Cross-Sections and Their Applications to Number Theory

Vortrag von Gaurav Aggarwal

Datum: 29.10.25  Zeit: 13.30 - 14.30  Raum: Y27H28

Cross-sections provide a powerful tool for translating problems about continuous flows into discrete dynamical systems. In this talk, I will introduce the basic theory of cross-sections, illustrating it with examples and applications. I will show how this framework can be used to establish a version of the Lévy–Khintchine theorem for almost every point with respect to a wide class of measures that are singular to Lebesgue measure—in particular, for almost every point in the middle-third Cantor set equipped with its natural self-similar measure. I will then discuss how the notion of cross-section extends to multi-parameter flows, the challenges that arise in this setting, and conclude with an application of this theory to a conjecture of Y. Cheung.

The talk is based on joint work with Anish Ghosh.