相关论文: Potpourri, 6

These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.

These notes deal with a few properties of convolutions in the role of approximations to the identity.

These informal notes consider Fourier transforms on a simple class of nice functions and some basic properties of the Fourier transform.

These informal notes deal with Fourier series in one or more variables, Fourier transforms in one variable, and related matters.

These are the notes from my courses on the arithmetic of quadratic forms.

These Course Notes provide an introduction to mathematical proofs for undergraduate students transitioning from computational calculus to abstract mathematics. Topics include propositional logic, proof techniques, mathematical induction,…

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…

Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.

These informal notes concern some basic themes of harmonic analysis related to representations of groups.

In these lectures notes I discuss the Linearization Theorem for Lie groupoids, and its relation to the various classical linearization theorems for submersions, foliations and group actions. In particular, I explain in some detail the…

These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…

These notes gather recent results on robust statistical learning theory. The goal is to stress the main principles underlying the construction and theoretical analysis of these estimators rather than provide an exhaustive account on this…

The note complements topological aspects of the theory of chiral algebras.

In this paper we give a simple Torelli type theorem for curves of genus 6 and 8 by showing that these curves can be reconstructed from their Brill-Noether varieties. Among other results, it is shown that the focal variety of a general,…

This is an informal set of lecture notes on moduli spaces of curves based on a set of lectures given at the ICTP last summer. It begins at an elementary level and discusses the genus 1 case in detail. The notes then give an informal…

The aim of these notes is to give a introduction to the ideas and techniques of handling rational curves on varieties. The main emphasis is on varieties with many rational curves which are the higher dimensional analogs of rational curves…

These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.

We give some results on quadratic normality of reducible curves canonically embedded and partially extend this study to their projective normality.

These informal notes briefly discuss some basic topics in harmonic analysis along the lines of convolutions and Fourier transforms.

These are notes from a mini-course about the main results of arXiv:2206.03438: I explain how, using suitable valued fields, one obtains a natural notion of canonical stratifications (of e.g. algebraic subsets of $\mathbb{R}^n$). I also…