On July 13, 2022 at 16:00 EEST, Paulo Oliva (Queen Mary University of London) will give a talk in the Proof Mining Seminar.
Title: On the Borel-Cantelli Lemmas, the Erdős–Rényi Theorem, and the Kochen-Stone Theorem
Abstract: In this talk we present a quantitative analysis of the first and second Borel-Cantelli Lemmas and of two of their generalizations: the Erdős–Rényi Theorem, and the Kochen-Stone Theorem. We will see that the first three results have direct quantitative formulations, giving an explicit relationship between quantitative formulations of the assumptions and the conclusion. For the Kochen-Stone theorem, however, we can show that the numerical bounds of a direct quantitative formulation are not computable in general. Nonetheless, we obtain a quantitative formulation of the Kochen-Stone Theorem using Tao’s notion of metastability.
Google Meet link: https://meet.google.com/xwm-syvx-bbr