ATMW Geometry & Topology (2012)

This workshop is primarily aimed at the research scholars who have attended AIS in Geometry/Topology at NEHU Shillong, during June 2011 . Of course it is open to all research workers in the country interested in Geometry/ Topology, with as much background in Geometry/Topology as these participants of AIS, if not more. The main theme of the workshop is the series of talks by Prof. F. T. Farrell on ‘Topological Rigidity’. Some of the other topics will aid in understanding this main topic.

List of Resource Persons and Topics:

1) F. T. Farrell: Topological Rigidity

Borel Conjecture. Let M and N be compact boundaryless manifolds whose universal covers are homeomorphic to Euclidean spaces. Then M and N are homeomorphic provided their fundamental groups are isomorphic.
Work on this conjecture is currently a very active area in topology. We will describe in this series of lectures the current state of this work and the tools needed to arrive at it.

2)  Himadri Mukherjee: Surgery on Compact Manifolds and L-groups

The general theory of surgery of compact manifolds with finite fundamental groups (in topological and pl classification context) is in place. However, when one actually deals with concrete examples this general theory is not directly applicable. So one needs to improvise the computations depending on the situation and appeal to the classical surgery exact sequence. The purpose of this series of talks is to develop surgery exact sequence and give some concrete classification results.

3)  P. Sankaran: Characteristic Classes

Axiomatic treatment, existence and uniqueness, Thom isomorphism theorem, Steifel Whitney classes and Pontrjagin classes.

4)  C. S. Aravinda: Farrell-Jones examples

Demonstrating the failure of smooth version of Borel’s conjecture.

5)  A. R. Shastri: Vector Bundles and Classifying Spaces

Generalities about Fibre bundles, Homotopy classification of numerable principal G-bundles, local coordinate description, change of structure groups, Computation of homotopy groups of classical groups and Steifel varieties.

6)  Akhil Ranjan: Kahler Geometry

7)  R. S. Kulkarni: TBA

The selected students will be provided with III-AC return train fare from their workplace to the venue of the ATM-school (IITB) and free accommodation and boarding on the campus (Main Guest House) strictly from 19th Feb to 28th Feb 2012. The selected participants should confirm their participation immediately by writing an email to anant.shastri at gmail.com. They should also communicate the arrival and departure details as soon as they are finalised.

HOW TO GET TO IITB IIT Bombay is located at Powai, which is an eastern suburb in the North-Eastern part of Mumbai.

Mumbai is in the form of a long narrow island, almost a peninsula, thrusting south wards into the Arabian Sea. It can be broadly divided into four zones. 

South Bombay (Colaba, CST,Fort, Chruchgate, Nariman Point etc.) 
Central Bombay (Dadar, Bombay Central, Worli etc) 
The Western suburbs (Bandra, Juhu, Andheri, Borivali etc) 
The Eastern Suburbs(Kurla, Chembur, Ghatkopar, Mulund, Kanjur Marg, Vikhroli etc.) 

There is also New Bombay (Vashi, Turbhe etc.) across Thane Creek on the mainland. 

Public Transport
Mumbai has one of the most efficient and reliable public transport network. One can travel by Autorickshaws / Taxis to reach IIT from the nearest stations(Autorickshaws, however do not go further south than Sion and Bandra). For longer distance, you can use either the BEST Bus Network or the Mumbai Local train System.

Suburban Railway Transport
Those coming by Central Railway Suburban train will have to get down at Kanjur Marg, Vikhroli or Ghatkopar which are the nearest stations from IITB. If you are coming by the Western Railway Suburban train you will have to get down at Andheri, Bandra, Goregoan or Malad. We give below the Road Network to reach IITB along with the approximate Bus/ Autorickshaws/ Taxi fare. (Click here to see the Road companion for IITB )