|Dates:|| 8 June-4 July ,2009
|Convener(s)||Speakers, Syllabus and Time table||Applicants/Participants|
|Name||S. A. Katre||A. R. Shastri|
Dept. of Mathematics,
AFS-II being organised in Pune in June 2009 is the Fifth of the 2nd Annual Foundation Schools being organised on behalf of NBHM.
(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.
(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.
(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)
|I. B. S. Passi (coordinator) email: ibspassi at yahoo.co.in|
|Upendra Kulkarni email: upendra at isibang.ac.in|
|Anupam K. Singh email: anupamk18 at gmail.com|
|S. A. Katre email: sakatre at gmail.com|
|A. R. Shastri (co-ordinator) e-mail: ars at math.iitb.ac.in|
|S. S. Bhoosnurmath email: ssbmath atgmail.com|
|Sameer Chavan email: chavansameer at gmail.com|
|R. R. Simha (co-ordinator) e-mail: simhahome at yahoo.com|
|Satya Deo Tripathi e-mail: vcsdeo at yahoo.com|
|A. R. Shastri e-mail: ars at math.iitb.ac.in|
|email: punekulk at yahoo.com||email: thakur at math.arizona.edu||email: dprasad at math.tifr.res.in|
|Devendra Shirolkar email: devendra_shirolkar at rediffmail.com||Jagmohan Tanti email: jtanti at math.bprim.org|
|Pavinder Singh email: pavinder at mri.ernet.in||Pratul Gadagkar email: pratul1980 at yahoo.co.in|
Available as attachment at the end of page
|How to reach|