学术报告报告主题: Siegel-Veech Constants of Cyclic Covers of Generic Translation Surfaces
报 告 人: David Aulicino (Associate Professor)
报告时间: 2024年1月9日（星期二）下午15:30-17:00
报告地点: 清清文理楼 3A02
邀 请 人: 潘会平 副教授
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数学学院
2024年 1月4日
报告摘要：We consider generic translation surfaces of genus g>0 with marked points and take covers branched over the marked points such that the monodromy of every element in the fundamental group lies in a cyclic group of order d. Given a translation surface, the number of cylinders with waist curve of length at most L grows like L^2. By work of Veech and Eskin-Masur, when normalizing the number of cylinders by L^2, the limit as L goes to infinity exists and the resulting number is called a Siegel-Veech constant. The same holds true if we weight the cylinders by their area. Remarkably, the Siegel-Veech constant resulting from counting cylinders weighted by area is independent of the number of branch points n. All necessary background will be given and a connection to combinatorics will be presented. This is joint work with Aaron Calderon, Carlos Matheus, Nick Salter, and Martin Schmoll.
报告人介绍：David Aulicino is an Associate Professor at Brooklyn College and the Graduate Center of CUNY. He received his Ph.D. from the University of Maryland under Giovanni Forni and held postdoctoral positions at the University of Chicago and the University of Paris. He has been funded by the National Science Foundation and currently the Simons Foundation.