We'll discuss three examples (lattices, translation surfaces, hyperbolic surfaces) of computing the variance of natural counting problems for random geometric structures. All of them can be viewed as generalizations of the space of flat structures on the two-dimensional torus. We'll carefully discuss this base example, and the three different generalizations. This talk should be accessible to those with some familiarity with real and complex analysis at a first-year graduate level. In the first example, we'll discuss lattices, and some joint work with G. Margulis; in the second, translation surfaces, and joint work with Y. Cheung and H. Masur, and in the third, hyperbolic surfaces, and joint work with F. Arana-Herrera.
Colloquium
Thursday, March 24
4:30pm MST/AZ
Virtual via Zoom
Zoom: https://asu.zoom.us/j/89069977590?pwd=YVpKVGdUSFc0UzZUQmVTdzZueXNnUT09
Jayadev Athreya
Professor
University of Washington