Silico Facets of Biochemical Research: Accounts from Protein Folding and Protein-Ligand Interaction Studies
(2020-09-04)
Exponential advancements in computer technology over the last five decades have ubiquitously benefited science and humanity as a whole. Consequent beneficiaries of this surge of computational power include all subfields ......
A geometric approach to the embedding calculus knot invariants
(2020-10-09)
In this thesis we consider two homotopy theoretic approaches to the study of spaces of knots: the theory of finite type invariants of Vassiliev and the embedding calculus of Goodwillie and Weiss, and address connections ...
Efficient Algorithms for Routing a Net Subject to VLSI Design Rules
(2020-12-17)
In this thesis we consider detailed routing, an important step in the design of integrated circuits. On large instances detailed routing requires packing millions of node-disjoint Steiner trees into a graph with hundreds ......
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. ...
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, ...
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 ...