notes

Personal notes that have grown enough over time to see the light of day.

1. Construction of dual spaces with respect to an isomorphism
   This short note describes a construction related to extrapolated spaces, spaces of negative norm and Gelfand triples, in which one uses an isomorphism together with three spaces connected by inclusions to construct a new space. This space identifies isometrically with the topological dual of the intermediate space and admits a natural extension of the initial isomorphism that preserves this property.

2. Anil Hirani’s lectures on discrete exterior calculus (DEC) - Oxford
   These notes pertain to a series of lectures on Discrete Exterior Calculus (DEC) given by Prof. Anil Hirani at the University of Oxford, from 31 August to 4 September, while hosted by Prof. Kaibo Hu. The material was taken primarily from my handwritten lecture notes. However, I have tried to elaborate and formalise ideas drawing on the relevant references. In addition, I have added my own perspective whenever it seemed helpful for my own understanding. [In process..]