T
he Thematic Program on Teichmüller
Theory and its Connections to
Geometry, Topology and Dynamics
was a tremendous success. There were a number of
exciting activities throughout this six-month program that
attracted hundreds of visitors from all over the world to
the Fields Institute for collaborative research, discussion
and lectures. The visitors represented an impressive
breadth of mathematical areas, such as Teichmüller
theory, homogeneous dynamics, algebraic geometry, and
geometric group theory. It was particularly exciting to see
so many women and young people represented among
the speakers and participants. Some highlights include an
introductory summer school, three workshops including
a Sage Days workshop, the 2018 Fields Medal Symposium
celebrating the work of Maryam Mirzakhani, the Coxeter
Lecture Series by Fields Medallist Curtis McMullen, and
three graduate courses, one of which was taught by the
Dean’s Distinguished Visiting Professor, Mladen Bestvina.
The Sage Days workshop (Sage Days 96) was held on
August 13-16. It brought together students, researchers,
and advanced programmers for a fruitful exchange. It
was an occasion for newcomers to learn about Sage
and for more advanced users to exchange their views.
There was also time set aside for individuals to work
on their personal coding projects with the help of the
experts that were present. These included projects in
Teichmüller theory, interval exchanges transformations,
translation surfaces and train-tracks. There was also new
code developed that was added to the source code of
SageMath and so made available to the community.
The Thematic Program represents a large and
interconnected area of mathematics where major results
use techniques and tools from disparate areas. To acquaint
young researchers with these tools, an introductory
summer school was held on August 20-24. This five-day
school featured four exciting mini-courses: Arithmeticity
of discrete subgroups by Yves Benoist (Université Paris-
Sud), Homogeneous Dynamics and Hyperbolic Manifolds
of Infinite Volume by Hee Oh (Yale University), Random
walks on weakly hyperbolic groups by Giulio Tiozzo
(University of Toronto), and Mirzakhani’s Work on
Earthquakes by Alex Wright (University of Michigan).
Each speaker gave four lectures. To facilitate learning
by graduate students and people outside of the field,
problem/discussion sessions were held in the afternoon.
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