Fall 2026
October 21, 2026, 4:00–5:00pm, EH4088
Speaker: Chun-Kai Tseng (MSU)
Title: Small Moments of the Sensitivity of Polynomial Threshold Functions
Abstract: Polynomial threshold functions (PTFs) are a central class of Boolean functions with important roles in learning theory and approximation. A fundamental question is to understand the complexity of their behavior under small perturbations of the input. On the Boolean cube, this is captured by notions such as sensitivity, average sensitivity, and Boolean surface area. In this talk, we revisit a recursive approach used to derive bounds for the average sensitivity and Boolean surface area of PTFs and obtain a polylogarithmic bound for small moments of their sensitivity. We will also explore the interplay between Fourier expansion and induction on scales from harmonic analysis, random averaging from probability, and decision trees and regularization from combinatorics.
October 28, 2026, 4:00–5:00pm, EH4088
Speaker: Haoyu Liu (PKU/MIT)
Title: Conformal removability and bubble connectivity of non-simple SLE
Abstract: Schramm-Loewner evolution (SLE_\kappa) is a one-parameter family of random fractal curves arising as scaling limits of interfaces in two-dimensional statistical mechanics models. For \kappa \in (4, 8), the SLE_\kappa curve is self-intersecting but not space-filling, forming complementary connected components known as bubbles. In this talk, I will discuss the relationship between the conformal removability of SLE traces and connectivity of the bubble adjacency graph, as well as a sharp phase transition as \kappa varies. Joint work with Zijie Zhuang (UNIGE).
November 4, 2026, 4:00–5:00pm, EH4088
Speaker: Brayden Letwin (UWashington)
Title: TBA
Abstract: TBA
November 18, 2026, 4:00–5:00pm, EH4088
Speaker: Han Huang (MIT)
Title: TBA
Abstract: TBA