What is an "a priori estimate"?

Posted: Tue 18 December 2018
Filed under mathematics
Tags: analysis

One of the things a math major learns in their first proof based course is that one must prove existence of objects before going on to prove any properties about them. After a few years, this becomes almost second nature, and most pure mathematicians are wary of making claims about …

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The most overloaded word in math

Posted: Sun 14 October 2018
Filed under mathematics
Tags: nomenclature

Last Wednesday, the conversation in my office veered towards the words we hated the most in math. Not surprisingly, the list included the usual suspects like normal, simple, and regular. It's probably the same reason that these words also make it to the top five of this MathOverflow post. These …

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An algebraic definition of the cotangent space

Posted: Sat 30 June 2018
Filed under mathematics
Tags: differential-geometry algebraic-geometry

I'm almost a week into the algebraic geometry workshop now, and I've learnt a lot. I've learnt a few things about varieties, and also a bit of commutative algebra, but the most important takeaway for me from the first week was the sheaf theoretic way of looking at smooth manifolds …

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Summer 2018 update

Posted: Sat 02 June 2018
Filed under personal
Tags: personal

I'm getting lazy. I thought I would be posting more often once the summer holidays started but May came and went with nary a post. In my defence, I was fairly busy, dealing with the usual bureaucratic nonsense that comes with leaving your institution for good and moving to another …

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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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