Joint PU/IAS Number Theory
Mordell-Schinzel Surfaces and Cluster Algebras
The set of positive integer points of the celebrated Markov surface admits the structure of a 3-regular tree. My objective in this talk is to unveil a similar phenomenon for Mordell-Schinzel surfaces; namely that the set of positive integer points of each such surface admits the structure of a 2-regular graph. The vertices of each graph naturally correspond to clusters in a suitable (generalised) cluster algebra. I will then explain how the structure theory of cluster algebras translates into a resolution of the positive Mordell-Schinzel problem. This is partly based on ongoing joint work with Robin Zhang (MIT).
Date & Time
February 05, 2026 | 3:30pm – 4:30pm
Add to calendar
02/05/2026 15:30
02/05/2026 16:30
Joint PU/IAS Number Theory
use-title
Topic: Mordell-Schinzel Surfaces and Cluster Algebras
Speakers: Antoine de Saint Germain, University of Hong Kong
More: https://www.ias.edu/math/events/joint-puias-number-theory-54
The set of positive integer points of the celebrated Markov surface
admits the structure of a 3-regular tree. My objective in this talk is
to unveil a similar phenomenon for Mordell-Schinzel surfaces; namely
that the set of positive integer points of each such surface admits
the structure of a 2-regular graph. The vertices of each graph
naturally correspond to clusters in a suitable (generalised) cluster
algebra. I will then explain how the structure theory of cluster
algebras translates into a resolution of the positive Mordell-Schinzel
problem. This is partly based on ongoing joint work with Robin Zhang
(MIT).
*Princeton University, Fine 214*
a7a99c3d46944b65a08073518d638c23
Location
*Princeton University, Fine 214*Speakers
Antoine de Saint Germain, University of Hong Kong