相关论文: Notes on universal algebra

These are expended notes of my talk at the summer institute in algebraic geometry (Seattle, July-August 2005), whose main purpose is to present a global overview on the theory of higher and derived stacks. This text is far from being…

After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…

These are lecture notes for a 4h mini-course held in Toulouse, May 9-12th, at the thematic school on "Quantum topology and geometry". The goal of these lectures is to (a) explain some incarnations, in the last ten years, of the idea of…

These lecture notes are meant to serve as an introduction to some geometric constructions and techniques (in particular the ones of toric geometry) often employed by the physicist working on string theory compactifications. The emphasis is…

This is the text of the lecture given by the author in Naples at "Giornata IndAM", June 7, 2005. The lecture is addressed at the general mathematical audience and reviews several topics in deformation theory of associative algebras.

This is an extended version of a talk presented by the second author on the Third Mile High Conference on Nonassociative Mathematics (August 2013, Denver, CO). The purpose of this paper is twofold. First, we would like to review the…

The aim of this note is to use the concept of algebra husks to prove an analog of the flattening decomposition theorem for simultaneous normalizations. Other applications improve earlier flatness criteria. Parts of this note were contained…

These are extended notes of a course given at Tulane University for the 2015 Clifford Lectures. Their aim is to present structure results for group schemes of finite type over a field, with applications to Picard varieties and automorphism…

These lecture notes are a personal introduction to signed graphs, concentrating on the aspects that have been most persistently interesting to me. They are just a few corners of signed graph theory; I am leaving out a great deal. The…

This article is an extended version of the minicourse given by the second author at the summer school of the conference "Interactions of quantum affine algebras with cluster algebras, current algebras and categorification", held in June…

These are notes for a mini-course given at the summer school and conference "The Six-Functor Formalism and Motivic Homotopy Theory" in Milan 9/2021. They provide an introduction to the formalism of Grothendieck's six operations in algebraic…

This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.

These notes reproduce the content of a short, 50-minutes, survey talk given at the Nice University in September, 2004. We added a few topics that have not been touched on in the lecture by lack of time.

This is a slightly edited version of the transparencies for a seminar at UCL, May 7, 2003. It is intended to give a quick view of background, ideas, and some calculations, in the applicatioon of some non commutative methods to algebraic…

A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs,…

The purpose of these notes is to give a categorical presentation/analysis of homotopy type theory. The notes are incomplete as they stand (October 2017). The chapter on univalent tribes is missing. The references are not always connected to…

The main purpose of this article is to develop an explicit derived deformation theory of algebraic structures at a high level of generality, encompassing in a common framework various kinds of algebras (associative, commutative, Poisson...)…

The aim of this paper is to review the deformation theory of $n$-Lie algebras. We summarize the 1-parameter formal deformation theory and provide a generalized approach using any unital commutative associative algebra as a deformation base.…

The present Lecture Notes have been prepared to back up a series of a few seminars given by the author at the Albert Einstein Institute in Potsdam. These Notes aim at reviewing a research project conducted over the last six years about a…

We develop some aspects of a general theory of presentations of subshifts by labelled directed graphs, in particular by compact graphs. Also considered are synchronization properties of subshifts that lead to presentations by countable…