Caltech-Tsinghua Joint Colloquium

Organizers：

Shoma Sugimoto, Song Yu, Roy Zhao

Time：

Wed., 8:00 - 9:00 am

Oct. 29, 2025

Online：

Zoom Link:

https://caltech.zoom.us/j/86314065023?pwd=EZe3c169dpKh33V7thZGe2Mdt0S6kw.1

Title：

Selector processes and combinatorial connections

Abstract:

Positive selector processes are natural stochastic processes driven by sparse Bernoulli random variables. Selector processes play a critical role in the study of suprema of stochastic processes, as reflected in Talagrand’s selector process conjecture. Interestingly, Talagrand also drew rich and influential connections between selector processes and the threshold phenomena in probabilistic combinatorics.

I will introduce selector processes and its connections with phenomena in probabilistic combinatorics. In particular, I will discuss a quantitative sharp version of Talagrand’s selector process conjecture, which strengthens both the selector process conjecture and the Kahn-Kalai conjecture on the location of thresholds.

As an application, I will discuss how this relates to another intriguing conjecture Talagrand about the “integrality gap” of a wide class of integer linear programs around the so-called expectation thresholds. Time permitting, I will discuss further connections between selector processes, thresholds and phenomena of interest in combinatorics, including hypergraph containers and probabilistic intuition for combinatorial games.