Characteristic Classes and Cobordism

Convener(s)

 
Name: Anant Shastri (retired Emeritus Fellow) Sudarshan Gurjar
Mailing Address: Department of Mathematics,
I.I.T. Bombay, Powai, Mumbai 4000 76.		 Department of Mathematics,
I.I.T. Bombay, Powai, Mumbai 4000 76.
Email: anant.shastri at gmail.com sgurjar at math.iitb.ac.in

Target Audience: Researchers in the country working in Topology.

This event is primarily aimed at those students who have successfully attended the AIS in Differential Topology at NEHU Shillong in July 2018. All research workers in the country who are interested in Algebraic/Differential
Topology are welcome to attend. No travel allowance is given to any participant. Local hospitality for the period 3rd to 16th March 2019 will be given as per NCM norms. Preference in paper presentation will be given to young research workers in Topology who are attending the entire event. There is no registration fee. However, all hopeful participants should register online on or before 31st Dec 2018.

Participants who are interested in presenting paper should send a brief write-up by 31st Dec 2018.Their selection will be intimated to them by email.

Please Note:  Participants have to arrange for their own travel.

Dates: 

Monday, March 4, 2019 - 09:00 to Friday, March 15, 2019 - 18:00

Venue: 

Venue Address: 

IIT Bombay

Venue State: 

Venue City: 

Chrono Order: 

307

Syllabus: 

 Week I:

Saurav:

1. Basic theory of vector bundles (real as well as complex).
2. Homotopical Aspects and classification.
3. Fibre bundles, reduction and extension of structure groups.

Shastri:
1. CW-complexes, CW-structure of Grassmannians and flag manifolds.
2. Cohomology algebra of real and complex projective spaces, of Grassmannians.
3. Orientation on vector bundles, Thom’s isomorphism theorem (proof may be omitted), Leray-Hirsch Theorem.

Tiken:
1. Steifel-Whitney Classes.
2. Euler Classes.
3. Chern and Pontryagin Classes.

Week II:

  1. Hirzebruch Riemann Roch (Yogish)
  2. Chern-Weil Theory.(Arvind)
  3. Thom’s Cobordism Theorem (unoriented and oriented).(Raghunathan)

References

  1. Milnor and Stasheff - Characteristic Clases
  2. Allen Hatcher - Vector Bundles and K-Theory
  3. Shigeyuki Morita - Geometry of Characteristic Classes
  4. Dale Husemoller - Fibre Bundles
  5. Hirzebruch - Topological Methods in Algebraic Geometry.
  6. Anant Shastri - Basic Algebraic Topology.

List of Resource Persons:List of Resource Persons:

  1. Arvind Nair (TIFR)
  2. M. S. Raghunathan (CEBS)
  3. Nitin Nitsure (TIFR)
  4. Anant R. Shastri (IITB)
  5. Saurav Bouwmik (IITB)
  6. Yogish Holla (TIFR)
  7. Angkom Tiken Singh (NEHU)
  8. Rekha Santanam (IITB)
  9. Sudarshan Gurjar(IITB).

Time Table: 

Week I: 4th to 9th March 2019

  9-30– 11-00 Tea 11-30– 13-00   15-00–00 16-30 Tea/ Snacks 17-00– 18-00
Mon Saurav   Shastri L Nitin   DISCUSSION
Tue Saurav   Shastri U Nitin  
Wed Saurav   Shastri N Nitin  
Thu Saurav   Tiken C Nitin  
Fri Saurav   Tiken H Nitin  
Sat Shastri   Tiken   Nitin  

Week II: 11th to 15th March 2019

  9-30– 11-00 Tea 11-30– 13-00   15-00–00 16-30 Tea/ Snacks 17-00– 18-00
Mon Yogish   Raghunathan L Arvind   DISCUSSION
Tue Yogish   Raghunathan U Arvind  
Wed Yogish   Raghunathan N Arvind  
Thu Yogish   Raghunathan C Arvind  
Fri Yogish   Raghunathan H  Arvind  

Selected Applicants: 

Instructions to the candidates.
 
  1. We are happy to announce that the program has received a  large number of applications mostly from deserving candidates. 
    However at present, the program can accommodate only 30 participants. We are trying our  best to increase the capacity to 40 or 45, in an attempt to reach out to as many as possible.  
  2.  Each selected  candidate is required to send a (scanned or photo) copy of the forward journey ticket  to the organizers by email at the earliest at the following addresses anant.shastri@gmail.com/sgurjar@math.iitb.ac.in Accordingly, the confirmation of participation will be announced on the webpage on a first-cum-first served basis.  This information will be updated every week.
  3. At any stage before the program starts,   if a confirmed participant decides to drop out of the program for any reason, he/she is requested to inform this to the organizers so that some other deserving candidate gets a chance to attend the program.
  4. Time to time check the  Selection Status.
 
Sr.n SID Full Name Gender Affiliation Position in College/ University University/ Institute M.Sc./ M.A. Ph.D. Degree Date
1 23597 Mr. Umar Mohammad Khan Male Aligarh Muslim University PhD Student Aligarh Muslim University  
2 23601 Mr. Saikat Panja Male IISER,Pune PhD IISER-Kolkata  
3 23610 Mr. Ajay Raj Male IISER Tirupati Project Assistant The Maharaja Sayajirao University of Baroda  
4 23617 Mr. Ayush Jaiswal Male IIT , Gandhinagar Research Scholar Indian Institute of Technology, Kanpur  
5 23625 Mr. Joji Benny Male IIT, Madras Research Scholar UM DAE CEBS  
6 23627 Ms. Anju Kumari Female University of Delhi PhD student Hindu College, University of Delhi  
8 23659 Dr. Shameek Paul Male Ramakrishna Mission Vivekananda Educational and Research Institute Assistant Professor University of Mumbai 07/01/2012
9 23673 Mr. Arijit Mukherjee Male University Of Hyderabad Ph.D Ballygunge Science College,University Of Calcutta  
13 23683 Mr Pritthijit Biswas Male Chennai Mathematical Institute PhD. Ramakrishna Mission Vivekananda University  
14 23688 Mr Praphulla Koushik Male IISER Trivandrum PhD student University of Hyderabad  
16 23697 Mr. Adittya Chaudhuri Male IISER-TVM PhD IISER-TVM  
17 23702 Dr Subhash B Male IISER Tirupati Asst Prof Pondicherry university 10/08/2009
19 23709 Mr. Sagar Balasaheb Kalane Male IISER MOHALI PhD IIT Madras  
21 23716 Mr. Reebhu Bhattacharyya Male IIT, Bombay Integrated Masters Student IIT, Bombay  
22 23718 Mr. Avijit Nath Male IMSc Senior Research Fellow (SRF) in Mathematics Ramakrishna Mission Vivekananda University, Howrah  
23 23719 Mr Navnath Balasaheb Daundkar Male Chennai Mathematical Institute PhD Student Pune University  
25 23730 Mr. Lokenath Kundu Male IISER Bhopal. PhD VISVA-BHARATI  
26 23736 Ms. Apeksha Sanghi Female IISER BHOPAL PhD Delhi University  
27 23742 Mr. Arindam Das Male BITS Pilani Goa PhD Nit Rourkela  
28 23744 Mr. Kartick Ghosh Male IISc Bangalore Int. PhD Student IISc Bangalore  
29 23759 Mr. Sambit Senapati Male Chennai Mathematical Institute MSc Student Chennai Mathematical Institute  
30 23768 Mr. Sridhar Venkatesh Male Chennai Mathematical Institute MSc Student Chennai mathematical Institute  
31 23771 Mr. Abhijeet Atmaram Ghanwat Male Chennai Mathematical Institute Ph.D. Student University Of Pune, Pune  
32 23774 Mr Selvakumar A Male IIT Madras Ph.D Ayya Nadar Janaki Ammal College, Sivakasi  
33 23795 Ms. Arifa Naz Female Aligarh Muslim University Ph.D Aligarh Muslim University  
34 23805 Mr. Prashant Shivaji Arote Male TIFR Ph.D. University of Pune.  
35 23819 Ms. Roma Pathak Female Dayalbagh Educational Institute Ph. D. Student Dayalbagh Educational Institute  
36 23832 Mr Mohit Upmanyu Male TIFR Reasech Scholar    
37 23837 Mr. Amit Kumar Paul Male IIT KANPUR PhD VISVA BHARATI  
40 23876 Mr Harsh Prasad Male Shiv Nadar University BS Student NA  
42 23887 Mr. Abhishek Sarkar Male I.I.T. Kanpur PhD VISVA BHARATI  
43 23890 Mr. Yashasvi Aulak Male NISER, Bhubaneswar Integrated MSc student NISER/Int. M.Sc. Physics  
44 23898 Mr. Paramjit Singh Male Chennai Mathematical Institute MSc Student Chennai Mathematical Institute  
45 23902 Mr. Praneet Srivastava Male Shiv Nadar University B. Sc. Student    
46 23920 Mr Arijit Nath Male IIT Madras Ph.D student Ramakrishna Mission Vivekananda University  
47 23929 Mr. Puneet Kumar Gupt Male University of Lucknow, Lucknow PhD University of Lucknow, Lucknow  
49 23942 Mr Jitendra Rathore Male TIFR Mumbai P.hD IISER MOHALI  
50 23946 Mr. Subhankar Sau Male IIT Madras PhD Student IIT Madras  
51 23951 Mr. Soham Mondal Male IIT MADRAS PH.D VISVA-BHARATI 02/01/2018
52 23968 Ms. Aparajita Karmakar Female Indian Statistical Institute, Kolkata PhD Burdwan University  
53 23977 Mr. Bikramjit Kundu Male Ramakrishna Mission Vivekananda Educational and Research Institute Ph.D.    
54 23987 Mr Anantadulal Paul Male National Institute Of Science And Research PhD University of Pune, Pune  
56 23995 Mr. Koushik Brahma Male IIT Madras PhD IIT Madras  
57 24007 Mr. Jeyarambharathi A.M. Male Hindustan Institute Of Technology And Science,
Hindustan Institute Of Technology And Science		 PhD Meenakshi Academy Of Higher Education And Research  
58 24021 Mr. Debjit Basu Male IISER Mohali  Int.PhD student IISER MOHALI  
59 24025 Mr. Jyotirmoy Ganguly Male IISER, Pune PhD Student University of Hyderabad  
60 24034 Mr. Akshay P R Male Indian Institute of Science education and research Trivandrum Bs-Ms dual degree student IISER Trivandrum  
61 24044 Mr. Rohit Suhas Joshi Male Bhaskaracharya Pratisthan Pune Post. doc. student IIT Kanpur 25/05/2018
62 24054 Mr. Buddhadev Hajra Male IIT Bombay PhD IIT Bombay  
 
  

School Short Name: 

ccc

Last Date Application: 

Friday, March 15, 2019

School Type: 

NCMW