Being on a school about Feynman graphs and Motives, I just learned how these are related. It's a cute story! Actually, you don't need any physics to appreciate it, though physics might let you appreciate it even more.

A Feynman graph is just a (non-directed) graph with a finite number of vertices and a finite number of edges. Physicists are interested in computing certain integrals defined in terms of Feynman graphs, which they call amplitudes.

Continue reading «Feynman Graphs and Motives»

In this short rant, I want to convince you to try out some new beautiful fonts for your editor, terminal, wiki or website. In particular, I want you to take a look at Adobe's Source Pro Fonts. I'll explain where you can preview fonts online and how to employ them in various settings.

Continue reading «Beautiful New Fonts»

I have to admit that I try to read more than I actually do, in particular blog posts. In this post I give you some links from 2010 that I now read skimmed a few weeks ago and found to be fresh enough to be shared again.

Continue reading «From the Backlog 2010»

Given a vector bundle E-->X of rank r+1 one can take the projective space of lines in each fiber, which results in a projective bundle P(E)-->X. A projective bundle formula for a functor F from spaces to rings tells us that F(P(E)) is a free F(X)-module of rank r.

In this post I look at some computations around projective bundle formulae for the Chow ring, the algebraic K-Theory and the (Chow) motive of some spaces, in particular flag varieties. We recover some results from the previous posts on cohomology, cycles & bundles and motive of projective space.

Continue reading «Motives of Projective Bundles»

I want to explain a particularly easy example of a motivic cellular decomposition: That of $n$-dimensional projective space. The discussion started with cohomology (part 1), continued with bundles and cycles (part 2) and in this part 3, we discuss motivic stuff.

Continue reading «Invariants of projective space III: Motives»

I want to explain a particularly easy example of a motivic cellular decomposition: That of $n$-dimensional projective space. The discussion started with cohomology (part 1) and in this part 2, we discuss intersection-theoretic and bundle-theoretic invariants. In part 3 we will see the motivic stuff.

Continue reading «Invariants of projective space II: Cycles and Bundles»