Institute for Fundamental and Interdisciplinary Mathematical Research Seminar:

Speaker: Prof. Giorgi Khimshiashvili

“Analytically solvable pursuit problems with geometric constraints”

Planar pursuit problems with geometric constraints of the lifeline type and non-zero capture radius type will be considered. It will be shown that an analytic solution to the Apollonius pursuit problem with non-zero capture can be given in terms of the so-called Cartesian ovals of the fourth degree. Specifically, the minimal pursuit time can be expressed as the minimal positive root of a certain quartic polynomial, which implies that the optimal direction of pursuit can also be expressed by an explicit formula. In the Apollonius setting with a lifeline we’ll compute the optimal pursuit direction for a given direction of escape, which will yield the direction of escape with the maximal capture time. Several open problems for further exploration will also be presented.

Time: November 3, 17:00-19:00