Trickle-down Theorems for High-dimensional Expanders via Log-concave Polynomials

Jonathan Leake (University of Waterloo) https://simons.berkeley.edu/index%2ephp/talks/jonathan-leake-university-waterloo-2026-09-21 Local to Global Principles High-dimensional expanders (HDX) generalize expander graphs and have found various applications in math and TCS. One approach to proving that a simplicial complex is an HDX uses trickle-down theorems, where expansion of certain low-dimensional links implies expansion properties throughout the complex. In this talk, we will discuss some recent trickle-down theorems for partite HDX, with applications to approximate sampling. We will also show how these theorems arise from the theory of Lorentzian and log-concave polynomials. Joint work with Kasper Lindberg and Shayan Oveis Gharan.