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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
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
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
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
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 GaussBonnet theorem. 1. Triangles in Hyperbolic Space Suppose we are given … Continue reading
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