In the Field
Dynamics in Number Theory and Geometry surfaces " aimed at presenting a unified theory of rigidity which would include the acclaimed results of Eskin-Mirzakhani- Mohammadi, Benoist-Quint, Brown-Rodriguez Hertz-Wang and his recent work on the Zimmer conjecture with Fisher and Hurtado. The talk " On the local Hölder exponent of the entropy function " by Giulio Tiozzo( University of Toronto) advertised a novel question about Holder exponent of functions of dynamical nature.
A special lecture was delivered by Damien Roy( University of Ottawa) on his acclaimed work on " Parametric geometry of numbers ". Professor Roy, a leading number theorist, brought this new topic of research to our dynamically-minded participants. The conference also featured an afternoon without presentations, in which many participants broke up into small groups to discuss some details of the presentations and start new projects.
The Conference on Dynamics in Number Theory and Geometry was the first Fields funded event in Dynamics at Queen ' s University in Kingston, Ontario. Our main goal was to give starting and early-career mathematicians the opportunity to meet with leaders in the field, as well as initiate new projects and collaborations, thus fostering a more inclusive network for the next generation of dynamicists.
This event was sponsored by the Fields Institute, the Department of Mathematics and Statistics of Queen ' s University, and the Vice-Principal( Research) of Queen ' s University. �
— Francesco Cellarosi
We gathered about 50 people from 8 countries, including 28 graduate students and postdocs. Of the 19 talks, 15 were delivered by promising junior mathematicians.
The scientific activities in this conference covered a wide range of topics, including homogenous dynamics, Diophantine geometry, partially hyperbolic systems, translation surfaces, and Teichmüller theory. We were able to bring together two groups of scientists working in adjacent areas: those working on application of dynamics to Number Theory, and those working on dynamical systems of geometrical origin. Several themes appeared transversally in many presentations; for instance the connection between Farey fractions, homogeneous flows, and Diophantine approximation. Another common theme was rigidity and flexibility within different families of dynamical systems.
The week-long conference opened with " Farey statistics and applications " by Florin Boca( UIUC) who surveyed the connections between the statistical features of point processes of number-theoretical origin and ergodic theory, with emphasis on recent developments and open problems. Aaron Brown ' s( University of Chicago) talk " Groups acting on
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