## Peter J. Olver (09/06/17)

Math Colloquium

### Speaker: Peter J. Olver, University of Minnesota

### Title: Equivalence, Invariants, Puzzles, and Cancer

Location: Tg-227 (Tæknigarður, 2. hæð)

Time: Friday 9 June at 16:00

### Abstract:

A fundamental issue in computer vision is recognizing when two objects in an image are the “same”. The underlying mathematical apparatus for studying such equivalence problems is transformation group (or, more generally, groupoid) theory. Cartan’s solution to the equivalence and symmetry problem for submanifolds relies on the associated geometric invariants, through what is now known as the differential invariant signature. Furthermore, the new equivariant approach to the method of moving frames provides a systematic and algorithmic approach that can be applied to very general Lie group and even Lie pseudo-group actions. The talk will conclude with recent applications to automated assembly of broken objects, such as jigsaw puzzles, and cancer detection.