 Date: June 30 (Fri) 16:00  18:00

Place: 27325 (SNU)
 Speaker: Seung uk Jang (University of Chicago)
 Title: Do Tropical Markov Cubics dream of Hyperbolic Origami?
 Abstract:
Nonarchimedean fields and varieties over them admit the operation of tropicalizations, which provides a piecewiselinear approximate sketch of varieties that encapsulates many key aspects. For Markov surfaces $x^2+y^2+z^2+xyz=D$, this viewpoint was initiated by works of Spalding and Veselov, who focused on its tropical and dynamical aspects.
In this talk, we will be working on a more general family of Markov surfaces and discover that, for any parameters, we have a copy or a shadow of the hyperbolic plane with the $(\infty,\infty,\infty)$triangle reflection group action. Such a viewpoint easily yields corollaries in Fatou domains (dynamical side) or the finiteness of orbits of rational points with prime power denominators (number theory side). Some interesting numbertheoretic aspects of this system may be introduced, such as Farey triples.
2023.06.26 19:06
[SNU Number Theory Seminar 30 June] Do Tropical Markov Cubics dream of Hyperbolic Origami?
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