NCMW - Ergodic Theory and Fractals (2024)
Speakers and Syllabus
Name of the Speaker with their Affiliation |
No. of Lectures |
Detailed Syllabus |
Dr. Shrihari Sridharan |
6 x 1.5 hrs |
Title: Ergodic Theory
|
Dr. Sabyasachi Mukherjee |
6 x 1.5 hrs |
Title: Conformal measures on Julia and limit sets
|
Dr. Nishant Chandgotia |
6 x 1.5 hrs |
Title: Thermodynamic Formalism - a quick introduction
|
Prof. A.K.B.Chand |
6 x 1.5 hrs |
Title: Fractal Interpolations
|
Dr. Amit Priyadarshi |
6 x 1.5 hrs |
Title: Various Fractal Dimensions
|
Dr. Senthil Raani |
6 x 1.5 hrs |
Title: Fourier Transform and fractals
|
Prerequisite: Real Analysis, Complex Analysis, Measure Theory, Point-Set Topology
References:
- Kenneth Falconer, Fractal Geometry: Mathematical Foundations and Applications, Wiley–Blackwell, 2014.
- Pertti Mattila, Geometry of Sets and Measures in Euclidean Spaces, Cambridge Studies in Advanced Mathematics, 2012.
- Pertti Mattila, Fourier Analysis and Hausdorff Dimension, Cambridge University Press, 2016.
- M.F. Barnsley, Fractals Everywhere, Academic Press, Orlando, Florida, 1988.
- Peter Massopust, Fractal Functions, Surfaces and Wavelets, Academic Press, 1995.
- C.S. Aravinda and V.S. Bhat, Elements of Dynamical Systems: Lecture Notes from NCM School, Edited by A Nagar, R Shah, S Sridharan, Chapter 3, Springer Nature Singapore.
- P Walters, An Introduction to Ergodic Theory, Springer-Verlag New York, Inc. 1982.
- David Ruelle, Thermodynamic Formalism, Cambridge University Press, 2004.
- Robert Burton and Jeffrey E. Steif, Non-uniqueness of measures of maximal entropy for sub shifts of finite type, Ergodic Theory and Dynamical Systems, 14(2):213-235, 1994.
- Burton, R., Steif, J.E. New results on measures of maximal entropy. Israel J. Math. 89, 275–300, 1995.
- Keller G. Equilibrium States in Ergodic Theory. Cambridge: Cambridge University Press; 1998.
- Milnor J., Dynamics in One Complex Variable: Princeton University Press, 2006.
- Przytycki F. and Urbanski M., Conformal Fractals: Ergodic Theory Methods: 371: Cambridge University Press, 2009.
- Nicholls P.J., The ergodic theory of discrete groups, Cambridge University Press, 2008.
Names of the tutors with their affiliations:
1. Dr Shilpak Banerjee, IIT Tirupati
2. Dr Sharvari Tikekar, TIFR Mumbai
3. Ms M Megala, IIT Tirupati
4. Ms Harsha Gopalakrishnan, IIT Tirupati
Time Table
Tentative timetable, mentioning names of the speakers and tutors with their affiliations:
Day |
Date |
Lecture 1 (9:30–11:00) |
Tea |
Lecture 2 (11:30–13:00) |
Lunch (13:00 to |
Lecture 3 (14:00–15:30) |
Tea |
Discussion (16:00-17:00) |
Snacks |
Mon |
09/12/24 |
AP |
AC |
SR |
AP+ MM+ HG |
||||
Tues |
10/12/24 |
AP |
AC |
SR |
AC+ MM +HG |
||||
Wed |
11/12/24 |
SR |
AP |
AC |
SR+ MM+ HG |
||||
Thu |
12/12/24 |
SR |
AP |
AC |
AP+ MM+ HG |
||||
Fri |
13/12/24 |
AC |
SR |
AP |
AC+ MM +HG |
||||
Sat |
14/12/24 |
AC |
SR |
AP |
SR+ MM+ HG |
||||
Mon |
16/12/24 |
SS |
NC |
SM |
SS+ SB+ ST |
||||
Tues |
17/12/24 |
SS |
NC |
SM |
NC+ SB+ ST |
||||
Wed |
18/12/24 |
SM |
SS |
NC |
SM+ SB+ ST |
||||
Thu |
19/12/24 |
SM |
SS |
NC |
SS+ SB+ ST |
||||
Fri |
20/12/24 |
NC |
SM |
SS |
NC+ SB+ ST |
||||
Sat |
21/12/24 |
NC |
SM |
SS |
SM + SB+ ST |
Full forms for the abbreviations of speakers and tutors:
Speakers:
SS: Dr Shrihari Sridharan
SM: Dr Sabyasachi Mukherjee
NC: Dr Nishant Chandgotia
AC: Prof. A.K.B. Chand
AP: Dr Amit Priyadarshi SR: Dr Senthil Raani
Tutors:
SB: Dr Shilpak Banerjee
ST: Dr Sharvari Tikekar MM: M Megala
HG: Harsha Gopalakrishnan