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, Pune-411 007. 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. 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. |
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