normal number talk update

_events/normal_numbers.md

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+---
+#
+# This file generates an event.
+#
+layout:      event
+title:       Normal numbers in a nutshell
+speaker:     Aafko Boonstra
+dt_start:    08-04-2024 15:00
+dt_end:      08-04-2024 16:00
+location:    VU Amsterdam, NU-09A46 (Maryam)
+---
+
+The digits of _normal numbers_ show very specific behavior in the limit. In many settings, the Birkhoff Ergodic Theorem implies that such numbers are ubiquitous, yet they are very difficult to find. In this talk, we'll focus on Lüroth expansions. We'll present a method for constructing Lüroth normal numbers x by concatenating all finite Lüroth expansions using a binary rooted tree, the Lüroth Tree, and prove that x is Lüroth normal in the classical sense. (If there's time, we can also generalize the Lüroth Tree to prove the normality of a similar construction in a context of Generalized Lüroth Series.)