Fields Notes 17:3 | Page 22

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