Monthly Archives: September 2009

How to see the genus

Let be a polynomial in two variables; i.e. where each is non-negative, and the coefficients are complex numbers which are nonzero for only finitely many pairs . For a generic choice of coefficients, the equation determines a smooth complex curve … Continue reading

Posted in Visualization | Tagged , , , , | 7 Comments

Geometric structures on 1-manifolds

A geometric structure on a manifold is an atlas of charts with values in some kind of “model space”, and transformation functions taken from some pseudogroup of transformations on the model space. If is the model space, and is the … Continue reading

Posted in Lie groups | Tagged , , , , , , , , , , | 1 Comment

Roth’s theorem

I am in Kyoto right now, attending the twenty-first Nevanlinna colloquium (update: took a while to write this post – now I’m in Sydney for the Clay lectures). Yesterday, Junjiro Noguchi gave a plenary talk on Nevanlinna theory in higher dimensions … Continue reading

Posted in Diophantine approximation, Ergodic Theory | Tagged , , , | 10 Comments

The Goldman bracket

I was in Stony Brook last week, visiting Moira Chas and Dennis Sullivan, and have been away from blogging for a while; this week I plan to write a few posts about some of the things I discussed with Moira … Continue reading

Posted in Lie groups, Surfaces | Tagged , , , , , , | 5 Comments