MPLW Kervaire Invariant Problem and its solution (2012)


ISI, Kolkata

Dates: 14th-25th May, 2012


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


School Convener(s)

Name Goutam Mukherjee
Mailing Address

Stat-Math. Division,
Indian Statistical Institute,
203, B.T. Road,
Calcutta 700 108


Basic homotopy theory; spectra, use of spectral sequences in the computation ofhomotopy groups of spheres, formal groups laws and complex cobordism, some methods and techniques to understand Kervaire invariant problem and its recent solution.

Speakers and Syllabus 

Day 9:30 – 10 10 – 11:30 Tea 12-1:30 Lunch 3:30-5:00 Tea
May 14 Introduction –SB

Basic homotopy theory


  Spectral Sequences
I - NP
  Spectra I  
May 15   Basic Homotopy
  Spectral Sequences
  Spectra II -
May 16   Complex Cobordism
I - PS
  Kervaire Invariant I
- HM
  Steenrod Algebra -
May 17   Complex Cobordism
  Kervaire Invariant II
- HM
  Adams Spectral
Sequence - SB
May 18   Quadratic forms over
F_2 - RB
  Adams spectral sequence
computations - SB
  Browder's theorem -
May 19   Equivariant homotopy
theory - RS
  Idea of the solution - RS   The slice spectral
sequence - SB

ARS- A.R.Shastri (IIT, Bombay)

 NP- N. Pandey (BKC College, Kolkata)

 RS- R. Santhanam (IIT, Kanpur)

 PS- P. Sankaran (IMSC, Chennai)

 HM- H. Mukherjee(NEHU, Shillong)

 RB- R. Banerjee(TIFR, Bombay)

 GM-G. Mukherjee(ISI, Kolkata)

 SB- S. Basu(RKMVU, Belur)


 From May 21 -25 Prof Michael Hopkins will lecture about the Kervaire invariant one problem and related topics.



Selected Applicants


  • The selected participants are requested to confirm their participation by 10th April 2012 for booking accommodation.
  •  Confirmation mail should be sent to homotopy0512 at
  • Travel by 3rd AC Train fare is allowed to the participants


Sr SID Full Name Gender Affilation State Position in College/University
1 1380 Ms. Yajnaseni Dutta Female CMI Chennai Tamil Nadu  
2 1382 Ms. Jaspreet Kaur Female Department of Mathematics University of Delhi DELHI Research Scholar
3 1384 Mr Subhash B Male IMSc, Chennai Tamil Nadu  
4 1413 Mr Ramesh Kasilingam Male IIT Bombay Maharashtra Research Scholar
5 1403 Mr. Prateep Chakraborty Male IMSc, Chennai Tamil Nadu Research Scholar
6 1414 Mr. Rajesh Kumar Singh Male IIT KANPUR Uttarpradesh  
7 1440 Mr. Vivek Tewary Male IIT Kanpur Uttar Pradesh Research Scholar
8 1428 Mr. Apurv Nakade Male CMI Chennai Tamil Nadu  
9 1433 Mr. Aneesh Karthik Chandrasekhar Male   Tamil Nadu  
10 1436 Mr Samir Shukla Male IIT Kanpur UTTAR PRADESH Research Scholar
11 1439 Ms Shilpa Suresh Gondhali Female T.I.F.R., Mumbai Maharashtra Research Scholar
12 1496 Mr Sayan Chakraborty Male CMI Chennai Tamil Nadu Research Scholar
13 1518 Dr. David Farris Male Indian Institute of Science Karnataka  
14 1520 Mr. Divakaran D Male Indian Institute of Science Karnataka SRF

 Local participants

  1. Ashis Mandal
  2. Swagata Sarkar
  3. Apurba Das
  4. Shubhabrata Das
How to reach


How to reach the venue: ISI, Kolkata


The Indian Statistical Institute (ISI), Kolkata campus lies six kilometers North of the Shyambazar five-point crossing. An important
landmark is Dunlop Bridge, which is 500 metres north of ISI campus.The cars coming from the airport take the elevated Belghoria
expressway from Jessore road, get out near Dunlop Bridge at Dakshineswar. Alternatively, they come 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.

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. 130-150 from the airport, Rs. 130 from Howrah station, and Rs. 110 from Sealdah station) but it is a surer and safer mode of transport. While hiring a prepaid taxi, mention Dunlop Bridge as your destination.
Meter information : The blue-bordered yellow taxis of Kolkata run on meter. There are also few red colored taxis which run on LPG fuel.
However, the final fare has to be converted from the amount shown on the meter. The taxi driver should carry a conversion chart, but here is a quick conversion formula. Initial Reading: Rs. 10.00 . Total Fare: Rs. 2 x meter reading + Rs. 2.

In case of any trouble, you should contact Traffic Control Room at

9830010000 or 9830811111.
ISI Kolkata campus:
A map of ISI Kolkata campus is available at this link. The institute Guest House is marked 13 on the map and the ISEC guest house is
located in the Neils Bohr Hall, marked 4 on the map. The lectures will be held in the lecture hall in the ground floor of A. N. Kolmogorov
Bhavan, marked 28 on the map. A. N. Kolmogorov Bhavan can be reached through the Pedestrian Subway, marked 15 on the map and then passing through the portico under R. A. Fisher Bhavan, marked 22 on the map.

Phone calls:
Each room in the Guest House has a phone connection with its four digit number written on it. The complete number can be obtained by putting 2575 before them. You may receive calls directly on that phone. To call the phone from outside Calcutta, but within India, put
033 before those eight digits. To call from abroad, put 009133 before the eight digits.
Unfortunately, you cannot make direct external phone calls from the guest house. However, there are many public call phone booths in the cross road across the B. T. Road, as you come out through 205, B. T. Road gate from the Guest House campus.Alternatively, you can buy prepaid India Telephone Card and use them from any telephone.

Useful phone numbers:
In case of need, you may contact one of the local organizers at:
Mahuya Datta: +91-33-2575 3402
Goutam Mukherjee: +91-33-2575 3429 (09830120707)
A few more useful phone numbers are: Guest House reception: +91-33-2575 5900
Guest House office: +91-33-2575 4060, +91-33-25755970
Stat-Math Office: +91-33-2575 3400, +91-33-25754300