Related papers: Two minicourses on analytic microlocal analysis
Explaining sophisticated machine-learning based systems is an important issue at the foundations of AI. Recent efforts have shown various methods for providing explanations. These approaches can be broadly divided into two schools: those…
These are lecture notes for a mini-course given at the Cornell Probability Summer School in July 2013. Topics include lozenge tilings of polygons and their representation theoretic interpretation, the (q,t)-deformation of those leading to…
Recent advances in nano-fabrication techniques allow for the manufacture of optical metamaterials, bringing their unique and extra-ordinary properties to the visible regime and beyond. However, an analytical description of optical…
In this thesis, we address several important issues concerning the morphological analysis of Arabic language applied to textual data and machine translation. First, we provided an overview on machine translation, its history and its…
Most existing real estate appraisal methods focus on building accuracy and reliable models from a given dataset but pay little attention to the extensibility of their trained model. As different cities usually contain a different set of…
Four lectures on holography and the AdS/CFT correspondence applied to condensed matter systems. The first lecture introduces the concept of a quantum phase transition. The second lecture discusses linear response theory and Ward identities.…
Neural network pretraining is gaining attention due to its outstanding performance in natural language processing applications. However, pretraining usually leverages predefined task sequences to learn general linguistic clues. The lack of…
We summarize the parallel session B4: 'Analytic approximations, perturbation theory effective field theory methods and their applications' and the joint session B2/B4: 'Approximate solutions to Einstein equations: Methods and Applications',…
These lecture notes were written with the aim to provide an accessible though technically solid introduction to the logic of systematical analyses of statistical data to both undergraduate and postgraduate students, in particular in the…
This is the second volume of a textbook for a two-semester course in mathematical analysis. This second volume is about analysis of multi-variable functions. The topics covered include Euclidean spaces, convergence of sequences, open sets…
These are informal lecture notes for a three-hour minicourse on Kac-Moody groups, given at the workshop "Kac-Moody geometry" in July 2023 in Kiel. They provide a concise overview of the book "An introduction to Kac-Moody groups over…
This paper investigates the learning theory of Transformer networks for regression tasks on the compact Euclidean domain $[0,1]^d$ and $d$-dimensional compact Riemannian manifolds. We propose a novel constructive approximation framework for…
The aim of this paper is to give the text of a recent introduction to nonlinear generalized functions exposed in my talk in the congress gf2011, which was asked by several participants. Three representative topics were presented: two…
These are lecture notes from the Austral Winter School on Microlocal Analysis and Non-elliptic Fredholm Theory, held at the Australian National University, Canberra, June 30 -- July 11, 2025.
We develop a refined theory of microlocal analysis in the algebra ${\mathcal G}(\Omega)$ of Colombeau generalized functions. In our approach, the wave front is a set of generalized points in the cotangent bundle of $\Omega$, whereas in the…
This article contains the lecture notes for the short course ``Introduction to Econophysics,'' delivered at the II Brazilian School on Statistical Mechanics, held in Sao Carlos, Brazil, in February 2004. The main goal of the present notes…
This habilitation thesis is cumulative and, therefore, is collecting and connecting research that I (together with several co-authors) have conducted over the last few years. Thus, the absolute core of the work is formed by the ten…
In this second installment of a series of two papers on the $\tfrac{1}{2}$-BPS Wilson line defect CFT in $\mathcal{N}=4$ super Yang-Mills, we focus on dynamical aspects of the theory, in particular studying four-point functions with…
These lecture notes give an exposition of microlocal analysis methods in the study of Quantum Field Theory on curved spacetimes. We concentrate on free fields and the corresponding quasi-free states and mainly on Klein-Gordon fields.Updated…
This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of…