Related papers: Potpourri, 11
These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.
Motivated by recent interest concerning "puncture repair" in the conformal geometry of compact Riemannian manifolds, a brief exposition on generalisation to the setting of quasiconformal mappings on certain metric measure spaces is…
Lectures notes (in italian) of some arguments of classical analysis, with exercises. A particular emphasis to functional analysis and elementary operator algebra theory is given, by means of exercises and examples.
These notes provide an elementary (and incomplete) sketch of the objects and ideas involved in monstrous and umbral moonshine. They were the basis for a plenary lecture at the 18th International Congress on Mathematical Physics, and for a…
Here we consider a few topics related to Lipschitz classes for functions and curves in metric spaces.
These notes briefly discuss basic notions concerning locally compact abelian topological groups and Fourier transforms of functions on them.
This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.
This short note describes a connection between algorithmic dimensions of individual points and classical pointwise dimensions of measures.
The purpose of this short note is to show the interplay between math outreach and conducting original research, in particular how each can build off the other.
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 are the notes from my courses on the arithmetic of quadratic forms.
This note is a survey of Analysis on Metric spaces, in connection with the upcoming AMS Mathematics Research Communities program in June 2020.
We survey recent results on the study of metric measure spaces satisfying a Poincar\'e inequality. We overview recent characterizations in terms of objects of dimension 1, such as pencil of curves, modulus estimates and obstacle-avoidance…
This article discusses several matters related to Sobolev, Poincare, and isoperimetric inequalities in various settings.
We give an informal survey, emphasizing examples and open problems, of two interconnected research programs in moduli of curves: the systematic classification of modular compactifications of $M_{g,n}$, and the study of Mori chamber…
These notes deal with a few properties of convolutions in the role of approximations to the identity.
These notes briefly discuss Fourier transforms of finite measures and extensions of Fourier integrals to points in complex domains.
In the recent work [Metrically round and sleek metric spaces, \emph{The Journal of Analysis} (2022), pp 1--17], the authors proved some results on metrically round and sleek linear metric spaces and metric spaces. In continuation, the…
These are notes on adic spaces. They are made available upon some requests in order to make quoting them easier.
This informal note collects key results and open problems on the (co)homology of the Deligne-Mumford moduli spaces of real marked rational curves. The open problems are both of topological nature, aiming to investigate the (co)homology of…