Pauli Lectures 2015

In recent years, mathematical algorithms have helped art historians and art conservators putting together the thousands of fragments into which an unfortunate WWII bombing destroyed world famous frescos by Mantegna, decide that certain paintings by masters were “roll mates” (their canvases were cut from the same bolt), virtually remove artifacts in preparation for a restoration campaign, get more insight into paintings hidden underneath a visible one,…
The presentation will review these applications, and give a glimpse into the mathematical aspects that make this possible.

The talk will present mathematical explorations motivated by the need of biological morphologists to compare different phenotypical structures. At present, scientists using physical traits to study evolutionary relationships among living and extinct animals analyze data extracted from carefully defined anatomical correspondence points (landmarks). Identifying and recording these landmarks is time consuming and can be done accurately only by trained morphologists. This necessity renders these studies inaccessible to non-morphologists and causes phenomics to lag behind genomics in elucidating evolutionary patterns.

Unlike other algorithms presented for morphological correspondences, the approach presented in the talk does not require any preliminary marking of special features or landmarks by the user. It also differs from other seminal work in computational geometry in that the algorithms are polynomial in nature and thus faster, making pairwise comparisons feasible for significantly larger numbers of digitized surfaces.

This approach has already been used by biologists to obtain new results.
And there are many further avenues to be explored!

Via internet we can download images from all over the world. Most of these are compressed in some way, to make the transmission and storage more efficient. Mathematics plays an important role in these compression techniques, which we shall explore in the lecture.