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 
Name  S. A. Katre  A. R. Shastri 
Mailing Address  Dept. of Mathematics, Univ. of Pune, Pune411 007. sakatre at math.unipune.ernet.in 
IIT, Bombay Mumbai ars at math.iitb.ac.in 
Speaker  Detailed Syllabus 
Algebra  

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. Primepower Groups. Nilpotent Groups. Soluble Groups. Matrix Groups. Groups and Symmetry. 
R. C. Cowsik  Integral dependence, Noether normalization lemma, principal ideal theorem, Hilbert’s Nullstellensatz, 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. CasoratiWeierstrass theorem, BlochLandau 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 CWcomplexes, JordanBrouwer separation theorem, invariance of domain, Lefschetz fixed point theorem etc.. 
G. K. Srinivasan  Axiomatic homology theory. 

Click here to download selected applicants list
How to reach
