# Mathematical Sciences Research Institute

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# Seminar

RAS Postdoc Seminar: Geodesic currents and the smoothing property October 15, 2020 (09:00 AM PDT - 10:30 AM PDT)
Parent Program: Random and Arithmetic Structures in Topology -- Virtual Semester MSRI: Online/Virtual
Speaker(s) Didac Martinez Granado (University of California, Davis)
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Video

#### Geodesic Currents And The Smoothing Property

Abstract/Media

To attend this seminar, please register here: https://www.msri.org/seminars/25205

Abstract:

Geodesic currents are measures that realize a suitable closure of the space of multi-curves on a surface. They were introduced by Bonahon in 1986, when he proved that the Teichmueller space embeds inside the space of currents and, furthermore, hyperbolic length of curves can be extended to currents.

Since then, many other geometric structures on surfaces have been realized as currents and other functions on curves have been extended to currents, such as, recently, lengths coming from certain Anosov representations.

One of the key properties of these functions is that they decrease under surgery of an essential crossing of a curve, a phenomenon we refer to as the smoothing property''. In this talk we introduce the concept of geodesic current and discuss recent results which highlight the prominent role of the smoothing property. For example, functions on the space of curves that satisfy the smoothing property together with some other mild conditions, can be extended to geodesic currents continuously.