AIS Homotopy Theory (2019)

 Speakers/Tutors with their affiliations:

Syllabus:

Aim of the school and syllabus

Homotopy theory has turned out to be one of the most prominent topics in Algebraic Topology starting from the 1950s. The celebrated computations of Serre and Toda of ho- motopy groups of spheres led to the systematic calculation of cobordism groups by Thom, Milnor, Wall, Stong and others. From the 1970s, it was clear that the stable homotopy cal- culations are very important and bear a lot of applications to problems in differential topology.

The homotopy theory for G-spaces (called equivariant homotopy theory), that is spaces with an action of a specific group G, has also been of great interest. One of the starting points of the subject was the spherical space form problem which was finally solved by Madsen, Wall and Thomas. The analogous statement for a product of spheres is one of the major unsolved problems in this subject called the rank conjecture. The techniques in equivariant homotopy theory also give a nice proof of the Atiyah-Segal completion the- orem, among many other such results. In the AIS, we studied homotopy theory with a view towards equivariant homotopy theory.

Generalized cohomology theories, cohomology operations and K-theory was discussed in detail in the first week, together with an introduction to Bredon cohomology. Some background in differential topology and basic homotopy theory was also reviewed. The second week comprised of three mini-courses on 1) Atiyah-Segal completion theorem, 2) Stable homotopy theory, 3) Computations in equivariant homotopy theory.

 Time Table

List of actual Participants

How to reach

Direction
The ISI campus lies five kilometers North of the Shyambazar five-point crossing. If you are coming from the airport, drive towards Dunlop Bridge (via Nager Bazar and Chiria More). If you are coming from the downtown area or one of the railway stations, you will have to drive past Shyambazar and Chiria More. As you approach Dunlop Bridge, the boundary wall of the ISI campus will be visible on your left. The residential campus is at the Bus Stop called Bon Hooghly and the office campus is at the Bus Stop called ISI or Statistical. The Bus Stop further to the Statistical Bus Stop is Dunlop Bridge, which is an important landmark. Dunlop Bridge is also a useful way of describing the general destination when you are asking for directions.

If you miss the ISI gates and reach the Dunlop Bridge intersection, take a sharp left turn into Gopal Lal Tagore Road. The ISI campus will be on your left. The first entrance on your left leads you straight into the Library Building.
 
Taxi
If you are coming from the airport or one of the railway stations, it is better to hire a taxi from the prepaid taxi booth. The prepaid taxi fare is marginally higher than normal (approximately Rs. 130 from the airport, Rs. 120 from Howrah, and Rs. 100 from Sealdah) but it is a surer and safer mode of transport. While hiring a prepaid taxi, mention Dunlop Bridge as your destination.

Meter information (as of December, 2004):

    Mechanical meters (an old box attached outside the cab):
    Intial Reading: Rs. 5.00
    Total Fare: Rs. 3 x meter reading
    Electronics meters (usually attached inside the cab):
    Intial Reading: Rs. 10.00
    Total Fare: Rs. 1.50 x meter reading
    Extra charges for taking a taxi to the airport: Rs. 10

The taxi driver is also supposed to carry a conversion chart with the validation date clearly marked on it.
 

Buses
There are a large number of buses and minibuses that pass by the Institute campus. Almost any bus that goes to Dunlop Bridge passes by the ISI gates. The buses that pass by the ISI gates are 11, 32A, 34B/1, 78, 78/1, 78/2, 78A, 78B, 78C, 201, 214, 230, 234, DN9, DN9/1, L9A, L11, L20, L20A, M1, M2, M6, S9, S11, S32, GL32, GLS32, and SS4. The minibuses plying from Howrah to Nimta/Belgharia/Rathtala, from BBD Bag to Dunlop Bridge, from Babughat to Sodepur/New Barrackpore and from Metiaburuj to Srirampur go past the ISI gates before reaching Dunlop Bridge. While riding the bus from the city, the major bus stops on your way (from South to North) would be Shyambazar, Chiria More, Sinthi More and Tobin Road. The Bon Hooghly Bus Stop is just North of the Bus Stop at Ananya Cinema. This is where you have to get down in order to enter the residential campus. The next Bus Stop is ISI/Statistical, which is located just outside the entrance of the main office campus at 204, B.T. Road.