The Annual Foundation School I (2010 )
| Venue: | PU, Chandigarh |
| Dates: | 9-29 December 2010 |
| Convener(s) | Speakers, Syllabus and Time table | Applicants/Participants |
| Name | Sudesh Kaur Khanduja |
Gurmeet Kaur Bakshi |
| Mailing Address | Professor, Centre for Advanced Study in Mathematics Panjab University Chandigarh-160014 |
Associate Professor, Centre for Advanced Study in Mathematics Panjab University Chandigarh-160014 |
Speakers
| Algebra | SKK-Sudesh Kaur Khanduja
Panjab University, Chandigarh |
PS-Parvati Shastri
University of Bombay |
GKB-Gurmeet Kaur Bakshi
Panjab University, Chandigarh |
| Analysis | AK - Ajay Kumar
University of Delhi |
SB-Savita Bhatnagar
Panjab University, Chandigarh |
RBJ-Renu Bajaj
Panjab University, Chandigarh |
| Differential Geometry &Topology | CSA - C.S. Arvinda
TIFR, Banglore |
SD-Satya Deo
HRI, Allahabad |
ARS-A.R. Shastri
IIT Bombay |
| UM-Lecture Series | I.B.S.P-I.B.S. Passi
Panjab University, Chandigarh |
Syllabus
| Speaker | Lectures | Detailed Syllabus |
| Algebra | ||
| Prof Parvati Shastri | 8 | Modules over commutative rings, Modules over a PID, Matrices over a PID and Structure Theorem, canonical forms |
| Prof Sudesh Khanduja | 8 | Review of basic field theory, Separable and normal extensions, algebraically closed fields, splitting fields, Norm and Trace and their properties. Hilbert Theorem 90, The idea behind Galois theory , Fundamental theorem of Galois theory. |
| Dr Gurmeet K. Bakshi | 8 | Cyclotomic Extensions & Cyclic Extensions, Application of the Cyclotomic extensions and Galois theory to the constructability of regular polygons. Historical aspects of the solvability of polynomial equations, Solvability of polynomial equations by radicals, The inverse problem of Galois theory. Computation of Galois groups over Q for small degree polynomials. |
| Analysis | ||
| Prof Savita Bhatnagar | 12 | Measures, Integration, Normed spaces, Baire category theorem.Open mapping theorem, Closed graph theorem, Uniform boundedness theorem. |
| Prof Ajay Kumar | 6 | Review of Fourier series, Basic Fourier Analysis on groups Z of integers, unit circle T and the real line R generalized Reimann lebesgue lemma, The Gibb’s Phenomenon. |
| Dr Renu Bajaj | 6 | Existence of local solutions for first order systems, maximal time of existence, finite time blow-up, global solutions. Gronwall inequality,Continuous dependence on initial data and on the vector field on bounded intervals. Examples of linearsystems, Fundamental solutions. |
| Topology | ||
| Prof A R Shastri | 12 | Revision of Calculus of n-variables, smoothness of maps defined on arbitrary subsets of Rn Inverse and implicit function theorem. Manifolds in Rn(as `submanifolds'), tangent space, induced map on the tangent spaces. Regular and critical points, Sard's theorem(statement only), regular inverse image. Classification of 1-dim. Manifolds.
Richness of smooth functions, smooth partition of unity, immersions,submersions, embeddings. Abstract manifolds, different definitions of tangent space, examples Orientability. Embedding theorems for manifolds in to Euclidean spaces. Normal bundleand tubular nbd theorem. Homotopy and stability. Transversality, Vector fields and isotopies. |
| Prof C S Aravinda | 6 | Frenet-Serret Theory of Curves, congruence of curves, classification of compact surfaces with boundary (examples, and statement), tangent and cotangent bundles, Riemannian metrics, differential forms, first and second fundamental form of surfaces in E3, normal curvature, Codazzi equations, congruence of surfaces, Gauss Bonnet theorem(statement). |
| Prof Satya Deo | 6 | Transversality, Oriented intersection theory, Brauwer degree Winding number and Brauwer separation theorem, Borsuk-Ulam Theorem
Hopf Degree theorem Lefschetz Theory of vector fields, Poincare-Hopf Theorem. |
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AFS-I being organised in Chandigarh in December 2010 and is funded by NBHM.
List of selected participants
| Ms Margam Archana | University of Hydrabad |
| Mr Anuj Kumar More | IISER Pune |
| Ms Debika Dey | Hydrabad University |
| Ms Dilpreet Kaur | IISER, Mohali |
| Mr Husney Parvez Sarwar | IIT Bombay |
| Mr James Philip | ST Dominc's college ,Kerala |
| Ms Julee Srivastava | University of Allahabad |
| Mr K. Premkumar | Pondicherry University |
| Ms Kalpana | Banasthali University |
| Mr Koteswara Rao Gulla | University of Hyderabad |
| Ms Kuldeep Kaur | IIT Ropar |
| Ms Leetika | PU ,Chandigarh |
| Mr Madhav Reddy B | University of Hydrabad |
| Ms Megha Goyal | PU ,Chandigarh |
| Mr Munish Kansal | PU, Chandigarh |
| Mr Nilesh Dagadu Mundlik | University of pune |
| Ms Nisha Sharma | PU ,Chandigarh |
| Mr P.Ramulu | University Of Hydrabad |
| Mr Parkash E | Madurai Kamraj University |
| Mr Prasad Tayaji Bathe | Pune University |
| Ms Pratibha Manohar | University of Rajasthan |
| Ms Pratima Rai | PU ,Chandigarh |
| Ms Priyanka Rastogi | University of Rajasthan |
| Ms Radhamani V | Madurai Kamraj University |
| Mr Rakesh Ratnakar Pawar | IIT, Bombay |
| Mr Ramandeep Behl | PU, Chandigarh |
| Mr Ramesh K | IIT Bombay |
| Mr Rami Reddy Pasupula | University of Hyderabad |
| Ms Rani Kumari | University of Delhi |
| Ms Rashmi Agarwal | University of Rajasthan |
| Ms Revathi V.M. | Madurai Kamraj University |
| Mr Sanjeev Kumar | PU ,Chandigarh |
| Mr Sayan Chakraborty | IIT Bombay |
| Mr Shiv Prasad | IISER Mohali |
| Mr Surinder Kumar | PU, Chandigarh |
| Mr Surya Ratna Prakash Dumpa | NIT, Karnataka |
| Mr Vikash | IIT Ropar |
| Mr Srinivas Majeti | Osmania University, Hyderabad |
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How to reach
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AFS-I being organised in Chandigarh in December 2010 and is funded by NBHM.
How to reach Panjab University
The city beautiful of Chandigarh located at the foot hills of Himalayas is the capital of both Punjab and Haryana states. The city is situated at a distance of 250 kms from Delhi. Chandigarh is well connected by public transport (rail, road, air). Panjab University is within a distance of 12-14 km from ISBT/Railway Station / Airport. The weather during December is cold. Woolen clothes are required here in the month of December. All participants will be provided accommodation.
How to reach Panjab University from ISBT
There are two inter state bus terminus, ISBT-sector 17 and ISBT-sector 43. ISBT-sector 17 is about 4 km and ISBT-sector 43 is about 8 km from Panjab University. Cycle rickshaw/Auto rickshaw/Taxi charging approx. Rs. 30/ Rs 50/ Rs 100 from ISBT-sector 17 and Rs. 40/ Rs 80/ Rs 125 from ISBT- sector 43 are available at these inter state bus terminus. Local buses are also available.
How to reach Panjab University from Railway Station
Chandigarh railway station is about 10 km from Panjab University. Auto rickshaw/ taxi charges approximately Rs. 100/ 150 for transporting to Panjab University. Local buses are also available from the local bus stand near the railway station.
How to reach Panjab University from Air Port
Chandigarh air port is about 14 km from Panjab University. Auto rickshaw/ taxi charges are approximately Rs. 125/ 200.
Postal Address & telephone numbers:
Prof Madhu Raka & Dr. Gurmeet K. Bakshi
Department of Mathematics, Panjab University
Chandigarh -160014
Tel 0172- 2534501(O)
0172-2541132 (O)
09872989234 (M)
09914001444(M)