After 10 months of being unable to come up with anything interesting to post on the blog, I realized it might be a good idea use this blog to keep track of the math I've been working on. That way my blog can act as a public version of my …

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 …

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 …

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 …

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 …

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 …