Field of Science:
Mathematics
Call 1
Host Instituion:
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Supervisor:
Zoltan Vidnyánszky
Garrett Theodore Ervin
Arithmetic of order types, one-dimensional dynamics, and orbit equivalence relations
Short Description of the Research Project:
A linear order is a collection of points arranged from left to right in ascending order. Linear orders generalize the familiar lines from Euclidean geometry. And just as Euclidean lines can represent many different things — the trajectory of a particle through space, a unit of time that can be traversed, or a length of distance that can be added and multiplied with other lengths — linear orders have their own dynamics and arithmetic.
In this project, we study linear orders both as objects that can be added and multiplied (their arithmetic) and as objects that can be traversed or transformed (their dynamics). We do this by tracking how their points move and shift as we add, multiply, and transform these orders. By doing so, we hope to better understand the laws governing these arithmetical and dynamical operations.
