Construction of Chern classes

Posted: Fri 20 April 2018
Filed under mathematics
Tags: differential-geometry vector-bundles

Characteristic classes

Given a manifold \(M\), one way to study vector bundles over \(M\) is to use the theory of characteristic classes. A characteristic class is a way of assigning to each vector bundle over \(M\) an element of the cohomology ring \(H^{\ast}(M, G)\). This assignment is not …

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A week at Berlin Mathematical School

Posted: Sat 24 February 2018
Filed under mathematics
Tags: travel math-talks

I spent the last week (18th to 24th February) at Berlin, courtesy Berlin Mathematical School, who invited me over for the BMS Days (where I had an interview for a PhD position), as well as the BMS Student Conference which immediately followed the BMS Days. I heard a lot of …

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Setting up GitLab to automatically generate PDFs from committed LaTeX files

Posted: Wed 17 January 2018
Filed under LaTeX
Tags: gitlab LaTeX

I had been meaning to get started with GitLab's continuous integration to generate PDFs of my assignments and notes, rather then generating the PDFs offline and committing them to the repository as well, but I always kept delaying the migration because of the lack of sufficient documentation on the matter …

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Cohomology as a measure of local to global failure

Posted: Mon 25 December 2017
Filed under mathematics
Tags: cohomology sheaves topology

Motivation for cohomology

In most introductory algebraic topology courses, cohomology is rather poorly motivated. It's most commonly seen form in an algebraic topology course is singular cohomology, which arises as a the homology of the dual of the singular chain complex, but that doesn't really tell you why it's of …

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