AIS Ergodic Theory and Dynamical Systems (2017)

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Venue: Indian Institute of Technology Delhi,  Delhi, Delhi
Date:  4th, Dec 2017 to 23rd, Dec 2017



School Convener(s)

Name Prof. Anima Nagar Prof. Riddhi Shah Prof. Shrihari Sridharan
Mailing Address Department of Mathematics, IIT Delhi. Department of Mathematics, JNU, Delhi. School of Mathematics, IISER-TVM.




Speakers and Syllabus 

Speakers ,affiliation and topics covered

Real Dynamics Topological Dynamics Symbolic Dynamics
Lecturers Lecturers Lecturer
V. Kannan, Anima Nagar, Siddharth Bhattacharya,
University of Hyderabad IIT Delhi TIFR - Mumbai
Shrihari Sridharan, CRE Raja,  
IISER-TVM ISI - Bangalore  
Tutor Tutor Tutor
Perikala Chiranjeevi, Manoj Choudhuri, Puneet Sharma,
University of Hyderabad HRI, Allahabad IIT - Jodhpur
  Manpreet Singh, IIT Delhi  
Ergodic Theory Complex Dynamics Arithmetic Dynamics
Lecturer Lecturer Lecturer
CS Aravinda, Kaushal Verma, Anish Ghosh,
TIFR - Bangalore IISc Bangalore TIFR - Mumbai
Tutor Tutor Tutor
Nikita Agarwal, Shrihari Sridharan, Rajkumar Krishnan,


Syllabus covered by the Resource Persons

Real Dynamics:

  • Shrihari Sridharan (Dec 4): Interval dynamics, The set of all fixed points, periodic points, recurrent points, non-wandering points.
  • V. Kannan (Dec 4 - 6): Stability of periodic points, Sharkovskii’s theorem, Li-Yorke chaos, Logistic maps, Bifurcation, Transitivity, Sensitivity, Devaney’s chaos, Markov maps, Generalisations to higher dimensions.

Topological Dynamics:

  • Anima Nagar (Dec 7 - 9): Recurrence, Minimality, Equicontinuity, Mixing, Enveloping semigroups.
  • CRE Raja (Dec 7 - 9): Topological transformations, Multiple Recurrence, Applications – Van der Waerden’s theorem, Distal and proximal systems.

Symbolic Dynamics:

  • Siddharth Bhattacharya (Dec 11 - 16): Shifts and subshifts, Subshifts of finite type and sofic shifts, Factors, irreducibility, entropy, shift equivalence, Multi-dimensional shifts.

Ergodic Theory:

  • CS Aravinda (Dec 11 - 16): Measurable dynamics, Measure preserving dynamics, Poincare recurrence, Ergodicity, Unique ergodicity, von Neumann ergodic theorem, Birkhoff ergodic theorem, Horocycle and geodesic flows on closed surfaces of constant negative curvature.

Complex Dynamics:

  • Kaushal Verma (Dec 18 - 20): Quadratic polynomials, Mandelbrot set, Rational maps,Fatou-Julia dichotomy, Various characterisations of the dichotomy, Properties of the Fatou and the Julia set, Rational maps with empty Julia sets, Quadratic-like maps.

Arithmetic Dynamics:

  • Anish Ghosh (Dec 21 - 23): Manin conjecture for group varieties, Quantitative density of rational points, optimal distribution of points on spheres following Lubotzky-Phillips- Sarnak and Clozel. Useful tools from Geometry and Harmonic analysis on semisimple groups in Dynamics.


Time Table

Day Date Lecture I Tea Lecture II Lunch Tutorial I Tea Tutorial II Snacks
Mon Dec 4 R. Dynamics   R. Dynamics   R. Dynamics   R. Dynamics  
Tue Dec 5 R. Dynamics   R. Dynamics   R. Dynamics   R. Dynamics  
Wed Dec 6 R. Dynamics   R. Dynamics   R. Dynamics   R. Dynamics  
Thu Dec 7 T. Dynamics   T. Dynamics   T. Dynamics   T. Dynamics  
Fri Dec 8 T. Dynamics   T. Dynamics   T. Dynamics   T. Dynamics  
Sat Dec 9 T. Dynamics   T. Dynamics   T. Dynamics   T. Dynamics  
Sun Dec 10                
Mon Dec 11 S. Dynamics   E.Theory   S.Dynamics   E.Theory  
Tue Dec 12 S. Dynamics   E.Theory   S.Dynamics   E.Theory  
Wed Dec 13 S. Dynamics   E.Theory   S.Dynamics   E.Theory  
Thu Dec 14 S. Dynamics   E.Theory   S.Dynamics   E.Theory  
Fri Dec 15 S. Dynamics   E.Theory   S.Dynamics   E.Theory  
Sat Dec 16 S. Dynamics   E.Theory   S.Dynamics   E.Theory  
Sun Dec 17                
Mon Dec 18 C. Dynamics   C.Dynamics   C.Dynamics   C. Dynamics  
Tue Dec 19 C. Dynamics   C.Dynamics   C.Dynamics   C. Dynamics  
Wed Dec 20 C. Dynamics   C.Dynamics   C.Dynamics   C. Dynamics  
Thu Dec 21 A. Dynamics   A.Dynamics   A.Dynamics   A. Dynamics  
Fri Dec 22 A. Dynamics   A.Dynamics   A.Dynamics   A. Dynamics  
Sat Dec 23 A. Dynamics   A.Dynamics   A.Dynamics   A. Dynamics  



Actual Participants 


Sr SID Full Name Gender Affiliation Position in College/ University University/ Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A

Ph.D Deg

1 13584 Ms. Arpita Ghosh Female University of Kalyani PhD IIT Kanpur 2013  
2 13595 Mr. Anil Singh Male University of Jammu PhD University of Jammu 2012  
3 13596 Mr. Hrisikesh Devendra Singh Male Indian Statistical Institute PhD Student Indian Institute of Technology Guwahati 2010  
4 13782 Ms Haritha C Female Indian Institute of Science Education and Research, Bhopal BS-MS Dual Degree student IISER BHOPAL 2017  
5 13947 Ms Shreyasi Datta Female TIFR PhD IIT Kanpur 2015  
6 14035 Mr. Manish Raghav Male IIT Jodhpur PhD Dr B R A University Agra 2004  
7 14065 Mr. Rohit Kumar Male IIT Jodhpur PhD IIT KANPUR 2015  
8 14086 Ms. Sharvari Neetin Tikekar Female IISER-TVM Ph.D.      
9 14160 Mr Atma Ram Tiwari Male IISER-TVM Ph.D. JMI,DELHI 2014  
10 14163 Mr Yogesh Yogesh Male IISER TVM IPHD IISER TVM Appeared  
11 14231 Mr Prashant Kumar Male IIT JODHPUR PhD IIT KANPUR 2016  
12 14352 Ms Divya Gupta Female INDIAN INSTITUTE OF TECHNOLOGY JODHPUR PhD C.C.S. University Meerut 2011  
13 14493 Mr Rinchen Tundup Male University of Jammu Ph.D Student University of Jammu 2012  
14 14494 Mr. Manish Kumar Male University of Jammu PhD scholar University of Jammu 2013  
15 14526 Mr. Nongthombam Dhyanchand Male Assam University PhD Assam University 2013  
16 14708 Mr. Pabitra Narayan Mandal Male University of Hyderabad PhD University of Hyderabad 2016  
17 14922 Mr. Purbayan Chakraborty Male Presidency University MSc Student Presidency University    
18 15137 Mr. Bhuwanesh Rao Patil Male Harish-chandra Research Institute Allahabad PhD IIT Delhi 2011  
19 14009 Mr. Rahul Shukla Male Visvesvaraya National Institute of Technology, Nagpur Ph. D. C. S. J. M. University, Kanpur 2010  
20 15916 Mr. Mahabub
Male TIFR - Mumbai PhD Indian Statistical Institute 2016  
21 15918 Mr. Vishwajeet
Sudhakar Bhoite
Male IISER-Pune BS-MS Student IISER Pune Awaiting Result  
22 14605 Mr. Animesh Roy Male Viswa-Bharati
PhD IIT DELHI 2014  
23 14612 Mr. Saheb Pal Male Viswa-Bharati
Research Scholar Visva-Bharati University 2014  
24 14527 Mr Thangjam
Birkramjit Singh
Male Assam University Silchar PH.D Manipur University 2009  
25 15913 Mr. Pradeep
Male IIT Delhi PhD IIT Delhi 2017  
26 14932 Mrs. Shikha Jain Female University of Delhi PhD Student M.Sc. 2013  
37 14856 Dr. Dinesh Kumar Male Deen Dayal Upadhyaya College, University of Delhi Asst. Prof. Hindu College, University of Delhi 2009  11/19/2016
28 14388 Mr. Pramod Kumar Das Male University of Delhi PhD IIT Bombay 2013  
29 14302 Ms. Mukta Garg Female Department of Mathematics, University of Delhi Ph.D. research scholar Hans Raj College, University of Delhi 2011  
30 13961 Mr. Kushal Lalwani Male University of Delhi Ph.D D.U. (M.A.) 2011  
31 14022 Mr. Abdul Gaffar Khan Male University of Delhi Ph.D. Scholar Hindu College,University of Delhi 2016  
32 13663 Mr. Manpreet Singh Male Indian Institute of technology PhD Punjabi University, Patiala. 2014  
33 13649 Ms. Geeta Gupta Female University of Delhi MPhil INDRAPRASTHA COLLEGE FOR WOMEN, UNIVERSITY OF DELHI 2013  
34 13684 Mr. Manoj Prajapati Male Jawaharlal Nehru University Ph.D Sardar Patel University 2014  
35 13699 Mr. Rajdip Palit Male Jawaharlal nehru University PhD IIT MADRAS 2012  
36 13731 Mr. Alok Kumar Yadav Male Jawaharlal Nehru University PhD D.D.U. Gorakhpur University, Gorakhpur 2011  
37 13551 Mr. Prashant Vasantrao Uswadkar Male Shiv Nadar University PhD student Pune University 2010  



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