Annual Foundation School - Part II (2012)

Venue: Pune University, Pune
Dates: 4th Jun - 30th Jun, 2012


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


School Convener(s)

Name S. A. Katre A. R. Shastri V. V. Joshi
Mailing Address

Centre for Advanced Study in Mathematics,
Dept. of Mathematics, Univ. of Pune

102 C, Department of Mathematics,
Indian Institute of Technology Bombay,
Mumbai - 400 076
Dept. of Mathematics,
Univ. of Pune



Speakers and Syllabus 

 2.1. Ring Theory.

(1) Module 1: (6 lectures) Commutative rings, nil radical, Jacobson radical, localization of rings and modules, Noetherian rings, primary decomposition of ideals and modules.
(2) Module 2: (6 lectures) Integral extensions of rings, Going up and going down theorems, finiteness of integral closure, discrete valuation rings, Krull’s normality criterion, Noether normalization lemma,Hilbert’s Nullstellensatz
(3) Module 3 : 6 lectures Semisimple rings, Wedderburn’s Theorem, Rings with chain conditions and Artin’s theorem, Wedderburn’s main theorem,
(4) Module 4 : 6 lectures Semisimplicity and tensor products, SkolemNoether theorem, Wedderburn’s theorem about finite division rings,Frobenious theorem about division algebras over the reals.

(1) S. Lang, Algebra, 3rd edition, Addison-Wesley, (2) D. S. Dummit and R.

M. Foote, Abstract Algebra, 2nd edition John-Wiley (3) N. Jacobson, Basic
Algebra, Vol. 1 and 2, Dover, 2011. (4) A. W. Knapp, Advanced Algebra,
Birkhauser, 2011.

 2.2. Functional Analysis. Chapters refer to the ones in [K].

(1) Module 1 : 6 lectures Normed linear spaces, Continuous linear transformations, application to differential equations,Hahn-Banach theorems-analytic and geometric versions, vector valued integration
(2) Module 2 : 6 lectures Baire’s theorem and applications: Uniform boundedness principle and application to Fourier series, Open map-
ping and closed graph theorems, annihilators, complemented subspaces, unbounded operators and adjoints
(3) Module 3 : 6 lectures Weak and weak* topologies, Applications to reflexive separable spaces, Uniformly convex spaces, Application to calculus of variations
(4) Module 4 : 6 lectures : Chapter 7 of [K] Hilbert spaces, Riesz representation theorem, Lax-Milgram lemma and application to variational inequalities, Orthonormal bases, Applications to Fourier series and examples of special functions like Legendre and Hermite polynomials.


2.3. Algebraic Topology. Numbers in brackets indicate sections from [Sh].

(1) Module 1: 6 lectures: Statement of basic problems in Algebraic Topology: extension problems and lifting problems; homotopy, relative homotopy, deformation, contraction, retracts etc.(1.1),Typical constructions: Adjunction spaces, Mapping cones, Mapping cylinder, Smash-product, reduced cones reduced suspension etc.(1.2,1.3), Categories and Functors. Definition and examples. Equivalence of functors, adjoint functors, examples.(1.4), Computation of fundamental group of the circle and applications. (3.1,3.2).
(2) Module 2: 6 lectures: Spaces obtained by attaching n-cells. Basic topological properties. Tubular neighbourhood theorem. Examples (2.1), CW-complexes and basic topological properties. Products of CW complexes. (2.1), Homotopy theoretic properties of CW compelxes.(2.1), Abstract Simplicial complexes and geometric realization. (2.2), Barycentric subdivision and Simplicial Approximation theorem.(2.3), Cellular Approximation theorem and applications.(2.4)
(3) Module 3: 6 lectures: Covering Spaces. (4.1), Lifting properties.(4.2), Relation with fundamental group. (4.3) Classification (proof of existence may be skipped).(4.4), Computation of Fundamental groups: simpler cases of Van-Kampen theorem. Effect of attaching n-cells.(4.6).
(4) Module 4: 6 lectures: Chain complexes, exact sequences of complexes, snake lemma, four lemma and five lemma. Homology long exact sequence, Axioms for homology, Construction of Singular chain complex, verification of axioms (except homotopy axiom and excisionaxiom), Simplicial and Singular simplicial chain complexes. Statement of equivalence of all these homologies, Computations, Separation theorems, Invariance of Domain. Euler charasteristic.

[H] A Hatcher, Algebraic Topology, Cambridge University Press.
[M] Algebraic Topology, C. R. F. Maunder, Van Nostrand Reinhold Companay. London.
[Sp] E. H. Spanier, Algebraic Topology, Tata McGraw-Hill.
[Sh] A. R. Shastri, Basic Algebraic Topology, http// ars


Selected Applicants
  • The selected participants are requested to confirm their participation by 31st March 2012 for booking accommodation.
  • Confirmation mail should be sent to sakatre at and to "Vinayak Joshi"  vinayakjoshi111 at
  • Travel by 3rd AC Train fare is allowed to the participants.
  • The participants are encouraged to bring along books related to topics of AFS-II.
Sr SID Full Name Gender Affiliation State Position University /Institute M.Sc./ M.A Year of Passing M.Sc./ M.A Ph.D. Deg. Date
1 923 Mr. Debashish Sharma M National Institute of Technology, Silchar Assam PhD scholar Assam University, MSc Mathematics 2011  -
2 941 Mr. Pritam Rooj M

Dept. Of Pure Mathematics. Univ. Of Calcutta

3 948 Mr Gopinath Panda M Indian Institute of Technology Odisha Research Scholar Utkal University 2008  -
4 962 Mrs Nidhi Chaudhary F BITS Pilani Rajasthan Research Scholar C C S University 2009  -
5 965 Ms Preeti Dubey F BITS Pilani Rajasthan Research Scholar CSJMU Kanpur, M.Sc. 2006  -
6 975 Mr. Laxmi Kant Mishra M Univ.y of Allahabad Uttar Pradesh Research Scholar University of Allahabad 2009  -
7 994 Mr. Sumit Kumar Kumar M Indian Institute of Science, Bangalore Karnataka Student Depatment Of Mathematics , Indian Institute Of Science , Bangalore  - -
8 996 Mr. Sachin Vitthalrao Sarode M Shri Muktanand College Maharashtra Assistant Professor Pune University 2010  -
9 1019 Mr. Chiranjit Ray M Indian Institute of Technology, Guwahati Assam research scholar Ramakrishna Mission Vidyamandira 2010  -
10 1045 Mr. Manish Chhabanrao Agalave M Fergusson College, Pune Maharashtra Assistant Professor University of Pune 2006 -
11 1050 Mr. Rahul Gupta M IIT Delhi Delhi Research scholar IIT Delhi 2011  -
13 1060 Ms Kumari Saloni F IIT Guwahati Assam Research Scholar IIT Guwahati 2010  -
14 1066 Mr. Pralhad Mohan Shinde M IISER Pune Maharashtra Ph.D student University of Pune (M.Sc) 2011  -
15 1070 Ms Dishari Chaudhuri F Indian Institute of Technology, Guwahati Assam Research Scholar Indian Institute of Technology, Kharagpur 2010 -
16 1072 Ms. Manidipa Pal F IISER PUNE Maharashtra Research Fellow IIT BOMBAY / M.Sc. 2011  -
17 1073 Mr Palraj J M

PSG College Of Arts And Science

Tamil Nadu Research Scholar Sri Ramakrishna Mission Vidyalaya College of Arts & Science, Coimbatore 2009  -
18 1079 Mrs. T. Yogalakshmi T.Yogalakshmi F

Sri Sarada College For Women

Tamil Nadu Research Scholar (student) University of Madras 2008  -
19 1090 Mr Sushil Bhunia M IISER PUNE Maharashtra Research Scholar JADAVPUR UNIVERSITY/ M.Sc 2010  -
20 1091 Ms. Rana Noor F Banaras Hindu University Uttar Pradesh Research Scholar Banaras Hindu University 2010  -
21 1102 Ms Vijayalakshmi Palanisamy F PSG College Of Arts And Science Tamilnadu Research Scholar PSG College Of Arts And Science 2009  -
22 1106 Mr. Abhash Kumar Jha M NISER, Bhubaneswar Orissa research scholar Banaras hindu university 2010  -
23 1109 Mr Loganathan Seenivasan M VHNSN College Tamilnadu Assistant Professor Gandhigram Rural University 2006  -
24 1111 Mr. Hitesh Ramesh Raundal M IISER, Pune. Maharashtra 2nd year Ph.D. Student M.Sc. from University of Hyderabad, Hyderabad. 2010  -
25 1114 Ms Gunja Sachdeva F

Dayalbagh Educational Institute, Deemed University

26 1119 Mr. Sheo Kumar Singh M Banaras Hindu University Uttar Pradesh Research Scholar Banaras Hindu University 2006  -
27 1120 Mr. Prabhat Kumar Kushwaha M IISER, PUNE Maharashtra Research Scholar

Dept. Of Mathematics, Faculty Of Science, B.H.U. , Varanasi

2011  -
28 1136 Mr. Gugan Chandrashekhar Thoppe M TIFR Maharashtra Research Scholar -  -  -
29 1140 Mrs Visalakshi Vairavan F Sri Sarada College for women Tamil Nadu student Sri Sarada College for women (autonomus) 2008  -
30 1143 Mr. Sasi Kumar Palanisamy M Gobi Arts & Science College, Gobichetti - palayam Tamil Nadu Research Scholar Gandhigram Rural University, Dindigul 2004 -
31 1144 Mr. Abdul Nadim Khan M

Aligarh Muslim University, Aligarh

Uttar Pradesh Research Scholar M.SC 2009  -
32 1162 Mr. Pabitra Debnath M St. Xavier's college (Autonomous), Kolkata West Bengal Assistant Professor. I.I.T KANPUR 2004 -
33 1171 Mr. Chirag Garg M IIT Delhi New delhi Research scholar Punjabi university Patiala 2010  -
34 1172 Mr . Yogesh Kumar M IIT Delhi New delhi Phd. Research Scholar M.D.U. ROHTAK 2008  -
35 1179 Mr D Chellapillai M

Bharathidasan University

Tamil Nadu Research Scholar M.Sc Mathematics, Bharathidasan University, Tiruchirappalli, Tamil Nadu 2009  -
36 1191 Mr Azeef Muhammed Pa M University Of Kerala Kerala Research Scholar University Of Hyderabad, M Sc Mathematics 2011  -
37 1194 Mr. Saurabh Chandra Maury M University of Allahabad U.P. Research scholar University of Allahabad, Allahabad 2007  -
38 1201 Ms. Ishrat Jahan Md.Haroon Ansari F M.C.E Society's Abeda Inamdar Sr.College Maharashtra Assistant Professor Department of Mathematics ,University of Pune 2007  -
39 1203 Ms. Sonali Vishnu Mandavkar F M.C.E.Society's Abeda Inamdar Senior College Maharashtra Assistant Professor M.C.E.Society's Abeda Inamdar Senior College 2008  -
40 1204 Mr Dillip Kumar Pradhan M

Sambalpur University

ODISAH Student Sambalpur University 2011  -
41 1206 Ms. Nasreen Bano Muslim Shaikh F Abeda Inamdar Senior College Maharashtra Assisstant Professor Abeda Inamdar Senior College 2010  -
42 1222 Mr. Hardeep Singh Singh M JNU, New Delhi DELHI Pre. Ph.D.

Punjabi University, Patiala

2009  -
43 1230 Mr. Ramdas Raosaheb Shiketod M

School Of Mathematical Sciences,
SRTM Univ., Vishnupuri,

Maharashtra Student School Of Mathematical Sciences,
SRTM Univ., Vishnupuri,
---  -
44 1232 Ms. Priyanka Mahajan Ambulge F

Swami Ramanand Teerath Marathwada University, Nanded

Maharashtra Student --  -- -
45 1248 Mr Rajiv Ganthi M Gandhigram Rural Institute, Deemded University Tamil Nadu Research Scholar 2007  -


How to reach

University of Pune is on the University Road, and it is about 5 km from the Main Railway Station and Main Bus stand. The nearest Railway Station is Shivajinagar Railway Station (3km) and it is most convenient while coming from Mumbai side, but one should make sure that the train stops there. The  autorickshaw fare is about 10 times the meter reading.

From airport the University is about 16 km.

When one enters the university there are 2 roads, take the right road to go to Mathematics Dept. or to University Guest House/ Univ. SET Guest House. Dept. of Math. comes first on this road on the left side, and it is a building  with Green Colour Fence. To go to SET Guest House, one goes ahead and at the end turns to the
left, to go near main Guest House. The main Guest House is very near the main building (with Flag) and is next to VC Bungalow and from the main Guest House, a road goes to IUCAA. The SET Guest House is located on this road about 150 meters from main Guest House on the right side.