Category Archives: Geometric structures

Slightly elevated Teichmuller theory

Last week at my invitation, David Dumas spoke in the U Chicago geometry seminar and gave a wonderful introductory talk on the theory of convex real projective structures on surfaces. This is the first step on the road to what is colloquially known … Continue reading

Posted in Complex analysis, Geometric structures, Projective geometry, Surfaces | Tagged , , , , , | 1 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

Characteristic classes of foliations

I recently learned from Jim Carlson’s blog of the passing of Harsh Pittie on January 16 this year. I never met Harsh, but he is very familiar to me through his work, in particular for his classic book Characteristic classes … Continue reading

Posted in Foliations, Geometric structures, Lie groups | Tagged , , , | 1 Comment

Hyperbolic Geometry Notes #2 – Triangles and Gauss Bonnet

In this post, I will cover triangles and area in spaces of constant (nonzero) curvature. We are focused on hyperbolic space, but we will talk about spheres and the Gauss-Bonnet theorem. 1. Triangles in Hyperbolic Space Suppose we are given … Continue reading

Posted in Euclidean Geometry, Geometric structures, Hyperbolic geometry, Surfaces, Uncategorized | 2 Comments

Causal geometry

On page 10 of Besse’s famous book on Einstein manifolds one finds the following quote: It would seem that Riemannian and Lorentzian geometry have much in common: canonical connections, geodesics, curvature tensor, etc. . . . But in fact this … Continue reading

Posted in Geometric structures, Lie groups, Symplectic geometry | Tagged , , , , , , | 2 Comments