Explore this comprehensive trimester program that brings together researchers from three interconnected areas of combinatorics: asymptotic representation theory, random maps and dimer models, and enumerative geometry and moduli spaces. Participate in an intensive academic experience designed to foster collaboration and deep interactions between these mathematical communities through multiple learning formats including an introductory winter school at CIRM near Marseille, three international workshops, graduate and research courses, weekly seminars, and outreach activities. Delve into five major course sequences covering enumerative combinatorics of maps (10 sessions), asymptotic and probabilistic aspects of representation theory (8 sessions), integrable probabilities (8 sessions), topological recursion (8 sessions), and partitions, modular forms and moduli spaces (8 sessions). Engage with leading researchers during long and short visits, attend specialized lectures that bridge theoretical concepts with practical applications, and benefit from the cross-pollination of ideas between traditionally separate mathematical fields. Experience a unique blend of rigorous mathematical training and collaborative research opportunities culminating in special events including an evening conference and concert exploring the connections between music, mathematics, and the work of composer Tom Johnson.

Syllabus

Enumerative Combinatorics of Maps - 1/10
Enumerative Combinatorics of Maps - 2/10
Enumerative Combinatorics of Maps - 3/10
Enumerative Combinatorics of Maps - 4/10
Enumerative Combinatorics of Maps - 5/10
Enumerative Combinatorics of Maps - 6/10
Enumerative Combinatorics of Maps - 7/10
Enumerative Combinatorics of Maps - 8/10
Enumerative Combinatorics of Maps - 9/10
Enumerative Combinatorics of Maps - 10/10
Asymptotic and Probabilistic Aspects of Representation Theory - 1/8
Asymptotic and Probabilistic Aspects of Representation Theory - 2/8
Asymptotic and Probabilistic Aspects of Representation Theory - 3/8
Asymptotic and Probabilistic Aspects of Representation Theory - 4/8
Asymptotic and Probabilistic Aspects of Representation Theory - 5/8
Asymptotic and Probabilistic Aspects of Representation Theory - 6/8
Asymptotic and Probabilistic Aspects of Representation Theory - 8/8
Integrable Probablities - 1/8
Integrable Probablities - 2/8
Integrable Probablities - 3/8
Integrable Probablities - 4/8
Integrable Probablities - 5/8
Integrable Probablities - 6/8
Integrable Probablities - 7/8
Integrable Probablities - 8/8
Topological Recursion - 1/8
Topological Recursion - 2/8
Topological Recursion - 3/8
Topological Recursion - 4/8
Topological Recursion - 5/8
Topological Recursion - 6/8
Topological Recursion - 7/8
Topological Recursion - 8/8
Partitions, Modular Forms and Moduli Spaces - 1/8
Partitions, Modular Forms and Moduli Spaces - 2/8
Partitions, Modular Forms and Moduli Spaces - 3/8
Partitions, Modular Forms and Moduli Spaces - 4/8
Partitions, Modular Forms and Moduli Spaces - 5/8
Partitions, Modular Forms and Moduli Spaces - 6/8
Partitions, Modular Forms and Moduli Spaces - 7/8
Partitions, Modular Forms and Moduli Spaces - 8/8
Soirée Conférence et Concert : La musique, les mathématiques et Tom Johnson