Blog

Since I have had the experience to give two talks about maths topics which I found interesting, and in both cases I spent about a day researching them, I thought it would be a good idea to collect a list of things which one can spend a day or two and (I think) end up with a decent understanding of them (at least of the statement).1 These topics aren’t really in any particular order, and the content here might reflect my personal interests....

I gave a talk (to other undergraduates, and some PhD students here in Cambridge) about Groebner bases. I focused mostly on their applications, and did not really cover much about computing them, or the uniqueness (i.e. reduced Groebner bases). The notes can be found here.

I gave a talk (to fellow undergraduates in Maths here in Cambridge) about the topology, namely \(\pi_1(M)\) of manifolds with negative sectional curvature. In it, I covered Exponential map Sectional curvature Cartan-Hadamard (no proof) Cartan’s theorem about isometries with finite order Preissmann’s theorem Byers’ theorem (no proof) Milnor’s theorem about exponential growth of \(\pi_1(M)\) (no proof) The notes can be found here. The spaces are for diagrams which I drew in by hand (on paper)....