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Functional Inequalities and Heat Kernel Asymptotics on Some Classes of Singular Riemannian Manifolds
(2019-11-13)
This thesis consists of two parts.
In the first part we are focusing on stratified pseudomanifolds equipped with an iterated edge metric. More specifically, in Chapter 1 we give the basic definitions and review some ...
In the first part we are focusing on stratified pseudomanifolds equipped with an iterated edge metric. More specifically, in Chapter 1 we give the basic definitions and review some ...
Renormalisation in discrete elasticity
(2019-10-10)
This thesis deals with the statistical mechanics of lattice models. It has two main contributions. On the one hand we implement a general framework for a rigorous renormalisation group approach to gradient models. This ...
Open Topological Field Theories and 2-Segal Objects
(2019-10-17)
In this thesis we analyze 2-dimensional open topological field theories in both 1-categorical and ∞-categorical contexts. Making use of the formalism, introduced by Dyckerhoff and Kapranov, of graphs structured over a ......
Small embeddings, forcing with side conditions, and large cardinal characterizations
(2019-09-26)
In this thesis, we provide new characterizations for several well-studied large cardinal notions. These characterizations will be of two types. Motivated by seminal work of Magidor, the first type characterizes large ...
Statistical mechanics of gradient models
(2019-07-18)
In this thesis, we consider gradient models on the d-dimensional discrete lattice. These models serve as effective models for interfaces and are also known as continuous Ising models . The height of the interface is modelled ......
KPZ universality for last passage percolation models
(2019-09-12)
In this thesis we consider models of last passage percolation on the ℤ2. These models belong to the Kardar–Parisi–Zhang universality class, a class of stochastic growth models that have been widely studied ...
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 ...
Pointwise convergence, maximal functions and regularity issues in harmonic analysis
(2020-03-05)
This cumulative thesis is dedicated to the study of different maximal operators related to pointwise convergence in Fourier Analysis and is divided in three main parts.
The first part is dedicated to regularity results ...
The first part is dedicated to regularity results ...
Mapping Properties of Bäcklund Transformations and the Asymptotic Stability of Soliton Solutions for the Nonlinear Schrödinger and Modified Korteweg-de-Vries Equation
(2020-02-17)
We consider the cubic Nonlinear Schrödinger Equation (NLS) and the Modified Korteweg-de-Vries Equation (mKdV) in the one-dimensional, focusing case. For the mKdV, we also restrict ourselves to the case of real-valued ...
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 ...