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University of Cambridge > Talks.cam > Algebraic Geometry Seminar > Complex dynamics: degenerations, and irreducibility problems

## Complex dynamics: degenerations, and irreducibility problemsAdd to your list(s) Download to your calendar using vCal - Rohini Ramadas, University of Warwick
- Wednesday 12 October 2022, 14:15-15:15
- CMS MR13.
If you have a question about this talk, please contact Dhruv Ranganathan. Per_n is an affine algebraic curve, defined over Q, parametrizing (up to change of coordinates) degree-2 self-morphisms of P^1 with an n-periodic ramification point. The n-th Gleason polynomial G_n is a polynomial in one variable with Z-coefficients, whose vanishing locus parametrizes (up to change of coordinates) degree-2 self-morphisms of C with an n-periodic ramification point. Two long-standing open questions in complex dynamics are: (1) Is Per_n is irreducible over C? (2) Is G_n is irreducible over Q? We show that if G_n is irreducible over Q, then Per_n is irreducible over C. In order to do this, we find a Q-rational smooth point of a projective completion of Per_n. This Q-rational smooth point represents a special degeneration of degree-2 morphisms, and as such admits a tropical interpretation. This talk is part of the Algebraic Geometry Seminar series. ## This talk is included in these lists:- Algebraic Geometry Seminar
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