July 9th, 2024

Speaker:
Sergei Tabachnikov (The Pennsylvania State University)

Title:
Elastica, filament equation, and bicycle modelsAbstract:
Elastica are solutions to a classic variational problem of Bernoulli: to describe the curves of fixed lengths that extremize the bending energy. I will describe several problems where these ubiquitous curves appear.
One is the study of the filament equation, a completely integrable evolution on curves that models the propagation of vortices in liquid or gas. Another is a simple model of a bicycle, presented as a directed segment of a fixed length that can move so that the velocity of the rear end is always aligned with the segment. A bicycle path is a motion of the segment, subject to this nonholonomic constraint, and the length of the path, by definition, is the length of the front track. This defines a problem of subRiemannian geometry, and the respective geodesics are closely related to classical elastica and its "relatives". Another bicycle problem where elastica appears is as follows: given the front and rear bicycle tracks, can one determine which way the bicycle went?Schedule:
10:00  11:30 RTG Lecture 1 (Manuel Krannich)  5. OG, Konferenzraum
11:30  12:00 GetTogether with speaker  5. OG, Common Room
12:00  13:00 Common lunch  reserved at BräuStadel
13:00  13:30 Informal meeting of PhD students  5. OG, Common Room
13:30 14:30 RTG colloquium: Sergei Tabachnikov  EG, Seminarraum C
14:30  15:15 Common tea  5. OG, Common Room
15:15  16:45 RTG Lecture 2 (Manuel Krannich)  5. OG, Konferenzraum

Place:
HD