Maurice Duits, professor at the Royal Institute of Technology (Sweden) and lauerate of the FSMP Chair of Excellence in 2025, gave, in the frame of his chair, a 20-hour course on the topic of The Aztec Diamond: an analytic journey through random tilings.
This course took place at the IHP from January 15 to March 3, 2026.
Summary and lecture notes
Find the summary and lecture notes on the page: https://people.kth.se/~duits/#/Aztec
To learn more about Maurice Duits' work, visit his personal page.
Videos of the lectures
Lecture #1: Determinantal point processes
Notes of lecture #1
Slides of lecture #1
Lecture #2 : Non-intersecting paths, LGV Theorem, Eynard-Mehta Theorem, Schur processes
Notes of lecture #2 (chap. 2 and 5)
Slides of lecture #2
Lecture #3: Asymptotic study of the uniform Aztec diamond
Lecture #4: Shuffling algorithm and dynamics
Lecture #5: Doubly periodic tilings
Lecture #6: Height fluctuations and the Gaussian free field
Lecture #7: Orthogonal polynomials, Painlevé transcendents, and lozenge tilings of the hexagon