Room 509, Cosmology Building, NTU

**Speaker(s):**

Yann Bugeaud (Université de Strasbourg)

**Organizer(s):**

Chih-Hung Chang (National University of Kaohsiung)

Jung-Chao Ban (National Chengchi University)

**Due to the large-scale earthquake this morning, traffic in various sections was affected. To avoid aftershocks, the class will be suspended once today.

**1. ****Introduction & Purposes**

This series of lectures intends to illustrate the interplay between combinatorics on words and Diophantine approximation.

**2. Outline & Descriptions**

We will survey some classical results on Diophantine approximation (Roth’s theorem and its generalizations) and apply them to prove the transcendence of real numbers, whose sequence of decimal digits (or whose sequence of partial quotients) enjoys some specific combinatorial properties. We will discuss a very special Diophantine property of the real number whose sequence of partial quotients is given by the Fibonacci word 12112121… over the alphabet {1,2}. We will also show that the sequence of decimal digits of e=2.718128… is not too simple, in a suitable sense.

**3. Prerequisites**

Basic knowledge on real continued fractions is the only prerequisite.

**4. Registration**

https://forms.gle/M2zhuosg9p3eKWUX8

**Contact:**
Murphy Yu (murphyyu@ncts.tw)