MPLW Dynamics of Vector Fields 2012


TIFR Mumbai

Dates: 9 -14 April 2012


Convener(s) Speakers, Syllabus and Time table Applicants/Participants


School Convener(s)


Prof. S. G. Dani

Mailing Address

School of Mathematics, TIFR, Homi Bhabha Road
Colaba, Mumbai 400005

The 125th birth anniversary of Srinivasa Ramanujan falls in 2012. Government of India has declared it as the National Mathematics Year at the request of the Ramanujan Mathematical Society.Several mathematical activities are planned during 2012 and 2013. Among them a series of surveys called Mathematical Panorama Lectures are being planned. These are lecture courses given by eminent mathematicians on diverse topics of current research. These survey lectures will be accessible to research scholars and lead upto recent developments.


Speakers and Syllabus 

Professor Etienne Ghys is a Distinguished Professor of CNRS, France. He is a Fellow of the French Academy of Sciences of
”l’Institut de France” and was one of the Plenary speakers at the International Congress of Mathematicians at Madrid (2006).
D’Alembert medal of the French Mathematical Society (2010) and ”Docteur Honoris Causa” of the University of Geneva (2008) are some of his numerous other honours. He has made important contributions in various areas of mathematics including differential geometry, global analysis, dynamical systems and ergodic theory.


The dynamics of vector fields on surfaces is fairly well understood. Starting from dimension 3, one can encounter more complicated and interesting phenomena, like chaotic behaviour for instance. In this series of talks, I would like to give a general introduction to the qualitative dynamics of flows 3-manifolds. I will begin at a very elementary level and I will describe a great number of significant examples. Then, depending on time, I shall discuss the following three aspects : many attempts to describe all Anosov flows and some conjectures, search for periodic solutions, around the former Seifert and Weinstein’s conjectures, Kuperberg example, Hofer and Taubes’s theorem, and the conjecture in the volume preserving case.The construction of Birkhoff sections, the concept of left handed vector field, and conjectures concerning geodesic flows in negative curvature.


Selected Applicants


How to reach

From Airports

45-90 minutes by taxi.
From the international and domestic airports

Pre-paid taxis are the recommended way of reaching TIFR from Mumbai's airports. There are counters for pre-paid taxis before you exit the arrival hall. Specify your destination as "Navy Nagar, Colaba".

You will be given a receipt for your payment. Retain this till the end of your ride; then hand it over to the taxi driver. At the exit from the airport, the police may want to look at this slip.

From Railway Stations
From CST

20-30 mins by taxi.

Taxis are available from the Chatrapati Shivaji Terminus (CST). They charge by meter. Alternatively, one can board buses to Navy Nagar (bus terminal) from outside the local railway station at CST. TIFR is on the same road as the Navy Nagar bus terminus, which is where you should get off.
From Mumbai Central

30-45 mins by taxi.

Taxis are available from the ranks outside the railway station. Alternatively, you could cross over to the local railway station and board a Churchgate bound local. You have to buy a separate ticket for the local train. Taxis are available from outside Churchgate. Alternately, a bus (route 137) comes from Churchgate to the Navy Nagar bus terminus, down the road from TIFR.