ICTP MATH LECTURE SERIES ON DYNAMICS OF THE GEODESIC FLOW ON SURFACES WITHOUT CONJUGATE POINTS - 5 Lectures by Khadim War (IMPA)

[ICTP Math Section]

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


Speaker: Khadim War (IMPA)



Venue: Zoom Meetings


Dates:

Tuesday 1 December 2020 at 16:00 CET - Lecture 1: Geometry of surfaces 
without conjugate points.

Thursday 3 December 2020 at 16:00 CET - Lecture 2: Measure of maximal 
entropy via Patterson-Sullivan measures.

Tuesday 8 December 2020 at 16:00 CET - Lecture 3: Some statistical 
properties of the geodesic flow.

Thursday 10 December 2020 at 15:00 CET – *PLEASE NOTE CHANGE OF TIME* - 
Lectures 4 and 5: Counting the closed geodesics


Kindly note that Lectures 1 and 2 are 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_.


Kindly register in advance for these meetings (you only have to register 
once to attend all events): 
https://zoom.us/meeting/register/tJ0sd-igqjouE917PnJKgmidMHmi3lDa58se 
<https://zoom.us/meeting/register/tJ0sd-igqjouE917PnJKgmidMHmi3lDa58se>

After registering, you will receive a confirmation email containing 
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*Lecture 1: Geometry of surfaces without conjugate points.*

Date: Tuesday 1 December at 16:00.

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.

*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.