Related papers: Lectures on infinity categories
This is a write-up of a talk given at the CATMI meeting in Bergen in July 2023, and is an introduction to a category-theoretic perspective on metric spaces. A metric space is a set of points such that between each pair of points there is a…
This preprint concerns Banach spaces of functions converging at infinity. In particular, spaces of continuous functions, Lebesgue spaces and sequence spaces. In each framework we show versions of Riesz's representation theorem.
We study localizations of infinity categories that remain localizations after any base change.
These are lecture notes compiled for a short lecture series at the 2023 Condensed Matter Summer School at the University of Minnesota. They are designed to be conversational and fun, and not to take the place of review articles that do a…
Here we consider a few topics related to Lipschitz classes for functions and curves in metric spaces.
We define a notion of "theory of (1,infty)-categories", and we prove that such a theory is unique up to equivalence.
The authors describe their approach to teaching a course on finite fields and combinatorial applications, including block designs and error-correcting codes, using a hybrid of lectures and active learning. Under the discussed classroom…
This is a written version of a series of lectures aimed at undergraduate students in astrophysics/particle theory/particle experiment. We summarize the important progress made in recent years towards understanding high energy astrophysical…
This text is dedicated to the development of the theory of $(\infty,\omega)$-categories. We present generalizations of standard results from category theory, such as the lax Grothendieck construction, the Yoneda lemma, lax (co)limits and…
We study a metric-like structure on categories, showing that the concept of the limit of a sequence in a metric space and the concept of the colimit of a sequence in a category have a common generalization. The main concept is a norm on a…
PhD Thesis--A compilation of the papers: "Lower Bounds for Identifying Codes in Some Infinite Grids", "Improved Bounds for r-identifying Codes of the Hex Grid", and "Vertex Identifying Codes for the n-dimensional Lattics" along with some…
Notes from a course on linear dynamics given by the author at the University of Da Nang in January 2024.
Introduction to the Lecture Note Volume "ITEP Lectures in Particle Physics", including 25 years of personal reminiscences.
These are lecture notes on Floer and Rabinowitz-Floer homology written for a graduate course at UNICAMP August-December 2016 and a mini-course held at IMPA in August 2017.
These notes were written for a set of three lectures given in a school at the Max Planck Institute for the Physics of Complex Systems in October/2017 before the workshop "Critical Stability of Quantum Few-Body Systems". These lectures are…
These lectures on supersymmetry and extra dimensions are aimed at finishing undergraduate and beginning postgraduate students with a background in quantum field theory and group theory. Basic knowledge in general relativity might be…
These lecture notes have been converted to a book titled Network Information Theory published recently by Cambridge University Press. This book provides a significantly expanded exposition of the material in the lecture notes as well as…
Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study. In this paper, we consider the basic theory of infnite…
These notes represent approximately one semester's worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications:…
This preprint was split in two and became the first two parts of a four-part series (arXiv:1405.1956, arXiv:1405:1955, and two in preparation). The remaining relevance of this preprint is due to the series of videotaped lectures (wClips)…