Dr Viveka Erlandsson awarded an EPSRC New Investigator Award
25 February 2020
Dr Erlandsson's grant is for three years, from 1 January 2020 until 31 December 2022 and the project is entitled 'Geodesic Currents and Counting Problems'.
The main theme of the project is to generalize Mirzakhani’s curve counting theorem. In 2008, in her ground breaking thesis, Mirzakhani proved (among other things) that the number of simple curves on a hyperbolic surface of bounded length is asymptotic to a constant times a polynomial in the length. She later reproved this result, and generalized it to non-simple curves, using very different (and not well-understood) methods. In this project we will give a new, more accessible, unified proof of both results as well as generalizing it to different settings. The novelty of our methods is the use of the technical tool called geodesic currents.
The main impact of the project will be a book written by Dr Erlandsson, along with collaborator Juan Souto from the University of Rennes. It will be a self-contained book giving all necessary background on geodesic currents, the new proof of Mirzakhani’s theorem, and its applications. This is a very active area of research and there are, to our knowledge, no other books treating this topic.
This grant will allow Dr Erlandsson to hire a post-doc for two years and she stated that "I’m excited about starting to build my own research group. It also gives me the opportunity to invite researchers to visit Bristol as well as travel to conferences and visit collaborators."
Read more about the project.