The Annual Foundation School II (2010 )

Venue: Bhaskaracharya Pratishthana and Dept. of Mathematics, Univ. of Pune
Dates: 31 May - 26 June 2010


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.
sakatre at
IIT, Bombay
 ars at


Speakers and Syllabus 


Speaker Detailed Syllabus
Upendra Kulkarni 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
S. A. Katre, Anuradha Garge Group Theory: Group Actions. Prime-power Groups. Nilpotent Groups. Soluble Groups. Matrix Groups. Groups and Symmetry.
R. C. Cowsik Integral dependence, Noether normalization lemma, principal ideal theorem, Hilbert’s Null-stellensatz, structure of artinian rings, Dedekind domains.
Parvati Shastri Introduction to Algebraic Number Theory
Complex Analysis  
S. Bhoosnurmath Euclidean similarity geometry, inversive geometry, hyperbolic geometry and complex analysis, analytic functions Path integrals, Winding number, Cauchy integral formula and consequences.
H. Bhate P. Hadamard gap theorem, Isolated singularities, Residue theorem, Liouville theorem. Casorati-Weierstrass theorem, Bloch-Landau theorem.
Raghavendra Picard’s theorems , Mobius transformations, Schwartz lemma, Extremal metrics, Riemann mapping theorem, Argument principle, Rouche’s theorem..
(click here for notes by N. Raghavendra)
R R Simha, Kaushal Verma Runge’s theorem, Infinite products, Weierstrass p­function, Mittag­ Leffler expansion.
Algebraic Topology  
Mahuya Datta Categories and functors; 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.
A. R. Shastri Simplicial Complexes. 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..
G. K. Srinivasan Axiomatic homology theory.


 Selected Applicants



 Click here to download selected applicants list