Manon Stipulanti appointed FNRS Research associate at the University of Liège
Manon Stipulanti, who has a PhD in mathematics and is a researcher in the Discrete Mathematics Laboratory (Mathematics/Faculty of Science) at the University of Liège, has been awarded a research fellowship by the FNRS (Fonds National pour la Recherche Scientifique) to continue her research in the field of discrete mathematics and, more specifically, on the extension of Cobham's theorem to abstract numbering systems.
er passion for mathematics dates back to secondary school. At the time, Manon Stipulanti loved mathematics as much as Latin. A surprising duality? Not really! "For me, mathematics is like a game with more or less strict rules, the aim being to determine the right formalism to encode a problem and then solve it. In Latin, the game consists of a detailed analysis of the cases that make decoding an ancient text possible. So I naturally fell in love with word combinatorics in my Master's degree". This discipline is part of the field of discrete mathematics. The adjective 'discrete' is essentially opposed to 'continuous'. In statistics, a distinction is made between continuous variables (e.g. height), for which all values are possible, and discrete variables (e.g. the number of children), which can only take on specific precise values. "For example, a person could be 1.55 m tall, but not have 2.42 children. In discrete mathematics, we study fundamentally discrete objects. More specifically, in the combinatorics of words, the objects are... words! For us combinatorialists, a word is simply a sequence of letters. For example, "0110" is a word based on the letters 0,1. So, a word does not necessarily have a semantic meaning. In fact, mathematicians like abstraction, which allows them to detach themselves from real constraints and thus obtain a formalism that is as general as possible for dealing with strands of DNA and chunks of text".
Compared with other areas of mathematics, discrete mathematics is relatively recent, having been born with the advent of the computer. Consequently, discrete mathematics and computer science are two sciences that motivate and nourish each other. It is this link that makes them a rapidly expanding field. "What about my personal contribution to all this? I enjoy studying and understanding the structure of certain word families and detecting and understanding the patterns that occur in them." Manon Stipulanti's thesis work takes as its starting point an object well known to mathematicians: Pascal's triangle, which is built around binomial coefficients, and generalises it by using word combinatorics to obtain similar but more global properties than those known up to now.
Now that she has secured a permanent post at the FNRS, Manon Stipulanti plans to tackle more important questions, such as extending Cobham's theorem to abstract numeration systems. This theorem states that, if a word can be encoded in several ways and if these encodings are sufficiently different, then the structure of the starting word must be relatively simple. Here, the encodings are called "numbering systems". To date, only a small fraction of numbering systems have been studied, and my aim is to obtain the most general framework possible.
About Manon Stiupulanti
Manon Stipulanti holds a bachelor's degree and a master's degree in Mathematical Sciences from the University of Liège. She began her scientific career in 2010 when she was awarded the FRIA grant from the FNRS, which enabled her to do a thesis in the Discrete Mathematics research unit, under the co-supervision of Émilie Charlier and Michel Rigo. Manon Stipulanti will defend her dissertation 'Extensions of the Pascal Triangle to Words, and Related Counting Problems' on 2 April 2019. She will then be awarded a Francqui Foundation Fellow scholarship from the Belgian American Educational Foundation, Inc (B.A.E.F.) to spend a post-doctoral period in the Mathematics Department at Hofstra University (New York, USA), under the supervision of Eric Rowland. In 2021, she will be awarded the Karlson Prize for her thesis work. In parallel with her thesis subject and during her post-doctorates, Manon Stipulanti has been interested in many word combinatorics problems, joining forces with numerous international researchers (England, Canada, United States, France, Iran, Italy). An FNRS research fellow in the Discrete Mathematics Research Unit of the Mathematics Department at ULiège, under the co-supervision of Émilie Charlier and Michel Rigo, Manon Stipulanti is due to become a qualified researcher in 2023.