REFRESHER COURSE

for College Teachers in Kerala

 

Kerala School of Mathematics (KSOM) will conduct a series of orientation/refresher courses for college teachers in Kerala from August 2014at KSOM. Mathematicians from various research institutes in India will be conducting the classes.  Each course of 4 day duration will be on specific subjects such as Functional Analysis, Topology, Number Theory, Real & Complex Analysis, Algebra, and Measure Theory.

All Mathematics teachers from Colleges in Kerala are eligible to apply. Travel expense upto 3 AC will be met by KSOM and accommodation will be arranged at the KSOM guest house. Teachers are encouraged to apply for more than one course.

Tentative schedule of the programme  is as follows.


PROGRAMME-I
14-17 August, 2014 : Advanced Functional Analysis

Resource persons:
Prof. E. K. Narayanan, IISC, Bangalore
Prof. P. K. Sanjay, NIT, Calicut

Click here for Topics covered

Diagonalization of matrices
Singular value decomposition
Self adjoint operators
C* algebras
Gefland theory
Gelfand-Naimark theorem
Spectral theorem
Spectral measures
Compact operators etc.

The two series of lectures will complement each other; First one, demystifying the finite dimensional spectral theorem (diagonalization of self adjoint matrices) following a paper of Adam Koranyi by doing the singular decomposition first (see A. Koranyi: Around the finite dimensional spectral theorem, Amer. Math. Monthly 108 (2001) no.2 120-125) and the second, introducing the participants to the infinite dimensional version.

Time Schedule

List of Participants.


PROGRAMME-II
11-14 September, 2014 : Topology

Resource persons:

Prof. A.J. Parameswaran, TIFR Bombay

Prof. Parameswaran Sankaran, IMSc Chennai

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Homological Algebra:       Complexes and homology,  Exact sequences, Long exact sequence assciated to a short exact sequence of complexes.
Topology:       Simplicial complexes, CW Complexes.
Homology Thoeries:       Simplicial Homology,   Cellular Homology, Singular  Homology.
Main Theorems (Only statements with examples):   Excision Theorem, Homology sequence of a pair/tripple,  Functoriality. Invariance of domain.
Further if time permits:  Brouwer fixed point theorem, Lefschetz fixed point theorem and Borsuk-Ulam theorem.

 

Time Schedule

List of Participants


PROGRAMME-III
09-12 October, 2014 : Number Theory and Cryptography

Resource persons:

Prof. Surya Ramana, HRI Allahabad

Mr. Kasi Viswanadham, HRI Allahabad

Mr.  Jay G Mehta, HRI Allahabad

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D. Surya Ramana
Arithmetical functions
Proof of prime number theorem
G. Kasi Viswanadham
Some topics in Elementary Number Theory - Time estimates, divisibility and Euclidean algorithm, congruences, applications to factoring
Finite Fields and Quadratic Residues - finite fields, Quadratic residues and reciprocity
Jay Mehta
Classical Cryptography - some simple cryptosystems, different types of Ciphers, Cryptanalysis of Ciphers
Public Key cryptography - idea of public key cryptography, RSA and discrete log
Reference books
Introduction to analytic and probabilistic number theory- G. Tenenbaum
Introduction to analytic number theory -T. Apostol
Number theory and Cryptography- N. Koblitz
Cryptography Theory and Practice- Douglas R. Stinson

Time Schedule

List of Participants


PROGRAMME-IV
06-09 November, 2014 : Real and Complex Analysis

Resource persons:

Dr. K. Sandeep, TIFR-CAM, Bangalore

Dr. Venky Krishnan, TIFR-CAM, Bangalore

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Dr. K Sandeep
R^n calculus, continuity, various notions of differentiability, inverse function and implicit function theorems, extension of these notions to Banach spaces, finally some applications.

Dr. Venky Krishnan
From Cauchy Riemann equations to some advanced topics of Analytic continuation.

Time Schedule

List of Participants


PROGRAMME-V
08-11 January, 2015 : Algebra

Resource persons:

Prof. U. K. Anandavardhanan, IIT Bombay

Prof. A V Jayanthan, IIT Madras

Click here for Topics

Prof. U. K. Anandavardhanan : Representation Theory
Generalities on linear representations, characters, Schur's lemma, orthogonality relations, induced representations, Mackey's criterion.

Prof. A. V. Jayanthan : Commutative Algebra
Modules over Commutative rings, ascending and descending chain conditions, Noetherian rings and modules, Hilbert basis theorem.

References:

1. Abstract Algebra by Dummit and Foote
2. Algebra by Artin.
3. Algebra by Lang.
4. Introduction to Commutative Algebra by Atiyah and Macdonald.5. Linear Representations of Finite Groups by Serre.

Time Schedule
List of Participants


PROGRAMME-VI
19-22 February, 2015 : Measure Theory

Registration Closed.

Resource persons:
Prof. B. V. Rao, CMI, Chennai
Dr. A. K. Vijayarajan, KSOM
Prof. Joseph Mathew, KSOM

Click here for Topics

Prof. B V Rao & Prof. Joseph Mathew

1 Quick review of basic measure theory including Monotone Class theorem, Caratheodory extension; MCT, DCT, Fatou;

2  Radon-Nikodym theorem; Lebesgue decomposition; various notions of convergence;  

3. Product spaces and Fubini;

4. L_p spaces; Specializing to p=2 simple introduction to Fourier series.

Dr. A K Vijayarajan

Spectral Measures

Course Material

Prof. B V Rao

Time Schedule

List of Participants


Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Tel: 0495 2809001
Email: murugumanick@ksom.res.in
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics
Tel: 0495 2809004
Email: vijay@ksom.res.in

 

 

Registration for Programme-VI Closed

Selected List