Related papers: A Practical Mini-Course on Applied Holography
This is an updated version of the lectures notes for a course on condensed mathematics taught in the summer term 2019 at the University of Bonn. The material presented is joint work with Dustin Clausen. This is intended as a stable citable…
This is a concise review of holographic superconductors and superfluids. We highlight some predictions of the holographic models and the emphasis is given to physical aspects rather than to the technical details, although some references to…
The purpose of these lecture notes is to give a quick and introductory overview of holographic superconductors. Besides the actual description of the standard holographic superconductor, attention is paid to the motivations and the relation…
Recently delivered lectures on Self-Referential Mathematics, [2], at the Department of Mathematics and Applied Mathematics, University of Pretoria, are briefly presented. Comments follow on the subject, as well as on Inconsistent…
Matrix operations such as matrix inversion, eigenvalue decomposition, singular value decomposition are ubiquitous in real-world applications. Unfortunately, many of these matrix operations so time and memory expensive that they are…
These are lectures notes for a 4h30 mini-course held in Ulaanbaatar, National University of Mongolia, August 5-7th 2015, at the summer school "Stochastic Processes and Applications". It aims at presenting an introduction to basic results of…
In this article, we review recent progresses on the holographic understandings of the entanglement entropy in the AdS/CFT correspondence. After reviewing the general idea of holographic entanglement entropy, we will explain its applications…
These lecture notes are based on an introductory course given by the author at the summer school "Noncommutative Algebraic Geometry" at MSRI in June 2012. The emphasis throughout is on examples to illustrate the many different facets of…
The AdS/CFT correspondence is a realization of the holographic principle in the context of string theory. It is a map between a quantum field theory and a string theory living in one or more extra dimensions. Holography provides new tools…
The holographic principle asserts that the complete description of the interior of a sphere is a theory which not only lives on the surface of the sphere, but also has A/4 binary degrees of freedom. In this context we revisit the question…
These are lecture notes for a short course about spectral sequences that was held at M\'alaga, October 18--20 (2016), during the "Fifth Young Spanish Topologists Meeting". The approach was to illustrate the basic notions via fully computed…
The past few years have witnessed a remarkable crossover of string theoretical ideas from the abstract world of geometrical forms to the concrete experimental realm of condensed matter physics. The basis for this --- variously known as…
Inline holographic imaging presents an ill-posed inverse problem of reconstructing objects' complex amplitude from recorded diffraction patterns. Although recent deep learning approaches have shown promise over classical phase retrieval…
These are the notes for a series of Numerical Study group meetings, held in Lorentz institute in the fall of 2017. The aim of the notes is to provide a non-specialist with the minimal knowledge in numerical methods used in BVP for PDEs,…
Emerging learned holography approaches have enabled faster and high-quality hologram synthesis, setting a new milestone toward practical holographic displays. However, these learned models require training a dedicated model for each set of…
Humans are capable of learning new concepts from small numbers of examples. In contrast, supervised deep learning models usually lack the ability to extract reliable predictive rules from limited data scenarios when attempting to classify…
By 2025, holotomography (HT) has matured from a niche optical modality into a versatile platform for quantitative, label-free imaging in biomedicine. By reconstructing the three-dimensional refractive-index (RI) distribution of cells and…
These are the notes of the three lectures I delivered at the mini-workshop "Knot Theory and Number Theory around the A-Polynomial" at the Instituto Superior Tecnico (IST) in Lisbon in January 2014. The goal of the lectures was to…
In-context Learning (ICL) utilizes structured demonstration-query inputs to induce few-shot learning on Language Models (LMs), which are not originally pre-trained on ICL-style data. To bridge the gap between ICL and pre-training, some…
These notes contain part of the lectures of an introductory course on orthogonal polynomials and special functions that I gave in the joint PhD Program in Mathematics UC|UP in the academic years 2015-2016 (at University of Porto) and…