Conferences

 


Refresher Course for College Teachers in Kerala State:2016
-17

PROGRAMME - V

Venue: KSOM, Kozhikode

09-12 March, 2017

Topics of discussion:Differential Equations

Resourse Persons:

Prof. K Sandeep, TIFR-CAM Bangalore
Dr. A. K. Nandakumaran, Professor, Indian Institute of Science, Bangalore

Topics covered:
1- Existence and Uniqueness of solution for ODE
2- Smooth dependence on the data
3- Stability of linear systems
4- First order partial differential equations- Method of characteristics

Visit the link at  http://nptel.ac.in/courses/111108081/

Time Schedule

List of Participants.

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics



Refresher Course for College Teachers in Kerala State:2016
-17

PROGRAMME - IV

Venue: KSOM, Kozhikode

09-12 February, 2017

Topics of discussion:Algebraic Number Theory

Resourse Persons:

Prof. Sanoli Gun, IMSc Chennai
Prof. Purushotham Rath, CMI Chennai

 

Time Schedule

List of Participants.

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics



Refresher Course for College Teachers in Kerala State:2016
-17

PROGRAMME - III

Venue: KSOM, Kozhikode

19-22 January, 2017

Topics of discussion:Semisimple Algebras and Group Representations

Resourse Persons:

Prof. K N Raghavan, IMSc Chennai
Prof. Vijay Kodiyalam, IMSc Chennai

Course Content

The resource persons for the program recommend the notes, exercises,  and lectures
in the following links:

Notes and exercises:
---> http://www.imsc.res.in/~knr/past/afs-II_iisertvm_2015/Notes/knr_2.pdf

Videos of lectures:
---> https://www.youtube.com/playlist?list=PLhkiT_RYTEU0CcvzU49C5AYmX7mLHUvOb

 

Time Schedule

List of Participants.

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics



KSOM Workshop for B.Sc. students in Idukki district, Kerala

28th, 29th, 30th November, 1st and 2nd December 2016

KSOM conducted a Workshop at Pavanatma College, Idukki district, Kerala during 28 November - 02 December 2016. The program was meant for BSc Mathematics students studying in colleges in Idukki, Kerala.

 

Resource Persons:
Prof. Sanoli Gun, IMSc Chennai
Prof. Purushotham Rath, CMI Chennai
Prof. B Ramakrishnan, HRI Allahabad

Special Lectures by:
Prof. Gautam Menon.IMSc Chennai
Prof. Murugan V, RKM Vevekananda College, Chennai

 

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

 

Local Co-ordinators

Mr. Sijo P. George

Assistant Professor
Dept. of Mathematics

Pavanatma College, Idukki

Email: sijopgorg@gmail.com

Mob: 9746105166

Mr. Bobin George
Assistant Professor
Dept. of Mathematics

Pavanatma College, Idukki

Email: bobinkgeorge@gmail.com

Mob: 9747905115

Mr. Tijo James

Assistant Professor

Dept. of Mathematics

Pavanatma College, Idukki

Email: tijojames@gmail.com

Mob: 9946884650

 



Refresher Course for College Teachers in Kerala State:2016
-17

PROGRAMME - II

Venue: KSOM, Kozhikode

03-06 November, 2016

Topics of discussion:Groups and their representations

Resourse Persons:

Prof. A J Parameswaran, TIFR Mumba
Prof. V Balaji, CMI Chennai

Course Content

Semisimple representations.Closed and  "algebraic" subgroups of GL(n,C). 

Nilpotent and semisimple elements:  simultaneous  upper triangulability of ommuting 
matrices (Jordan decomposition). Nilpotent and unipotent groups, Torus, Classification of connected abelian groups, Solvable groups,  Lie-Kolchin Theorem.  

Reductive groups:  If  a connected algebraic group has a faithful irreducible representation then it is a reductive group. Classification of finite subgroups of GL(n,C): Theorem of Jordan.

 

Time Schedule

List of Participants.

 

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics



Refresher Course for College Teachers in Kerala State:2016
-17

PROGRAMME - I

Venue: KSOM, Kozhikode

20-23 October, 2016

Topics of discussion:Linear Algebra in Control Theory - An Introduction

Resourse Persons:

Prof. Subramanian Moosath, IIST Thiruvananthapuram
Dr. Priyadarshnam, IIST Thiruvananthapuram

Course Content

Linear algebra, Linear systems, and Control concepts

Lecture Notes -1

Lecture Notes - 2

Time Schedule

List of Participants.

 

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics



Refresher Course for College Teachers in Kerala State:2015
-16

PROGRAMME - V

Venue: KSOM, Kozhikode

18-21 February, 2016

Topics of discussion:Complex Analysis

Resourse Persons:

Prof. Parameswaran Shankaran IMSc, Chennai
Prof. L Venkataraman Rtd Prof, Vivekananda College, Chennai

Course Content

Prof. Parameswaran Sankaran:  Weierstrass theorem on infinite product representation, Hadamard's theorem, Mittag-Leffler
theorem, Gamma and Zeta functions (basic properties). Weierstrass function.

Ref: Complex Analysis by Ahlfors (Chapter 5)

Prof. L Venkataraman : Cauchy theory (basically complex integration and its applications). Cauchy-Goursat Theorem, Cauchy Integration Formulas, Singularities, Residue Theorem, Evaluation of Ontegrals using Residues, Argument Principle, Maximum Modulus Principle. 
1. Conformal Mappings
2. Analytic Continuation
3. Riemann Mapping Theorem

Time Schedule

List of Participants.

 

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics



KSOM Workshop for B.Sc. students in Wayanad district, Kerala

 

09-13 December, 2015


KSOM conducted a Workshop at Wayanad during 09-13 December, 2015. The program was meant for BSc Mathematics students studying in colleges in Wayanad.

Resource Persons

Dr. S Kumaresan (Department of Mathematics,, Hyderabad University)
Dr. V. Muruganandam (Department of Mathematics, NISER, Bhuvaneswar)
Dr. M. Manickam (KSoM)
Dr. A. K. Vijayarajan (KSoM)

 

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

 

Local Co-ordinators

Dr. Pamy Sebastian

Head, Dept. of Mathematics

Mary Matha Arts & Science College, Mananthavady, Wayanad

Email: pamyseb@gmail.com

Mob: +919446970984

Mr. Latheesh Kumar A R
Head, Dept. of Mathematics
St. Mary's College,

Sulthan Bathery, Wayanad

Email: latheesby@gmail.com

Mob: +919947049112

Mr. Santhosh Kumar C G

Assistant Professor

Dept. of Mathematics

W M O Arts & Science College,

Muttil, Wayanad

Email: skumarcg@gmail.com

Mob: +919447780543

Time Schedule

 


Refresher Course for College Teachers in Kerala State:2015
-16

 

PROGRAMME - IV

Venue: KSOM, Kozhikode

12-15 November, 2015

Topics of discussion:Topologies, Filters and Uniformities

Resourse Persons:

Prof. K. N. Raghavan, IMSc Chennai

Course Content

Basic reference:   Bourbaki, General Topology,  Part I,  Chapters I and II
Other references: 
J L Kelley,  General Topology
Gilman & Jerison,  Rings of Continuous Functions

Abstract:

Following Bourbaki (Chapter I),  we will study filters and their limits.   Filters, like nets, generalize sequences.  They enable us to restore intuition to the notion of continuity:   a map between general topological spaces is continuous if and only if, for every filter in the domain that converges to a point,  the direct image filter converges to the image of that point.     Moreover,   Hausdorfness may be defined as the property that every filter has at most one limit point,  (quasi-)compactness as the property that every filter admits at least one cluster point.   

Following Gilman & Jerison,  we will illustrate the use of filters in the study of rings of continuous functions (such as C[0,1]).

Following Bourbaki again (Chapter II), we will study uniformities.   Cauchy sequences and uniform continuity are not topological notions (they are not preserved under homeomorphisms; their usual definitions presume a metric) but they are closely related to topological notions.     Uniform spaces generalize metric spaces.   Like a metric, a uniformity too induces a topology.   Uniform continuity, Cauchy filters, and completions may be defined in the context of uniform spaces. 

Some notes following Bourbaki may be found at http://www.imsc.res.in/~knr/past/top15 (these notes are being currently added to).

 

Time Schedule

List of Participants.

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics


 


Refresher Course for College Teachers in Kerala State:2015
-16

 

PROGRAMME - III

Venue: KSOM, Kozhikode

18-21 October, 2015

Topics of discussion: Differential Geometry

Resourse Persons:

Prof. S Kumaresan, University of Hyderabad

Prof. G Santhanam, IIT, Kanpur

Course Content
1. Review of Multivariable Calculus (3 lectures)
2. Curves: Definition, vector field, Frenet – n- frame, existence of curves with prescribed curvatures, curvature and torsion of a space curve, Frenet-Serret formula. (3 L)
3. Surfaces: Definition, vector field, quadratic form, first fundamental form, second fundamental form,   curvature of curves on a surface, Principal curvature,  Gaussian and mean curvatures. (6 L)
References:

  1. W. Klingenberg, A Course in Differential Geometry, Springer-Verlag, 1978.
  2. Manfredo P. do Carmo, Differential Geometry of Curves and Surfaces , Prentice-Hall, 1976.
  3. S. Kumaresan, A Course in Differential Geometry and Lie Groups, Hindustan Book Agency, 2002.

 

Time Schedule

List of Participants.

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics


 


Refresher Course for College Teachers in Kerala State:2015
-16

 

PROGRAMME - II

Venue: KSOM, Kozhikode

10-13 September, 2015

Topics of discussion: Matrix Analysis & Applications

Resourse Persons:

Prof. A. Chandrashekaran, Central University of Tamilnadu

Prof. Sachindranath Jayaraman, IISER, Thiruvananthapuram

 

Time Schedule

List of Participants.

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics


 


Refresher Course for College Teachers in Kerala State:2015
-16

 

PROGRAMME - I

Venue: KSOM, Kozhikode

23-26 August, 2015

Topics of discussion: Topology

Resourse Persons:

Prof. A J Parameswaran, TIFR Mumbai
Prof. A J Jayanthan, Goa University

Topics covered

Differentiable maps, Tangent space, Implicit function theorem, Critical Points, Structure Theorem for nondegenerate critical points, Topological and Differentiable manifolds,   Differentiability of functions on a manifold,   Sard’s theorem,  Partitions of unity, para compactness., Whitney’s Embedding Theorem,  Morse functions and their Existence,  CW complexes, Change of Topology as one passes a non degenerate critical point.

 

Time Schedule

List of Participants.

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics


 


Initiation into Mathematics 2015 - mini MTTS Programme

 

Venue: KSOM, Kozhikode

04-09 May, 2015

 

A one week long Mini Mathematics Training and Talent Search programme organized during May 4-9, 2015 at Kerala School of Mathematics, Kozhikode, Kerala with the funding of National Board of Higher Mathematics, Govt. of India.

The program was targeted to students in the second year/fourth semester B.Sc/Integrated M.Sc programmes having Mathematics as one of the compulsory papers. The topics which discussed in the program were Number Theory, Foundations of Set Theory, Real Analysis, Group Theory, and Linear Algebra. The program was conducted on the solid academic support of the prestigious Mathematics Training and Talent Search (MTTS) programme and it took up and implemented the meticulous teaching methodology of MTTS.

 

Resource Persons

Dr. P.S. Srinivasan : Foundations of Mathematics / Real Analysis

Dr. Subramanyan Moosath : Linear Algebra

Dr. Vishnu Namboothiri K : Group theory

 

Time Table

List of Participants.

Local Coordinator Academic Coordinator
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. Vishnu Namboothiri K
Department of Mathematics, BJM Govt. College
Chavara, Kerala


 


OUTREACH PROGRAMME: Refresher Course for M.Sc. students in Kerala State

 

Venue: KSOM, Kozhikode

17-26 April, 2015

 

KSOM conducted a refresher course during April 2015 for final year M.Sc. Mathematics students in Kerala.  The course covered some basic topics of Algebra, Analysis, and Number Theory.

Resource Persons

Prof. M Manickam, KSOM : Algebra

Dr. A K Vijayarajan, KSOM : Linear Algebra

Prof. B Ramakrishnan, HRI Allahabad : Number Theory

Prof. Joseph Mathew, Formerly KSOM : Analysis

Prof. A J Parameswaran, TIFR Mumbai : Topology ----------Lecture Notes

Time Table

List of Participants.

Co-ordinator
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics


 


Refresher Course for College Teachers in Kerala State:2014
-15

 

PROGRAMME - VI

Venue: KSOM, Kozhikode

19-22 February, 2015

Topics of discussion: Measure Theory

Resourse 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 Materials

Prof. B V Rao
Prof. Joseph Mathew

Time Schedule

List of Participants.

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics


 


Refresher Course for College Teachers in Kerala State:2014
-15

 

PROGRAMME - V

Venue: KSOM, Kozhikode

08-11 January, 2015

Topics of discussion: Algebra

Resourse 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.

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics


 


Refresher Course for College Teachers in Kerala State:2014
-15

 

PROGRAMME - IV

Venue: KSOM, Kozhikode

06-09 November, 2014

Topics of discussion: Real & Complex Analysis

Resourse Persons:

Dr. K. Sandeep, TIFR-CAM, Bangalore

Dr. Venky Krishnan, TIFR-CAM, Bangalore

 

Click here for Topics

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.

 

Course Materials

Real & Complex Analysis

 

Time Schedule

List of Participants.

 

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics


 


Refresher Course for College Teachers in Kerala State:2014
-15

 

PROGRAMME - III

Venue: KSOM, Kozhikode

09-12 October, 2014

Topics of discussion: Number Theory & Cryptography

Resourse Persons:

Prof. Surya Ramana, HRI Allahabad

Mr. Kasi Viswanadham, HRI Allahabad

Mr.  Jay G Mehta, HRI Allahabad

 

Click here for Topics covered

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

Course Materials

Cryptography Theory and Practice
Introduction to Cryptography
Course in Number Theory And Cryptography
Prime Number Theory

Time Schedule

List of Participants.

 

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics


 


Refresher Course for College Teachers in Kerala State:2014
-15

 

PROGRAMME - II

Venue: KSOM, Kozhikode

11-14 September, 2014

Topics of discussion: Topology

Resourse Persons:

Prof. A.J. Parameswaran, TIFR Bombay

Prof. Parameswaran Sankaran, IMSc Chennai

Click here for Topics covered

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.

 

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics


 


Refresher Course for College Teachers in Kerala State:2014
-15

 

PROGRAMME - I

Venue: KSOM, Kozhikode

14th, 16th & 17th August, 2014

Topics of discussion: Advanced Functional Analysis

Resourse 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.

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics


 


OUTREACH PROGRAMME

Refresher Course for B.Sc. Mathematics Students in Kerala State

Venue: KSOM, Kozhikode

22 - 30 April, 2014

KSOM conducted refresher course during April 2014 for B.Sc. Mathematics IV Semester students studying in Kerala state.  The course covered some basic topics of Algebra, Analysis, Linear Algebra and Number Theory.

The course with relaxed schedule and interactive sessions discussed abstract topics in Number Theory, Analysis, Algebra and Linear Algebra. The sessions were handled by Joseph Mathew, A. K. Vijayarajan, V Srivatsa, P Jisna, P Shankar(KSOM) and Kirankumar V B.

Topics covered:

Analysis:
Real number system, Rational numbers, Irrational numbers, Completeness axiom
Sequences, Cauchy sequences, Convergence
Series, Convergence
Topology of the real line
Algebra:
Groups-subgroups-Cyclic groups-Group homomorphisms and Isomorphisms-Normal subgroups
Introduction to Rings and Fields
Linear Algebra:
Vector spaces, Sums and Direct Sums
Linear Independence, Bases and Dimension
Linear maps, Matrices
Number Theory:
Divisibility
Congruences and some basic theorems
Quadratic reciprocity law
Some arithmetic functions
Primitive roots

Time Schedule

Participants

Co-ordinators
Dr. A K Vijayarajan
Associate Professor
e-mail: vijay@ksom.res.in
Phone: 0495 2809004
Fax: 0495 2809010
Prof. Joseph Mathew
Visiting Professor
e-mail: jmathew@ksom.res.in
Phone: 0495 2809005
Fax: 0495 2809010


 


Discussion Meeting on ANALYTIC & ALGEBRAIC GEOMETRY

 

Venue: KSOM, Kozhikode

24 - 28 March, 2014

Organizers

A. J. Parameswaran  &  Indranil Biswas
TIFR

Speakers Participants

Nitin Nitsure
D.S. Nagaraj
Sukhendu Mehrotra
Chanchal Kumar.
Amit Hogadi
V. Balaji
Joergen Ellegaard Andersen
Henning Haahr Andersen
Sergey Arkhipov
Jean-Baptiste Meilhan
Daniel Tubbenhauer
Niels Leth Gammelgaard
Florian Schätz
Søren Fuglede Jørgensen

Jens Kristian Egsgaard

Arijith Dey

Nitin Nitsure
Usha Bhosle
Amit Hogadi
Chanchal Kumar.          
Sukhendu Mehrotra 
D.S. Nagaraj
S. S. Kannan.
Arijit Dey
V. Balaji
Sergey Arkhipov
Jean-Baptiste Meilhan     
Jens Kristian Egsgaard
Florian Schätz.
Daniel Tubbenhauer
Joergen Ellegaard Andersen
Henning Haahr Andersen
Niels Leth Gammelgaard
Søren Fuglede Jørgensen          
Jens Jakob Kratmann Nissen
Arash Momeni
Kenneth Rasmussen
Simon Stoltze
Anders D. Jakobsen
Troels B. Andersen
Dennis H. Pedersen
Paolo Masulli

Title and Abstracts

Time Schedule

 


Orientation/Refresher Course for College Teachers in Kerala State
-2013
-14

 

PROGRAMME - VI

Venue: KSOM, Kozhikode

07-10 March, 2014

Topics of discussion: Measure Theory

Resourse Persons:

Dr. K. Sandeep, TIFR Centre for Applicable Mathematics, Bangalore
Dr. Joseph Mathew, KSOM

Click here for Time Schedule

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics

Click here for Participants

 


Orientation/Refresher Course for College Teachers in Kerala State
-2013-14

 

PROGRAMME - V

Venue: KSOM, Kozhikode

27 February - 02 March, 2014

Topics of discussion: Topology

Resourse Persons:

Prof. A J Parameswaran, TIFR Mumbai

Algebraic Topology:  (A J Parameswaran & Sagnik )

1:  $\pi_1$: definition, Homotopy, Exapmles.
2:  VanKampen Theorem; Computation of the Fundamental groups of various spaces.
3:  Covering Spaces: Path lifting, Homotopy lifting, Codition for arbitrary map  lifting....
4: Invariance of Domain, Separation Theorem, Jordan curve Theorem ...
5:  Universal covering (Existence - statement only) Relation between $\pi_1$ and fibres of covering maps.

Prof. Parameswaran Sankaran, IMSc, Chennai

General Topology:
Day 1: Basic notions--product spaces, connected, compactness.
Day 2: Countability axioms and separation axioms
Day 3: Metrizability theorems, Stone-Cech compactification
Day 4: complete metric spaces and Baire spaces
Tutorials:
Sagnik Chakraborty, TIFR, Mumbai
Prateep Chakraborty, IMSc., Chennai

Click here for Time Schedule

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics

Click here for Participants

 


Orientation/Refresher Course for College Teachers in Kerala State
-2013-14

 

PROGRAMME - IV

Venue: KSOM, Kozhikode

10-13 January, 2014

Topics of discussion: Functional Analysis

Resourse Persons:
Prof. Dr. T. Sengadir, Central University, Tamilnadu
Topic: Distribution Theory, Sobolev Spaces, Semigroup Theory , Basic PDE, Nonlinear Analysis, Fourier Transforms

Dr. D. Surya Ramana, HRI, Allahabad
Topic: The basic theorems of functional analysis - Hahn Banach, Completeness and Banach Spaces, Operators, Baire Category Theorem, Uniform Boundedness, Closed Graph Open Mapping together with some well-known applications.
Dr. A K Vijayarajan, Kerala School of Mathematics, Kozhikode
Topic: Topologies of B(H)

Click here for Time Schedule

 

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics

Click here for Participants

 


Orientation/Refresher Course for College Teachers in Kerala State
-2013-14

 

PROGRAMME - III

Venue: KSOM, Kozhikode

22-25 November, 2013

Topics of discussion: Complex Analysis

 

Time Schedule
Date 9:00-10:15 10:15- 10:30 10:30-11:45 11:45-12:00 12:00-1:15 1:15-2:30 2:30-3:30 3:30-3:45 3:45-4:45
22-Nov-13 AJP Hot Break EKN Cool Break AJP Lunch Break Tutorial EKN Hot Break Tutorial AJP
23-Nov-13 EKN AJP EKN Tutorial AJP Tutorial EKN
24-Nov-13 AJP EKN AJP Tutorial EKN Tutorial AJP
25-Nov-13 EKN AJP EKN Tutorial AJP Tutorial EKN

Resource Persons:

Prof. A J Prameswaran, TIFR Mumbai
Topic: Quick review of topological preliminaries, simply connectedness, homotopy etc. Definition of log and n^th roots, lifting of maps, covering maps. Covering spaces of C*, C** and D*. Applications: Characterization of nowhere vanishing functions, Picard Theorems, Fundamental Theorem of Algebra.
Prof. E K Narayanan, IISc, Bangalore
Topic: Quick review of holomorphic (analytic) functions, Cauchy-Riemann equations, Cauchy's theorem, power series. Properties of holomorphic functions, zeros, maximum modulus principle, Liouville's theorem, isolated singularities, arguments principle, open mapping theorem. If time permits some major theorems like, Montel's theorem, Riemann mapping theorem and Pciard's theorem (Ahlfors's proof).

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics

Participants

 


Orientation/Refresher Course for College Teachers in Kerala State
-2013-14

 

PROGRAMME - II

Venue: KSOM, Kozhikode

08-11 November, 2013

Topics of discussion: Real Analysis

 

Time Schedule
Date 9:00-10:15 10:15- 10:30 10:30-11:45 11.45-12:00 12:00-1:15 1:15-2:30 2:30-3:45 3:45-4:00 4:00-5:00
08-Nov-13 EKN Hot Break SS Cool Break EKN Lunch Break EKN Hot Break Tutorial SS
09-Nov-13 SS EKN SS EKN Tutorial JM
10-Nov-13 JM SS EKN EKN Tutorial EKN
11-Nov-13 EKN SS SS JM Discussion/ Feedback

Resource Persons:

EKN: E K Narayanan, IISc, Bangalore
Topic: Borel \sigma-algebra, outer measure, measurable sets, construction of Lebesgue measure on \mathbb R, measurable functions, introduction to Lebesgue integration and limit theorems.
SS: S. Somasundaram, Manonmaniam Sundaranar University,Tirunelveli
Topic: Nets and Ordinal Topology
JM: Joseph Mathew, Kerala School of Mathematics

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics

Participants

 


Orientation/Refresher Course for College Teachers in Kerala State
-2013-14

 

PROGRAMME - I

Venue: KSOM, Kozhikode

11-14 October, 2013

Topics of discussion: Galois Theory, Field Extension and Commutative Algebra

 

Time Schedule
Date 9:30-11:00 11:00-11:30 11:30-1:00 1:00-2:30 2:30-3:30 3:30-4:00 4:00-5:00
11-Oct-13 PS Tea Break PS Lunch Break PS Tea Break PS
12-Oct-13 PS PS PS PS
13-Oct-13 RT RT RT RT
14-Oct-13 RT RT RT RT

Resource Persons:

PS : Parameswaran Sankaran, IMSC, Chennai : Galois Theory

RT: R Thnagadurai, HRI, Allahabad : Commutative Algebra

Co-ordinators
Prof. M Manickam
Director
Kerala School of Mathematics
Dr. A K Vijayarajan
Associate Professor
Kerala School of Mathematics

Participants

 

Outreach Programme -
Refresher Course for B.Sc. Mathematics Students in Kerala State

 

Venue: KSOM, Kozhikode

14-22 September, 2013

 

KSOM conducted refresher course during September 2013 for B.Sc. Mathematics Final year students in Kerala state.  The course covered some basic topics of Algebra and Analysis. 

The course with relaxed schedule and interactive sessions discussed abstract topics in Number Theory, Analysis, Algebra, Linear Algebra and Graph Theory. The sessions were handled by V. Krishna Kumar(NICER, Bhuvaneswar), P. K. Sanjay(NIT, Calicut), Ananthavardhanan (IIT, Bombay), Jijo Sukumaran (Govt. College, Kasargod), M. Manickam, Joseph Mathew, A. K. Vijayarajan and Guram Donadze (KSOM).

Time Schedule
Date 9:30-11:00 11:00-11:30 11:30-1:00 1:00-2:30 2:30-3:30 3:30-4:00 4:00-5:00
14-Sep-13 MM Tea Break SPK Lunch Break JM Tea Break AKV
15-Sep-13 GD AKV SPK GD
16-Sep-13 MM GD JM AKV
17-Sep-13 MM JM No sessions No sessions
18-Sep-13 MM JM VK VK
19-Sep-13 JM AKV GD VK
20-Sep-13 JM VK JS GD
21-Sep-13 GD AKV JM Res. Sch.
22-Sep-13 AKV GD Discussion Discussion

MM: M. Manickam - Algebra

JM: Joseph Mathew - Topics in Analysis

VK:V Krishna Kumar - Construction of Number system

SPK: Sanjay P K - Topics in Analysis

GD: Guram Donadze - Graph Theory

AKV: A. K. Vijayarajan - Linear Algebra

JS : Jijo Sukumaran - Linear Algebra

Res. Sch.: Research Scholar, KSOM -  Tutorial

Co-ordinator

Dr. A K Vijayarajan
Associate Professor, KSOM

Participants

 

Short Term Discussion Meeting

31 December 2012 - 13 January 2013

 

Visitors

1. Bipin Balaram, Assistant Professor, Dept. of Mechanical Engineering, Amrita School of Engineering, Amrita Viswa Vidyapeetham, coimbatore.

2. Vinod V., Research Scholar, Dept. of Mechanical Engineering, NIT Calicut.

 

Venue: KSOM, Kozhikode

PLAN OF WORK

The basic objective of this work is to develop a robust numerical method for obtaining the periodic solutions of nonlinear ordinary differential equations and to device a strategy to quantitatively estimate the change in this solution when the system parameters are slowly varied. Historically, homotopy based methods like parametric continuation coupled with shooting algorithms has been used to perform this task. With the help of an arc-length reparameterisation technique at singular points in the parameter space, this can be used for practical bifurcation analysis too. But this scheme has two serious shortcomings.


First, it makes the assumption that the frequency of the solution is the same as that of the forcing function and hence, runs into trouble when dealing with self-excited systems like Van der Pol oscillators. This means that systems like coupled self-excited oscillators, which are of great
practical importance in areas like physics, engineering and biology and which show such intresting behaviour as synchronisation and clustering, cannot be studied using this simple continuation strategy. So, an effort will be made to develop a continuation strategy based on generalised shooting method which treats the frequency of the periodic solution also as an unknown. This means that the new scheme should converge to a point in the enhanced state space of dimension 2n+1; 2n being the dimension of the initial condition vector. Preliminary efforts show that the use of homotopy methods will reduce this problem to an algebraic one with 2n equations in 2n+1 variables. This poses a challenge which we hope to address. This scheme shall be used to study the synchronisation in (dissipatively and reactively) coupled Van der Pol oscillators in a ring by treating the coupling constant as the continuing parameter with an emphasis on tracking down possible bifurcation phenomenon.


Second, existing continuation strategies are equipped to carry out the solution continuation in the euclidean state space alone. But in many cases involving n coupled oscillators, the dynamics is restricted to a manifold embedded in the 2n dimensional state space. For example, the dynamics of a double pendulum can be studied on a 4 dimensional euclidean state space, but the modulo 2π nature of dynamics means that it is restricted to a torus. There can be significant computational gains if this continuation can be restricted to the manifold. Keeping this in mind, the possibility of adapting the developed continuation scheme to work on the appropriate manifold will be explored. This will involve the use of techniques from computational differential geometry.

 

Outreach Programme -
Refresher Course for B.Sc. Mathematics Students in Kerala State

 

Venue: KSOM, Kozhikode

23-29 December, 2012

 

This outreach programme was meant for B.Sc. Mathematics third year students, who were studying in Kerala state.  The course covered some basic topics of Algebra, Analysis and Number Theory.  Some first year students of M.Sc. Mathematics also participated.

Participants

 

Outreach Programme for Higher Secondary School Students

 

Venue: KSOM, Kozhikode

02 October, 2012

 

Second phase of outreach programme for Higher Secondary School Students in the nearby region was held at KSOM in continuation with the Outreach Programme for Higher secondary School Students conducted in May 2012. This programme connected students with mathematical role models and shared their knowledge of and passion for mathematics and its various subspecialities and related fields.

Speakers

1 Dr. M Manickam Director, KSOM
2 Prof. E. Krishnan Formerly Professor, University College, TVM
3 Prof.U. K. Anandavardhanan Professor, IITB
4 Prof.  A K Vijayarajan Associate Professor, KSOM
5 Prof. Joseph Mathew Visiting Professor, KSOM
     

Participants

 

Outreach Programme for Higher Secondary School Teachers

 

Venue: KSOM, Kozhikode

30 September- 01 October, 2012

 

A two days discussion meeting with MathematicsTeachers of Higher Secondary Schools in the nearby region was held at KSOM in continuation with the Outreach Programme for Higher secondary School Teachers conducted in May 2012.

Speakers

1 Dr. M Manickam Director, KSOM
2 Prof. E. Krishnan Formerly Professor, University College, TVM
3 Prof.U. K. Anandavardhanan Professor, IITB
4 Prof.  A K Vijayarajan Associate Professor, KSOM
5 Prof. Joseph Mathew Visiting Professor, KSOM
     

Participants

 

Outreach Programme for Higher Secondary School Students

 

Venue: KSOM, Kozhikode

5th May, 2012

 

In continuation with the discussion meeting with Higher Secondary School Mathematics Teachers held at KSOM on 7th April, 2007, an outreach programme for HSS students conducted at KSOM. KSCSTE Member Secretary Dr. K. K. Ramachandran inauguratede the programme.

 

Participants

 

Panorama Lecture

Venue : KSOM, Kozhikode

01 - 05 May, 2012

Prof. Ram Murty from Queens University, Canada delivered a series of "Panorama Lectures" on Ramanujan & L-functions from 01 to 04, May 2012.

Participants

Discussion meeting with Higher Secondary School Mathematics Teachers

 

Venue: KSOM, Kozhikode

7th April, 2012

 

Mathematics in Schools

Mathematics underpins so many aspects of our lives and provides the foundation for science, engineering, economics, finance and many other professional fields. For all these reasons, it is critical to help students early on to appreciate the beauty and power of mathematics and to begin to understand how it plays out in so many areas. Of course, teachers are already experts at encouraging and guiding students, but having the added support of a mathematical research institute provides obvious benefits not only for students but for the teachers and mathematicians as well.

Discussion Meeting

As a prelude to the outreach program for Higher Secondary School students, a one day discussion meeting held at KSOM with mathematics teachers of Higher Secondary Schools who are teaching for +1/+2 students in the near by region to discuss and find out the modalities of conducting the outreach program.


 

Prof. Michael A. Dritschel of University of Newcastle, UK visited KSOM

 

08 - 12 March, 2012

The visit was for a discussion meeting on `Operator Spaces and Operator Theory' with KSOM Faculty and researchers working in the area.


 

@2010 Kerala School of Mathematics