I will start with the well-known subject of addition chains, which describe the best possible ways of raising an element to a certain power, in any group (or even monoid). These are used by all computer algebra packages, when you request them to compute a high power of a large matrix, for example. Then I will say a word about the more general problem of computing in other groups, facing questions such as: when A and B are matrices, how many multiplications do you need to compute ABABABABABABABABABABABABABABABAB ? (Answer: just 4.) Very little is known in general. Finally, I will explain how similar ideas can be used to describe the "assembly index" of any object, as was recently exploited by chemists. It turns out that the assembly index of molecules can be measured experimentally rather than computed, and this opens up the possibility of detecting the presence of life on other planets. Accordingly, the talk will end with pictures of aliens.
The seminar will be also broadcasted via BBB: https://bbb.unistra.fr/b/hum-51d-suf-mzq
Pierre Guillot is a reader in mathematics at the university of Strasbourg, and a researcher at IRMA. He obtained his PhD at the university of Cambridge (UK) in 2004, was a postdoctoral fellow in Lille and Nice before being appointed lecturer at Strasbourg. His research interests include group cohomology, Galois theory, algebraic topology and computational algebra.