AFS - Fifth Annual Foundation School-II (2009)

Venue: BIM, Pune
Dates:  8 June-4 July ,2009


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


School Convener(s)

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

 Dept. of Mathematics,
 Univ. of Pune, Pune-411 007

IIT, Bombay

AFS-II being organised in Pune in June 2009 is the Fifth of the 2nd Annual Foundation Schools being organised on behalf of NBHM.

Speakers and Syllabus 



(1) Group Theory: Group Actions. Prime-power Groups. Nilpotent Groups. Soluble Groups. Matrix Groups. Groups and Symmetry. (6 lectures)
(2) Basic Commutative Algebra-I: Prime ideals and maximal ideals, Zariski topology, Nil and Jacobson radicals, Localization of rings and modules, Noetherian rings, Hilbert Basis theorem, modules, primary decomposition, integral dependence, Noether normalization lemma, principal ideal theorem, Hilbert’s Null- stellensatz, structure of artinian rings, Dedekind domains. (12 lectures)
(3) Introduction to Algebraic Number Theory: (6 lectures)


1. Algebra-I, I.S. Luther, I.B. S. Passi
2. M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra.
3. P. Samuel, Algebraic Number Theory.

Complex Analysis

 (1) Euclidean similarity geometry, inversive geometry, hyperbolic geometry and complex analysis.
(2) Analytic functions, Path integrals, Winding number, Cauchy integral formula and consequences. Hadamard gap theorem, Isolated singularities, Residue theorem, Liouville theorem.
(3) Casorati-Weierstrass theorem, Bloch-Landau theorem, Picard’s theorems, Mobius transformations, Schwartz lemma, Extremal metrics, Riemann mapping theorem, Argument principle, Rouche’s theorem..
(4) Runge’s theorem, Infinite products, Weierstrass p-function, Mittag-Leffler expansion.


1. Murali Rao & H. Stetkaer, Complex Analysis, World Scientific, 1991
2. L. V. Ahlfors, Complex Analysis, McGraw-Hill, Inc., 1996
3. A. R. Shastri, Complex Analysis
4. S. G. Krantz, Comlex Analysis: The Geometric View Points, Second edition, Carus Math. Monographs, MAA.
5. A. F. Beardon, Geometry of Discrete Groups, GTM Springer Verlag.

Algebraic Topology

(1) Basic notion of homotopy; contractibility, deformation etc. Some basic constructions such as cone, suspension, mapping cylinder etc. fundamental group; computation for the circle. Covering spaces and fundamental group. Simplicial Complexes.
(2) Homology theory and applications: Simplicial homology, Singular homology, Cellular homology of CW-complexes, Jordan-Brouwer separation theorem, invariance of domain, Lefschetz fixed point theorem etc..
(3) Categories and functors; Axiomatic homology theory.


1. E. H. Spanier, Algebraic Topology, Tata-McGraw-Hill.
2. A. Hatcher, Algebraic Topology, Cambridge University Press.
3. J. R. Munkres, Elements of Algebraic Topology,



Special Lecture Series (Unity of Mathematics Lectures)

Algebra II

I. B. S. Passi (coordinator) email: ibspassi at
  Upendra Kulkarni email: upendra at
  Anupam K. Singh email: anupamk18 at
  S. A. Katre email: sakatre at

Complex Analysis

A. R. Shastri (co-ordinator) e-mail: ars at
  S. S. Bhoosnurmath email: ssbmath
  Sameer Chavan email: chavansameer at
  Gowri Navda

Algebraic Topology

R. R. Simha (co-ordinator) e-mail: simhahome at
  Satya Deo Tripathi e-mail: vcsdeo at
  A. R. Shastri e-mail: ars at


Ravi Kulkarni

Dinesh Thakur

Dipendra Prasad

email: punekulk at email: thakur at email: dprasad at


Devendra Shirolkar email: devendra_shirolkar at Jagmohan Tanti email: jtanti at
Pavinder Singh email: pavinder at Pratul Gadagkar email: pratul1980 at


Selected Applicants

Available as attachment at the end of page

How to reach

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