|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
ars at math.iitb.ac.in
|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|
|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.|
|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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