Related papers: A Practical Mini-Course on Applied Holography
In this lectures given at the Morning side center of Mathematics in October 2016, we present in a very simple framework Hilbertian hypocoercive methods in the case of 1d kinetic inhomogeneous equations, and some illustrations concerning…
In this lecture note, we give a basic introduction to the rapidly developing concepts of generalized symmetries, from the perspectives of both high energy physics and condensed matter physics. In particular, we emphasize on the (invertible)…
The pseudo entropy is a promising recent generalization of the entanglement entropy to the situations in which both the initial and final state are involved, with the density matrix promoted to the transition matrix. However, in contrast to…
We will cover the basics of several complex variables in 4 lectures: Basic properties of holomorphic functions in several variables, the notion of pseudoconvexity, CR functions and CR geometry, and the $\bar\partial$-problem. The main…
This last document is showing the gradual introduction of hierarchical modeling techniques in image analysis. The first chapter is dealing with the first works carried out in the field of industrial applications of pattern recognition. The…
This lecture note is written for 'Courses on Light-Cone Techniques applied to QCD', Nov 21-25, 2022, IGFAE. It is intended to provide basic knowledge and selective perspectives on the application of light-front Hamiltonian approach to…
These lecture notes for the IAS/Park City Graduate Summer School in Geometric Combinatorics (July 2004) provide an overview of poset topology. These notes include introductory material, as well as recent developments and open problems. Some…
Dataset distillation is attracting more attention in machine learning as training sets continue to grow and the cost of training state-of-the-art models becomes increasingly high. By synthesizing datasets with high information density,…
This paper shares a classroom story from Fall 2022 to Spring 2025 about a learner centered routine in undergraduate mathematics. I use four steps: an opening question, a short mini lecture about meaning, structured small group work, and a…
We rederive AdS/CFT predictions for infrared two-point functions by an entirely four dimensional approach, without reference to holography. This approach, originally due to Migdal in the context of QCD, utilizes an extrapolation from the…
Over the last twenty five years, holographic duality has revolutionised our understanding of gauge theories, quantum many-body systems and also quantum black holes. This topical issue is a collection of review articles on recent advances in…
In this thesis, I study Interface Conformal Field Theories (ICFT) and their holographic dual, which is composed of two asymptotically Anti-de-Sitter (AdS) spaces glued through a thin gravitating membrane. I restrict the study to simple…
In this article we explore the holographic approach to neutron stars in the realm of Quantum Field Theory (QFT). We delve into the structures of neutron stars, emphasizing the application of the AdS/CFT duality in modeling them. We discuss…
Despite its potential for label-free particle diagnostics, holographic microscopy is limited by specialized processing methods that struggle to generalize across diverse settings. We introduce a deep learning architecture leveraging human…
These are lectures notes for the introductory graduate courses on geometric complexity theory (GCT) in the computer science department, the university of Chicago. Part I consists of the lecture notes for the course given by the first author…
The present lectures were prepared for the Faro International Summer School on Factorization and Integrable Systems in September 2000. They were intended for participants with the background in Analysis and Operator Theory but without…
These are the lecture notes that accompanied the course of the same name that I taught at the Eindhoven University of Technology from 2021 to 2023. The course is intended as an introduction to neural networks for mathematics students at the…
Since 2016, deep learning (DL) has advanced tomographic imaging with remarkable successes, especially in low-dose computed tomography (LDCT) imaging. Despite being driven by big data, the LDCT denoising and pure end-to-end reconstruction…
This is a short review of recent developments in the application of AdS/CFT methods to some condensed matter problems. In particular we present the holographic description of a local quantum critical state, related to (non)-Fermi liquids…
In this thesis we study two different approaches to holography, and comment on the possible relation between them. The first approach is an analysis of the high-energy regime of quantum gravity in the eikonal approximation, where the theory…