ICTP MATH LECTURE SERIES ON DYNAMICS OF THE GEODESIC FLOW ON SURFACES WITHOUT CONJUGATE POINTS - 5 Lectures by Khadim War (IMPA)
ICTP Math Section
math at ictp.it
Thu Nov 26 11:25:09 CET 2020
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
information about joining the meeting.
*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.
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