- Date: June 30 (Fri) 16:00 - 18:00
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Place: 27-325 (SNU)
- Speaker: Seung uk Jang (University of Chicago)
- Title: Do Tropical Markov Cubics dream of Hyperbolic Origami?
- Abstract:
Non-archimedean fields and varieties over them admit the operation of tropicalizations, which provides a piecewise-linear 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 number-theoretic 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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일정시작 | 2023-06-30 |
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배경색상 | #FF5733 |