DCL Seminar Series: Maxim Arnold "Evolutes of the ideal polygons"

Decision and Control Laboratory Lecture Series

Coordinated Science Laboratory

 

Evolutes of the ideal polygons

Maxim Arnold

Assistant Professor

Department of Mathematics

University of Texas at Dallas

 

Wednesday, October 31, 2018

3:00 p.m. to 4:00 p.m.

CSL Auditorium (B02)

Title:  Evolutes of the ideal polygons

Abstract:

Evolute of the plane curve - the locus of all normals to it, can be described as the set of centers of all osculating circles. Thus, one can consider an evolute of the polygon in the same manner, i.e. the set of the centers of particular discretization of osculating circles. The latter construction can be then propagated to the hyperbolic plane, inducing the mapping from hyperbolic polygon to its evolute. This mapping seems to have deep connections with various areas of mathematics. I will report on the progress in ongoing research of the properties of this mapping. The talk is based on joint work with I.Izmestiev, S.Tabachnikov and D. Fuchs.

Bio:

Maxim Arnold recieved his M.S. from Moscow State University in 2003, Then received PhD at Russian Academy of Sciences in 2005. Then spent one year as a Canada Research Chair postdoc in McMaster University, after which returned back to Moscow to spend four years as a head of the laboratory in the International Institute of the Earthquakes Prediction Theory. Then spent 2011-2013 as a Research Assistant at Math Department at UIUC. From 2014 until now he is an assistant professor at University of Texas at Dallas.