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Irreducibility of Gleason polynomials Implies Irreducibility of Per_n

Adventurous Berkeley Complex Dynamics May 02, 2022 - May 06, 2022

May 03, 2022 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Rohini Ramadas (University of Warwick)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Irreducibility Of Gleason Polynomials Implies Irreducibility Of Per_n

Abstract

Per_n is a punctured (nodal) Riemann surface parametrizing quadratic rational maps with an n-periodic critical point; its irreducibility over C is an open question. The Gleason polynomial G_n is the polynomial whose roots are {c such that 0 is n-periodic under z^2+c}; its irreducibility over Q is an open question. I will discuss very recent work-in-progress, finding a smooth Q-rational point “at infinity” on Per_n, and using this to conclude that if G_n is irreducible over Q, then Per_n is irreducible over C. This talk will also include joint work with Rob Silversmith.

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Irreducibility Of Gleason Polynomials Implies Irreducibility Of Per_n

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