Related papers: Lectures on algebraic categorification
A program for categorifying measure theory is outlined.
This is a lecture note for the course DS-GA 3001 <Natural Language Understanding with Distributed Representation> at the Center for Data Science , New York University in Fall, 2015. As the name of the course suggests, this lecture note…
In this paper the authors discuss their experiences with ungrading at a small public university in the U.S. as well as a large public university in Germany. The courses described are Calculus 1, Mathematics for Liberal Arts, and courses for…
These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…
These lectures discuss recent advances on syzygies on algebraic curves, especially concerning the Green, the Prym-Green and the Green-Lazarsfeld Secant Conjectures. The methods used are largely geometric and variational, with a special…
Lecture notes of a tutorial on Combinatorial Hodge Theory in Simplicial Signal Processing held at international conference for digital audio effects (DAFx-23) in Copenhagen, Denmark.
This in an introduction to free probability theory, covering the basic combinatorial and analytic theory, as well as the relations to random matrices and operator algebras. The material is mainly based on the two books of the lecturer, one…
The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…
This article contains a slightly expanded version of the lectures given by the author at the summer school "Algebraic stacks and related topics" in Mainz, Germany from August 31 to September 4, 2015. The content of these lectures is purely…
These notes are loosely based on lectures given at the CERN Winter School on Supergravity, Strings and Gauge theories, February 2009 and at the IPM String School in Tehran, April 2009. I have focused on a few concrete topics and also on…
This paper is an extended version of four lectures at PIMS in Vancouver given June 27 - 30, 2016. The primary goal of these lectures was to publicize the author's recent efforts to extend to representations of linear algebraic groups the…
This survey article is based on 10 lectures that we gave at the September 2019 Hausdorff School in Bonn on "the Emerton--Gee stack and related topics", and the sections correspond to the original lectures. We have retained the somewhat…
Lectures presented at the Les Houches 2016 Summer School "Integrability: from Statistical Systems to Gauge Theory".
Algorithmic classification of research publications has been created to study different aspects of research. Such classifications can be used to support information needs in universities for decision making. However, the classifications…
This is a survey on permutation classes for the upcoming book Handbook of Enumerative Combinatorics.
We classify gradings on matrix algebras by a finite abelian group. A grading is called good if all elementary matrices are homogeneous. For cyclic groups, all gradings on a matrix algebra over an algebraically closed field are good. We can…
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…
These lectures give a brief introduction to the Computer Algebra systems Reduce and Maple. The aim is to provide a systematic survey of most important commands and concepts. In particular, this includes a discussion of simplification…
The following is an exposition of a course of algebra that Prof. Aleksandr Aleksandrovich Zykov (1922-2013) distributed among the participants of his seminar in graph theory not far away from Odessa, Ukraine, on September, 1991. It is a…
Lecture given Thursday 22 October 1992 at a Mathematics-Computer Science Colloquium at the University of New Mexico. The lecture was videotaped; this is an edited transcript.