IST Algebraic Topology (2015)

Venue:  Goa University
Dates: 7th - 19th  Dec


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


School Convener(s)

Name C. S. Aravinda A. J. Jayanthan
Mailing Address TIFR Centre for Applicable mathematics
P. O. Box 6503, Sharada Nagara
G. K. V. K. Post, BANGALORE - 560 065.
Department of Mathematics
Goa University
Goa - 403 206.


Speakers and Syllabus 

Overview: Basic focus in this workshop is a discussion of the topology of curves, surfaces, and to give an introduction to Algebraic Topology through a discussion of homotopy, fundamental group, covering spaces and simplicial homology. Main emphasis will be to explain concepts through examples. Below is a more descriptive information about the syllabus.

Date 9:00-10:00 10:30-11:30 11:45-12:45 15:00-16:00 16:30-17:30
07/12/15 L1(CSA*) L2(BT) L3(AC) T1 T2
08/12/15 L4(BR) L5(AC) L6(BT) T3 T4
09/12/15 L7(BR) L8(AC) L9(BT) T5 T6
10/12/15 L10(BR) L11(AC) L12(BT) T7 T8
11/12/15 L13(CSA) L14(AC) L15(BT) T9 T10
12/12/15 L16(BR) L17(AC) L18(KV)
14/12/15 L19(HAG) L20(SP) L21(AC) T11 T12
15/12/15 L22(HAG) L23(SP) L24(KV) T13 T14
16/12/15 L25(HAG) L26(SP) L27(KV) T15 T16
17/12/15 L28(HAG) L29(SP) L30(KV) T17 T18
18/12/15 L31(HAG) L32(SP) L33(KV) T19 T20
19/12/15 L34(HAG) L35(SP) L36(KV)


Speakers  Affiliations Topics covered
C S Aravinda  (CSA*)  TIFR CAM, Bangalore Brief review of multivariable calculus.
Bankteshwar Tiwari (BT) BHU-DST Centre, Varanasi Bump functions, partition of unity, smooth Urysohn lemma; quotient topology, Group actions, quotient spaces, Projective
plane, Klein bottle.
Anisa Chorwadwala (AC)  IISER, Pune Definition of smooth manifolds as submanifolds of Rn, abstract definition by smoothness of transition functions, ‘medium form’ of the
Whitney embedding theorem for compact manifolds, embeddings of Projective plane and Klein bottle in R4 .
Binoy Raveendran (BR) TIFR CAM, Bangalore Proof of triangulation of closed surfaces.
Suhas Pandit (SP) IIT, Chennai Homotopy, path homotopy, homotopy equivalence, Fundamental groups, covering spaces.
H A Gururaja (HAG) TIFR CAM, Bangalore Transversality, proof of orientability of closed surfaces in R3 .
Keerti Vardhan Madahar (KV) Panjab University, Chandigarh Simplicial homology, singular homology, homotopy invariance, equivalence of simplicial and singular  homology, homology and fundamental group.

Course Associates:-A J Jayanthan, Goa University and Amith Shasthri, TIFR, Mumbai.

Selected Applicants


Name Affiliation
1. Mr. Mahesh Pravinsingh Solanki Navrachana University
2. Mr. Selvalumar Indian Institute of Technologfy, Chennai
3. Pprof. Pravin Singh Saini Panjab
4. Dr. Sameer Sharma DAV College, Janmdhar, Panjab.
5. Dr. Harindr Singh Govt Rajendra College.
6. Mr. Amith Sasthri TIFR
7. Ms. Dhanya P. M. Calicut University.
8. Dr. Randeep Ganguli DST, CIMS, BHU
9. Kedarnath Buda IISER, Mohali.
10. Praryush Mishra IISER, Mohali
11. Dr. Lucas Miranda Govt. College. Queppem, Goa.
12. Dr. M. Kunhanandan Goa University
13. Prof. C. S. Aravinda TIFR, Bangaluru.
14. Prof. H. A. Gururaja TIFR, Bangaluu.
15. Prof. Anisa Chorwadwala IISER, Pune.
16. Bankteshwar Tiwari DST, CIMS, BHU.
17. Prof. Keerti Vardhan Madahar Panjab University.
18. Prof. Suhas Pandit IIT Madras, Chennai.
19. Dr. Binoy Revindran TIFR Bangaluru.
20. Jayanthan, A. J. Goa University.


 Some of the confirmed participants canceled at the last minute due to floods in Tamil Nadu,
particularly in Chennai.

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