Category Archives: Complex analysis

Groups quasi-isometric to planes

I was saddened to hear the news that Geoff Mess recently passed away, just a few days short of his 54th birthday. I first met Geoff as a beginning graduate student at Berkeley, in 1995; in fact, I believe he gave the … Continue reading

Posted in 3-manifolds, Complex analysis, Groups, Hyperbolic geometry, Uncategorized | Tagged , , , , , | Leave a comment

Kähler manifolds and groups, part 2

In this post I hope to start talking in a bit more depth about the global geometry of compact Kähler manifolds and their covers. Basic references for much of this post are the book Fundamental groups of compact Kähler manifolds by … Continue reading

Posted in Algebraic Geometry, Complex analysis, Geometric structures, Groups | Tagged , , , , , , , , | Leave a comment

Kähler manifolds and groups, part 1

One of the nice things about living in Hyde Park is the proximity to the University of Chicago. Consequently, over the summer I came in to the department from time to time to work in my office, where I have … Continue reading

Posted in Algebraic Geometry, Complex analysis, Geometric structures, Lie groups | Tagged , , , , | 8 Comments

Liouville illiouminated

A couple of weeks ago, my student Yan Mary He presented a nice proof of Liouville’s theorem to me during our weekly meeting. The proof was the one from Benedetti-Petronio’s Lectures on Hyperbolic Geometry, which in my book gets lots … Continue reading

Posted in Complex analysis, Euclidean Geometry, Rigidity | Tagged , , , | 7 Comments

Kenyon’s squarespirals

The other day by chance I happened to look at Richard Kenyon’s web page, and was struck by a very beautiful animated image there. The image is of a region tiled by colored squares, which are slowly rotating. As the … Continue reading

Posted in Complex analysis, Euclidean Geometry | Tagged , , , , | 19 Comments

Circle packing – theory and practice

I am spending a few months in Göttingen as a Courant Distinguished Visiting Professor, and talking a bit to Laurent Bartholdi about rational functions — i.e. holomorphic maps from the Riemann sphere to itself. A rational function is determined (up … Continue reading

Posted in Complex analysis, Visualization | Tagged , | 5 Comments

Minimal laminations with leaves of different conformal types

The “header image” for this blog is an example of an interesting construction in 2-dimensional conformal geometry, due to Richard Kenyon, that I learned of some time ago; I thought it might be fun to try to explain where it … Continue reading

Posted in Complex analysis, Surfaces | Tagged , , , , , , | 8 Comments