PhD Position in Communication Structures in Tilings

This PhD position is hosted by the MOCQUA team at Inria, which specializes in the intersection of discrete computation and continuous mathematics. The research focuses on identifying and defining mathematical structures that capture the communication required between cells to produce valid tilings under specific constraints. The successful candidate will investigate the properties of these structures and develop techniques to determine if a given structure can generate valid tilings. This role involves a deep dive into symbolic dynamics, combinatorics, and topology to advance current understanding of local generation.

• Conduct literature reviews to gain expertise in symbolic dynamics and local generation of tilings.
• Study recent research articles regarding local generation of tilings and languages.
• Extend finite input alphabets to countably infinite ones to test existing classification models.
• Investigate communication structures beyond weakly mixing tilings to develop more general techniques.
• Analyze communication structures in graph colorings, specifically focusing on small numbers of colors.
• Define and characterize new mathematical structures for tiling constraints.