The thematic semester will explore the close interactions between algebra, the theory of formal languages and combinatorics, as well as a variety of fundamental questions that appear naturally when one interleaves principal threads from combinatorics, algebra, geometry, representation theory, and number theory.
Combinatorics has a strong tradition of fruitful interactions with other domains of mathematics, some of which are emerging. The program will be centered on the exploration of the various links: between automata, automatic sequences, algebra and number theory; between combinatorics on words and discrete geometry; between group representation theory, reflection groups and combinatorics; as well as several questions from algebraic geometry and knot theory linked to intriguing combinatorial considerations.
The aim of the workshops is to bring together junior and senior mathematicians working in these exciting areas to discuss their research and to foster collaborations. In total, there will be four major workshops; each workshop is preceded by a week-long school to introduce junior mathematicians to the most recent developments in these areas.
A central aspect of the program will be a focus on scientific computation and experimental mathematics as prominent research tools. There will be introductory sessions dedicated to presenting the cutting-edge research tools in the various research areas.