| Fri, Nov 10, 2017
|
Colloquium
3:30 PM
MSCS 514 | | What's in a Circle?
Kenneth Ward, American University
Host: David Wright
| | | Abstract: The study of circle packing and its relatives are owed to
Apollonius of Perga. This is not a talk about circle packing, although
- pardon the pun - packing appears within this! Instead, this is a
discussion of how we define a circle, and how we view its
symmetries. We'll begin with an introduction to arrangements of
circles on tori, and connections of division to topology. In addition
to producing evocative imagery, some of which will be displayed in
this talk and made available online shortly thereafter, these links
allow us to formulate certain precise conjectures about curvature and
how it manifests in number fields. One can ask questions about
curvature as it relates to quadratic reciprocity and Frobenius maps,
which we will explore from an algebraic point of view. We will give
some examples of ``Frobenius tapestries'', concluding with definitions
of curvature and tori for algebraic spaces, unique challenges
presented by nonconvexities in non-Archimedean hyperbolic planes, and
the construction of geodesics on valued fields. This talk requires no prior knowledge of advanced number theory -- all
are welcome! |
|
|
|