Monotone Twist Maps and Dowker-Type Theorems

Explore the fascinating world of monotone twist maps and Dowker-type theorems in this engaging lecture by Peter Albers from the University of Heidelberg. Delve into the intriguing relationship between planar ovals and inscribed or circumscribed polygons, examining the sequences formed by their areas. Discover how Dowker's theorem connects to the concavity and convexity of these sequences. Investigate the four classic results attributed to Dowker, Molnár, and Eggleston, which encompass areas and perimeters of inscribed and circumscribed polygons. Learn how these findings are manifestations of the convexity property in Mather's β-function within billiard-type systems. Gain insights into new geometric inequalities derived for various billiard systems, both well-studied and novel. Join this Western Hemisphere Virtual Symplectic Seminar to uncover the intricate connections between geometry, billiards, and mathematical theorems in this collaborative work with Sergei Tabachnikov.