Four theorems about entropy in ergodic theory TIFR-CAM, even semester, 2021.

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11:00 AM-12:30 PM on Wednesdays and Fridays
Office hours (up on appointment): 11:00 AM-12:30 PM on Mondays
Classes will take place on zoom and will start on the 17th of March. Please contact me if you want to follow the course.

General Information

The following are the notes and the video links. The video is stored on a cloud and might not work beyond a point (say couple of weeks from when it is posted).

Lecture 1, 17th March: Notes

Lecture 2, 19th March: Notes

Lecture 3, 24th March: Notes

Lecture 4, 26th March: Notes

Lecture 5, 31st March: Notes

Lecture 6, 2nd April: Notes

Lecture 7, 7th April: Notes

Lecture 8, 9th April: Notes

Lecture 9, 14th April: Notes

Lecture 10, 16th April: Notes

Lecture 11, 28th April: Notes

Lecture 12, 30th April: Notes Exercises: Some other ergodic theorems

Lecture 13, 5th May: Notes Some exercises on conditional expectation and answer's to Abhishek questions

Lecture 14, 7th May: Notes

Lecture 15, 12th May: Notes

Lecture 16, 14th May: Notes

Lecture 17, 19th May: Notes

Lecture 18, 21st May: Notes

Lecture 19, 26th May: Notes

Lecture 20, 28th May: Notes

Lecture 21, 2nd June: Notes

Lecture 22, 4th June: Notes

Lecture 23, 9th June: Notes

Lecture 24, 11th June: Notes

Lecture 25, 14th June: Notes

Lecture 26, 16th June: Notes

Lecture 27, 18th June: Notes

Lecture 28, 21st June: Notes

Lecture 29, 23rd June: Notes

Lecture 30, 25th June: Notes

Lecture 31, 30th June: Notes

Lecture 32, 2nd July: Notes

Supplementary material (some required and some just for fun):

A proof by Kalikow and Mccutcheon that the 3 shift is not a factor of the 2 shift Link

A discussion on spectral measures by Wiliam Parry Link

Martingales from the book Ergodic theory with a view towards Number Theory by Einsedler and Ward Link

General Theories Unifying Ergodic Averages and Martingales by Kachurovskii

Existence of Haar measure using Hall's marriage lemma Notes by Manjunath Look at Chapter 3.

What we will need from character's of compact abelian groups From Walter's book

A quick proof of Steinhaus's theorem Link

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