The Miracle of Integer Eigenvalues in Finite Poset Matrices

Explore a fascinating mathematical discovery in this 30-minute lecture by Maxim Kontsevich from the Institut des Hautes Etudes Scientifiques (IHES). Delve into the intriguing world of finite posets and their associated square matrices, where a remarkable phenomenon occurs: all eigenvalues of these matrices are integer linear combinations of variables. Learn how this property holds true even for trivial posets, leading to new insights into representations of the symmetric group. Gain an understanding of this groundbreaking joint work by Kontsevich, Kenyon, Ogievetsky, Pohoata, Sawin, and Shlosman, which unveils unexpected connections in mathematical structures.