***The class on July 25, 26, 28 will be online course due to the Typhoon Doksuri. Please join the meeting links to the course below. ***

1. Course Background & Purposes

The pioneering work of Fatou revealed a meaningful analogy between Kleinian groups (discrete subgroups of the group of Mobius transformations) and the dynamics of rational maps. Abel prizelaureateDennisSullivanusedthisanalogy,or"dictionary",togreat effectinproving his celebrated no-wandering domains theorem, and this dictionary has continued to be a source of inspiration for yet another generation of mathematicians.

2. Course Outline & Descriptions

This mini-course will begin with an introduction toKleinian groupsandsingle variable complexdynamics,emphasizingkey examples. The last two days will focus on both classical and modern developments in the Fatou-Sullivan dictionary.

7/25 Introduction toKleinian groups

        Single variable complexdynamics (I)

7/26 Single variable complexdynamics (II)

        Development of Fatou-Sullivan dictionary (I)

7/28 Development of Fatou-Sullivan dictionary (II)

3. Grading

Homework assigned in class

4. Registration

https://forms.gle/wjSB2PVb1TG4DsFi6

7/25 https://ntucc.webex.com/ntucc-en/j.php?MTID=m530f34677bf4062badc8b33b0174498a

7/26 https://ntucc.webex.com/ntucc-en/j.php?MTID=m5335ec07ab0f8746955a65dffa7056c1

7/28 https://ntucc.webex.com/ntucc-en/j.php?MTID=m642ecaefa30ca8b31d720927dcce2565