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Lucas Kaufmann, Commuting Pairs of Endomorphisms

May 27 @ 11:00 am - 12:00 pm KST

B266, IBS Korea, Republic of

     Speaker

Lucas Kaufmann
IBS, Center for Complex Geometry

The study of functional equations is at the origin of the early developments of the iteration theory of polynomials and rational functions, carried out by Fatou, Julia, Ritt and others. Among these equations, the commutation relation f g = g f is particularly interesting. In this talk I will discuss the following problem: can we classify commuting pairs of holomorphic endomorphisms of the complex projective space?

We will see that the relation f g = g f gives rise to special symmetries of several dynamical objects attached to these maps, such as their invariant currents and measures, their Julia sets and so on. This rigidity allows us to understand the structure of these maps and even give a full description in low dimensions.

Details

Date:
May 27
Time:
11:00 am - 12:00 pm KST
Event Category:
Event Tags:

Venue

B266
IBS Korea, Republic of

Organizer

Jaehyun Hong
IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 복소기하학연구단
대전 유성구 엑스포로 55 (우) 34126
IBS Center for Complex Geometry
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
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