Department of

# Mathematics

Seminar Calendar
for events the day of Friday, October 30, 2020.

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Friday, October 30, 2020

1:00 pm in Zoom,Friday, October 30, 2020

#### Permutable Quasiregular maps

###### Athanasios Tsantaris   [email] (University of Nottingham - Math)

Abstract: Do commuting holomorphic maps have the same Julia set? This question was first asked by Fatou and Julia around 1920 in their attempts to classify commuting rational maps. For rational maps the answer is affirmative but for transcendental entire maps the question is still open. In this talk we will first discuss the progress to the problem for transcendental entire maps over the years and then we shall describe generalizations of those results in the setting of quasiregular maps which are higher dimensional analogues of holomorphic maps.

4:00 pm in Zoom (email ruiyuan at illinois for info),Friday, October 30, 2020

#### What generic automorphisms of the random poset look like

###### Dakota Thor Ihli (UIUC Math)

Abstract: The Fraïssé limit of the class of finite posets, also called the random poset, admits generic automorphisms — that is, its automorphism group admits a comeagre conjugacy class. This result, due to D. Kuske and J. Truss, was proven without explicitly describing the automorphisms in question. Here we give a new, concrete description of the generic automorphisms, and we discuss the tools-and-tricks involved.