The Aztec Diamond: an analytic journey through random tilings (Maurice Duits)

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.

Download the poster

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