ICTP MATH LECTURE SERIES ON DYNAMICS OF THE GEODESIC FLOW ON SURFACES WITHOUT CONJUGATE POINTS - First Lecture TOMORROW5 Lectures by Khadim War (IMPA)

[ICTP Math Section]

ICTP MATH LECTURE SERIES ON Dynamics of the geodesic flow on surfaces 
without conjugate points



Tuesday 1 December 2020 at 16:00 CET



Speaker: Khadim War (IMPA)



*Lecture 1: Geometry of surfaces without conjugate points.*


*Abstract: *This lecture focuses on the general geometric aspect of 
surfaces without conjugate points. This includes properties of such 
surfaces and definition of the ideal boundary of the universal cover. We 
will also define the geodesic flow in this lecture.


Kindly note that lecture is to be considered as part of the ICTP Math 
Associates Seminars Series, being targeted to a more general audience. 
_See below for further information on each lecture_.




Venue: Zoom Meetings


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https://zoom.us/meeting/register/tJ0sd-igqjouE917PnJKgmidMHmi3lDa58se 
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*Lecture 2: Measure of maximal entropy via Patterson-Sullivan measures.*

Date: Thursday 3rd of December at 16:00.

Abstract: This lecture focuses more on the dynamical aspect of the 
geodesic flow. We will define the measure of maximal entropy and give 
its construction via the Patterson-Sullivan measures on the ideal boundary.

*Lecture 3: Some statistical properties of the geodesic flow.*

Date: Tuesday 8 December at 16:00.

Abstract: In this lecture we will prove that the measure of maximal 
entropy constructed above is unique and therefore ergodic. We will also 
prove that the geodesic flow is mixing with respect to the measure of 
maximal entropy.

*Lectures 4 and 5: Counting the closed geodesics.*

Date: Thursday 10 December from 15:00 to 17:00

Abstract: In these two lectures we prove a Margulis-type asymptotic 
estimate for the number of free homotopy classes of closed geodesics. 
This can be seen as the prime geodesic theorem in this setting of 
surfaces without conjugate points.



References:

[1] V. Climenhaga, G. Knieper, K. War, Uniqueness of the measure of

maximal entropy for geodesic flow on certain manifolds without conjugate

points. Accepted for publication in Advances in Mathematics.

[2] V. Climenhaga, G. Knieper, K. War, Closed geodesic on surfaces without

conjugate points.Preprint.

[3] G. Knieper, Differentialgeometrie, Lecture notes.