Supported by National Centre for Mathematics

Venue: KSOM, Kozhikode

01-28 May, 2014


M Manickam
Professor & Director(i/c)
Kerala School of Mathematics, Kozhikode
B Ramakrishnan
HRI, Ahmedabad

Description: The main objectives of AFS are to bring up students with diverse background to a common level and help them acquire basic knowledge in algebra, analysis and topology. This programme is organised by National Centre for Mathematics (NCM).

Syllabus :

Ring Theory.
(1) Modules over Principal Ideal Domains Modules, direct sums, free modules, nitely generated modules over a PID, structure of nitely generated abelian groups, rational and Jordan canonical form.
(2) Basics Commutative rings, nil radical, Jacobson radical, localization of rings and modules, Noetherian rings, primary decomposition of ideals and modules.
(3) Integral extensions of rings, Going up and going down theorems, niteness of integral closure, discrete valuation rings, Krull's normality criterion, Noether normalization lemma, Hilbert's Nullstellensatz
(4) Semisimple rings, Wedderburn's Theorem, Rings with chain conditions and Artin's theorem, Wedderburn's main theorem,

Functional Analysis.
(1) Normed linear spaces, Continuous linear transformations, application to di erential equations, Hahn-Banach theorems-analytic and geometric versions, vector valued integration.
(2) Bounded Linear maps on Banach Spaces Baire's theorem and applications: Uniform boundedness principle and application to Fourier series, Open mapping and closed graph theorems, annihilators, complemented subspaces, unbounded operators and adjoints
(3) Bounded linear functionals Weak and weak* topologies, Applications to re exive separable spaces, Uniformly convex spaces, Application to calculus of variations
(4) Hilbert spaces, Riesz representation theorem, Lax-Milgram lemma and application to variational inequalities, Orthonormal bases, Applications to Fourier series and examples of special functions like Legendre and Hermite polynomials.

Differential Topology.
(1) Review of di erential calculus of several variables: Inverse and implicit function theorems. Richness of smooth functions; smooth partition of unity, Submanifolds of Euclidean spaces (without and with boundary) Tangent space, embeddings, immersions and submersions, Regular values, pre-image theorem, Transversality and Stability. [The above material should be supported amply by exercises and examples from matrix groups.]
(2) Abstract topological and smooth manifolds, partition of unity, Fundamental gluing lemma with criterion for Hausdor ness of the quotient, classi cation of 1-manifolds. De nition of a vector bundle and tangent bundle as an example. Sard's theorem. Easy Whitney embedding theorems.
(3) Vector elds and isotopies Normal bundle and Tubular neighbourhood theorem. Orientation on manifolds and on normal bundles. Vector elds. Isotopy extension theorem. Disc Theorem. Collar neighbourhood theorem.
(4) Intersection Theory: Transverse homotopy theorem and oriented intersection number. Degree of maps both oriented and non oriented cases, winding number, Jordan Brouwer separation theorem, Borsuk- Ulam theorem.

Resource Persons

Prof. B Ramakrishnan, HRI, Allahabad

Prof. M. Manickam, KSOM, Kozhikode

Dr. Kavita Sutar, CMI, Chennai

Dr. Priyavrat Deshpande, CMI, Chennai

Prof. Purusottam Rath, CMI, Chennai

Prof. Sanoli Gun, IMSc, Chennai

Dr. Manoj Kummini, CMI, Chennai

Dr. Krishna Hanumanthu,CMI, Chennai

Prof. R. Thangadurai,HRI, Allahabad

Prof. D.Surya Ramana ,HRI, Allahabad

Prof. Satya Deo ,HRI, Allahabad



Time Schedule

ATM Workshop on Graph Theory(2014)
Supported by National Centre for Mathematics

Venue: KSOM, Kozhikode

17-22 March, 2014


M Manickam
Professor & Director(i/c)
Kerala School of Mathematics, Kozhikode
S S Sane
Department of Mathematics, IIT Bombay

Description and salient features of the syllabus: This workshop covered some topics in Graph Theory, including both algorithmic and non-algorithmic that are not normally covered in a first course on Graph Theory. The topics include spectral graph theory, some topics in algebraic graph theory leading to Tutte polynomial of a graph, extremal graph theory including the Szemeredi regularity lemma and some topics in algorithmic graph theory including reducibility of 3-SAT.

Resource Persons

Professor R. Balakrishnan, Department of Mathematics, Bharathidasan University, Trichy

Professor Ajit Diwan, Department of Computer Science, I.I.T. Bombay, Mumbai

Professor S.A. Choudum, (Retired) Professor, I.I.T. Madras, (at present in) Bangalore


Time Schedule

Annual Foundation School - Part I (2013)
Supported by National Centre for Mathematics

Venue: KSOM, Kozhikode

02-28 December, 2013


Group Theory:

Speaker: B. Ramakrishnan
Group actions, Sylow Theory, direct and semi-direct products, simplicity of the alternating groups, solvable groups, p-groups, nilpotent groups, Jordan-Holder theorem.

Speaker: M. Manickam
Free groups, generators and relations, finite subgroups of SO(3), SU(2), simplicity of  PSL(V).

  • Speaker: M. Manickam

Representations and characters of finite groups: Maschke’s Theorem, Schur’s lemma, characters, orthogonality relations, character tables of some groups, Burnside’s theorem.


  • Analysis:

Speaker: R. Thangadurai
Abstract measures, outer measure, completion of a measure, construction of the Lebesgue measure, nonmeasurable sets.
Measurable functions, approximation by simple functions, Cantor function, almost uniform convergence, Ego-roff and Lusin’s theorems, convergence in measure.

Speaker: P. K. Ratnakumar
Integration, monotone and dominated convergence theorems, comparison with the Riemann integral, signed measures and Radon-Nikodym theorem.

Speaker: K. Sandeep
Fubini’s theorem, Lp - spaces.


Differential Topology:

Speakers: A. J. Jayanthan
Review of differential calculus of several variables: Inverse and Implicit function theorems. , Richness of smooth functions; Smooth partition of unity, Submanifolds of Euclidean spaces (without and with boundary), Tangent space, embeddings, immersions and submersions, Regular values, pre-image theorem , Transversality and Stability

Speakers: P. K. Ratnakumar
Topological and smooth manifolds, partition of unity , Fundamental gluing lemma and classication of 1-manifolds, Vector bundle; Tangent bundle, Morse - Sard theorem, Easy Whitney embedding theorems.

Speakers: P. Sankaran
Orientation on manifolds. , Transverse Homotopy theorem and oriented intersection number , Degree of maps both oriented and non oriented case, Winding number, Jordan Brouwer Separation theorem, Borsuk - Ulam Theorem, Vector eld and isotopies (statement of theorems only) with application to Hopf Degree theorem.

Speakers: G. Santhanam 
Morse functions, Morse Lemma, Connected sum, attaching handles , Handle decompostion theorem, Application to smooth classication of compact smooth surfaces.


Workshop and International Conference on Automorphic Forms and Number Theory

Venue: KSOM, Kozhikode

30th August - 3rd September, 2013

Recent developments in various branches of mathematics and physics show an increasing interest in the explicit construction of Jacobi forms, in particular, Jacobi forms of matrix (or, equivalently, lattice) index. This has to do with their appearance in quantum field theory, module spaces of surfaces, infinite dimensional Lie algebras. Though Jacobi forms of matrix index are known since quite long it is only recently that there was an essential breakthrough in the theory. For example, recent work of Gritsenko, Skoruppa, Zagier shows that Jacobi forms can be constructed in a surprisingly explicit way. These constructions in turn are closely related to classical problems in the arithmetic theory of lattices and in the theory of trigonometric polynomials.

For getting interested researchers or graduate students up to date in recent developments we have conducted a 3 days instructional workshop on Jacobi forms of lattice index, followed by a 2 days conference, where participants of the workshop got an opportunity to report on their own research projects for initiating discussions, obtaining feedback or help.


Part 1: Workshop on Jacobi forms of lattice index
Organizers: Prof. M. Manickam, Prof. Ramakrishnan B., Prof. Nils Peter Skoruppa
Lecturers: Hatice Boylan (Istanbul Üniversitesi and Max-Planck-Institute Bonn), Fabien Cléry (University of Siegen), Nils-Peter Skoruppa (University of Siegen and Max-Planck-Institute Bonn)
Overview: The workshop aimed to give a careful and thorough introduction into the theory of Jacobi forms of lattice index with emphasis on explicit constructions, in particular, for low weights and maximal lattices as index. In addition, it showed how Jacobi forms can be used to construct other types of automorphic forms via the so-called additive and multiplicative liftings.
● Basic notions: Lattices, shadows, discriminant modules, definition of Jacobi forms, discussion of the definition, first examples, functorial properties
● Jacobi forms as theta functions: vector valued modular forms, relation between Jacobi forms and vector valued modular forms, dimension formulas
● Explicit constructions of Jacobi forms: Taylor expansion around 0, Theta blocks, invariants of Weil representations
● Maximal lattices as index, explicit description of forms of singular and critical weight and maximal index
● Additive and multiplicative liftings, product expansions

Friday to Sunday: each day 3 lectures of 90 min and 60 minutes for discussions, questions and problem session

Part 2: Conference on Automorphic Forms and Number Theory
List of Speakers

1 Mr. Ali Ajouz Siegen University, Germany
2 Dr. Anandavardhanan .U.K IIT, Mumbai
3 Dr. Brundaban Sahu NISER, Bhubaneshwar
4 Dr. Fabien Cléry France
5 Dr. Hatice Boylan Istanbul University and Max-Planck Institute for Mathematics, Bonn
6 Dr. Jaban Meher IMSc., Chennai
7 Dr. Jagathesan .T RKM vivekananda College, Chennai
8 Dr. Jayakumar R RKM vivekananda College, Chennai
9 Ms. Jisna P KSOM, Kozhikode
10 Dr. Karam Deo Shankhadhar IMSc., Chennai
11 Dr. Kumarasamy .K RKM vivekananda College, Chennai
12 Dr. Manickam .M KSOM, Kozhikode
13 Dr. Nils Peter Skoruppa Siegen University, Germany
14 Mr. Rahothaman .R Sona College of Technology, Salem
15 Dr. Ramakrishnan .B HRI, Allahabad
16 Mr. Shankar P KSOM, Kozhikode
17 Mr. Srivatsa .V KSOM, Kozhikode
18 Dr. Sujay Ashok IMSc. Chennai
19 Ms. Tamil Selvi Alpha College of Engineering, Chennai

The programme was partially suported by HRI, Allahabad


Instructional Workshop on Logic and Set Theory

Venue: KSOM, Kozhikode

18th February - 1st March, 2013

The workshop is meant to benefit research scholars and young teachers of Mathematics, Statistics and Computer Science. 

The course will cover fundamentals of propositional logic, first order logic, completeness theorem, model theory with applications in number theory, algebra and geometry.
Cardinal arithmetic, partially-ordered sets, well-ordered sets, transfinite induction, ordinal numbers, axiom of choice and its equivalent forms such as Zorn's lemma and well-ordering principle and their applications in mathematics, Zermelo-Fraenkel axioms.


Resource Persons

S. M. Srivastava (ISI, Kolkata)  
H. Sarbadhikari (ISI, Kolkata)  
B.V.Rao (CMI, Chennai) Lecture Notes
N. Raja (TIFR, Mumbai)  
R. Ramanujam  (IMSc, Chennai).  


Workshop on Number Theory and Dynamical Systems

Venue: KSOM, Kozhikode

04-08 February, 2013

Topics Covered:

Linear recurrent sequences and iterations of linear maps

Diophantine approximation and dynamical systems

Continued fractions and the geodesic flow

Scientific Committee

Prof. Yann Bugeaud, Strasbourg University, Mathematics, 7, rue Rene Descartes, 67084 STRASBOURG Cede, France
Prof. Pietro Corvaja, Dipartimento di Matematica e Informatica, University of Udine, Italy. 
Prof. S.G. Dani, Indian Institute of Technology, Mumbai, India 
Prof. Michel Waldschmidt, Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, Paris 6, France

Local Organising Committee
Prof. M Manickam, Kerala School of Mathematics, Kozhikode, India
Prof. Michel Waldschmidt, Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, Paris 6, France

ATMW Hilbert Modular forms and varieties (2013)

Venue: KSOM, Kozhikode

21-31 January, 2013


National Centre for Mathematics, a joint centre of IIT Mumbai and TIFR, Mumbai

Brief description of the workshop
The goal of the workshop will be to introduce researchers from scratch to some of the basic concepts in the theory of automorphic forms and varieties attached to GLn over totally real fields. We shall quickly treat some of the basic concepts over the first two or three days, and reserve the latter part of the first week for more advanced topics, some of these may include: p-adic Hilbert modular forms, Herzig's classification of the mod p representations of GLn over a local field and Taylor's recent construction of Galois representations for GLn over totally real fields.During the second week, there will be a short conference to collect together local experts in the area of modular forms and related areas of number theory. We will in particular concentrate on representation theoretic and p-adic aspects of the theory of automorphic forms. The conference will have several one hour research level talks every day.

Click here for details

School on Modular Forms

Venue: KSOM, Kozhikode

03 - 19 October, 2012

In connection with the National Mathematical Year celebrations we had conducted a Workshop on Theory of Prime Numbers and Related Areas from 06-10 May 2012 at KSOM. The workshop,School on Modular Forms conducted from 03rd October, 2012 to 19th october 2012 was also related to Ramanujan's work. 

Topics Covered:
Basic of modular forms for the full modular group and for its congruence subgroups and related areas.

Lectures delivered by:
Prof. M. Manickam, Kerala School of Mathematics, Kozhikode
Prof. B. Ramakrishnan, Harish Chandra Research Institute, Allahabad.
Prof. Nils-Peter Skoruppa, Siegen University, Germany

Special Lectures delivered by:
Prof. Ananda Vardhanan, IIT, Mumbai
Prof. Eknath Ghate, TIFR, Mumbai
Prof. A. Raghuram, IISER, Pune
Prof. J. Sengupta, TIFR, Mumbai
Dr. R. Thangadurai, HRI, Allahabad.
Dr. Brundaban Sahu, NISER, Bhubaneshwar

Theory of Prime Numbers and Related Areas

Venue: KSOM, Kozhikode

06 - 10 May, 2012

The Workshop was meant for research fellows, young teachers, PG and bright UG students of Mathematics. The course program covered: Ramanujan's Proof of Betrand's Postulate, Prime Number Theorem, Highly Composite Numbers and its applications and Ramanujan's way of summation.

Resource Persons:

Prof. Ram Murty
Queens University, Canada

Dr. Anirban Mukhopadyaya

Institute of Mathematical Sciences

Dr. D. S. Ramana
Harish-Chandra Research Institute

Dr. R. Thangadurai
Harish-Chandra Research Institute



Instructional Workshop on Ergodic Theory

Venue: KSOM, Kozhikode

17 October - 04 November 2011

The Workshop was meant to benefit research fellows and young teachers of Mathematics and Statistics. The course program covered: Basic Ergodic Theory and Topological Dynamics, Probabilistic Systems, Spectral Theory of Dynamical Systems, Ergodic Theory with groups and Diophantine Approximations, Ergodic Theory in Geometry.

Resource Persons:

M. G. Nadkarni (IIT, Indore) Lecture Notes
S. G. Dani (TIFR, Mumbai)  
S. C. Bagchi (ISI, Kolkata)  
Siddharta Bhattacharya (TIFR, Mumbai) Lecture Notes
B. V. Rao (CMI, Chennai) Lecture Notes
J. Dani (University of Mumbai)  
C. S. Aravinda (TIFR, Bangalore)  
Shiva Shankar (CMI, Chennai)  
J. Mathew (KSOM, Kozhikode)  



School on Algebra, Analysis & Topology

Venue: KSOM, Kozhikode

01-07 September, 2011

The School was aimed at M.Sc. Mathematics students of Kerala. The course covered some topics of Algebra, Analysis and Topology which are not usually covered in the M.Sc. curriculum

Resource Persons:

Basudeb Dutta (I.I.Sc., Bangalore)
U. K. Anandavardhanan (I.I.T., Mumbai)
A. J. Parameswaran (TIFR, Mumbai)
Jathavedan (CUSAT, Kochi)
Joseph Mathew (KSOM, Kozhikode)
A.K. Vijayarajan (KSOM, Kozhikode)



Workshop on Functional Analysis and Harmonic Analysis

Venue: KSOM, Kozhikode

01 June 2011 - 10 June 2011

The workshop was aimed at senior post-graduate students with aptitude for research and junior research fellows with research interests broadly in Analysis. The workshop also benefit young teachers of Mathematics teaching at post-graduate level.

Resource Persons

Prof. Gadadhar Misra (IISc, Bangalore)
Prof. M Krishna(IMSC, Chennai)
Prof. Rajarama Bhat ( ISI, Bangalore)
Prof. K. Parathasarathy(Ramanujan Institute, Chennai)
Prof. M N Narayanan Namboodiri (CUSAT, Cochin)
Prof. M Sundari (CMI, Chennai)
Prof. Joseph Mathew (KSOM, Kozhikode)



School on Analysis, Algebra & Topology

Venue: KSOM, Kozhikode

13 Dec 2010 - 07 Jan 2011

The programme was aimed at junior research fellows and final year post-graduate students in Mathematics from Universities/Colleges in Kerala. Those who have completed post-graduate programme recently and intending to pursue mathematics as a career also appllied. The School was conducted by eminent researchers from Universities/Institutions in India and covered some advanced topics in Algebra, Topology and Analysis which are generally considered to be prerequisites for research scholars in all disciplines of Mathematics. The course consist of rigorous class room lectures and problem solving tutorials.

Resource Persons

U. K. Anandavardhanan , IIT Bombay

Manoj Kumar Keshari , IIT Bombay

Balwant Singh , CBS Bombay

Sudhir Ghorpade  , IIT Bombay

Raja Sreedharan , TIFR Bombay

Rudra Pada Sarkar, ISI, Kolkatta

A K Nandakumaran, IISc Bangalore

K Sandeep, TIFR Bangalore

P K Rathnakumar, HRI Allahabad

P K Rathnakumar, HRI Allahabad

Mahuya Datta, ISI, Kolkatta

V Uma , IIT Madras

Amit Hogadi , TIFR Bombay

A J Parameswaran, KSOM

Advanced Instructional School on Schemes & Cohomology

Venue: KSOM, Kozhikode
28 June - 16 July, 2010
Conveners: A. J. Parameswaran & V. Balaji

A Brief Description of ATM Schools
Advanced Training in Mathematics (ATM) Schools are a joint effort of a large number of mathematicians in the country for training mathematics research scholars and teachers with generous support from the National Board for Higher Mathematics. The programmes are conducted in reputed mathematics departments in Summer and Winter each year. In these Schools, the emphasis is on problems solving and on understanding interrelations of basic subjects in mathematics. At the initial stage, ATM Schools consist of two Annual Foundation Schools (AFSI & II) in algebra, analysis, and topology. At a later stage, Advanced Instructional Schools (AIS) and workshops (ATMW) in all major areas are organised. Several advanced instructional schools (ATML) are organized each year exclusively for young lecturers in colleges and universities.

Advanced Instructional School on Schemes and Cohomology
The AIS was directed towards making young researchers in India familiar with the developments in Algebraic Geometry, with special emphasis on Grothendieck’s programme. The three week programme was primarily aimed at early researchers in this field to become familiar and users of the tools and techniques in this subject. To acquire a good knowledge of modern algebraic geometry it is essential to see the “local” aspects coming from Commutative algebra in its interplay in geometry as well as the immense machinery of cohomology. These two themes were the main ones for the workshop. To give a flavour of the manner in which these tools have lead to fundamental theorems in algebraic geometry, the final week stress on some research themes. A team of active researchers in the field had participated for this purpose.

Resource persons
TEV Balaji V. Balaji Vivek Mallik
D. S. Nagaraj Suresh Naik ,
A. J. Parameswaran, K. N. Raghavan

Unity of Mathematics Lectures
  Nitin Nitsure, Kapil Paranjape, S. Ramanan,
 Pramathanath Sastry , C. S. Seshadri, C. S. Rajan
Jugal Verma, Shiva Shankar

Summer School on Probability: Foundations & Applications

Venue: KSOM, Kozhikode

17 May - 04 June, 2010

The Summer School was meant to benefit senior post-graduate students, junior research fellows and young teachers of Mathematics, Statistics and Computer Science. The course covered fundamentals of discrete and continuous probability models, law of large numbers, weak convergence and limit theorems, conditional probability, Markov Chains and Martingales, large deviations and entropy. It also covered some applications to number theory, graph theory, computer science and other related fields.
Resource Persons

M. G. Nadkarni (Univesity of Mumbai) Lecture Notes
B. V. Rao (C. M. I., Chennai) Lecture Notes
B. Rajeev (I. S. I., Bangalore) Lecture Notes
Inder Rana (I. I. T., Mumbai) Lecture Notes
R. L. Karandikar (C. M. I., Chennai) Lecture Notes
S Ramasubramanian (I. S. I. Bangalore) Lecture Notes


Workshop on Statistics

Venue: KSOM, Kozhikode

05-06 March, 2010

The workshop was meant exclusively for the Scientists of KSCSTE and the R&D institutions under KSCSTE.
Resource Persons

T.Krishnan obtained his Master's and Ph.D. degrees from the Indian Statistical Institute, Kolkata.  He has been on the faculty of this Institute since 1965 until his retirement in 1998 as a Professor of Applied Statistics.  After retirement he worked as a full-time consultant for Cranes Software International Limited, Bangalore, on the development of a statistical software SYSTAT for eight years. Currently he is working for Strand Life Sciences, a Bioinformatics company in Bangalore as a Statistician.  His book  (with G.J. McLachlan) on the EM Algorithm is a definitive and standard reference on the subject.

R.V.Ramamoorthi  obtained his Master's degree from Utkal University and his Ph.D. degree from the Indian Statistical Institute, Kolkata.  Since 1982 he has been on the faculty of the Michigan State University, East Lansing, Michigan, U.S.A.  where he is currently a Professor of Statistics.  He is currently on  leave from this position and is a visiting professor at the Indian Institute of Science, Bangalore.  . His earlier research was on sufficiency and decision theory. For the last few years he has been working on Bayesian Nonparametric Inference and his book (with J.K.Ghosh) on Bayesian Nonparametrics is an authoritative book on the subject.


Time Schedule

Friday, 05 March 2010

09:30--10:00 Inauguration Dr. K. V. Jayakumar  
10:00--11:15 Introduction to Data Analysis TK (T. Krishnan) Lecture Notes
11:30--12:45 Basic Probability RVR (R. V. Ramamoorthi) Lecture Notes
12:45--14:00 Lunch    
14:15--15;30 Descriptive and Graphical Statistics TK

Lecture Notes

Lecture Notes

15;45--17:00 Sampling Distributions and Confidence Intervals RVR Lecture Notes

Saturday, 06 March 2010

10:00--11:15 Hypothesis Testing  RVR Lecture Notes
11:30--12:45 Analysis of Variance and Regression TK Lecture Notes
12:45--14:00 Lunch    
14:15--15;30 Experimental Designs and Survey Sampling TK

Lecture Notes

Lecture notes

15;45--17:00 Computer-Intensive Statistical Methods RVR, TK

Lecture Notes

Lecture Notes

Workshop on Functional Analysis and Harmonic Analysis

Venue: KSOM, Kozhikode

1-10, February 2010

The workshop was meant to benefit senior post-graduate students, junior research fellows and young teachers of Mathematics and aims to cover the necessary background material for understanding, pursuing and teaching advanced level topics in the two main areas of the workshop. The workshop is meant for senior MSc. students, Junior Research Scholars and young teachers from university departments and col leges from the country.

Topics covered:
Functional analysis: Banach algebras, maximal ideals, Gelfand-Naimark theorem, spectral theorem
Harmonic analysis: Fourier series, Fourier transforms and Paley-Wiener theorems

Resource persons

Prof. Gadadhar Mishra, Indian Institute of Science, Bangalore
Prof. E. K. Narayanan, Indian Institute of Science, Bangalore
Prof. Alladi Sitaram, Indian Institute of Science, Bangalore
Prof. V. S. Sunder, Institute for Mathematical Sciences, Chennai
Prof. B. V. Rajarama Bhat, Indian Statistical Institute, Bangalore

Instructional Workshop on Spectral Theorem

Venue: KSOM, Kozhikode

15th and 16th June 2009

Co-Sponsored by KSCSTE

Day 1, June 15, 2009, Monday:

Registration  : 8:30 a.m.      
Inauguration : 10:00 a.m. – 11:00 a.m.
Tea : 11:00 a.m. - 11:30 a.m.  
Lecture 1, 11:30 a. m-12.30 p.m.: Spectral theorem for normal matrices – Dr. Rajarama Bhat
Lecture 2, 12:30 p.m-1:30 p.m: Spectral theorem for compact self-adjoint operators - Dr. G. Ramesh
Lunch break: 1:30 p.m-2:30 p.m
Lecture 3, 2:30 p.m-3:30 p.m:  Topologies of B (H) –Dr. A K Vijayarajan
Tea: 3:30 p.m- 4:00 p.m.
Lecture 4, 4:00 p.m.-5:00 p.m.: General spectral theorem for bounded operators-I- Dr. Rajarama Bhat                                      

Day 2, June 16, 2009, Tuesday:

Lecture 1, 9:30 a.m-10:30 a.m.: General spectral theorem for bounded operators –II- Dr. Rajarama Bhat
Tea break: 10:30 a.m-11:00 a.m.

Lecture 2, 11:00 a.m-12:00 p.m: Double Commutant Theorem - Dr. A K Vijayarajan

Discussions: 12:00 p.m-12:30 p.m
Lunch break: 12:30 p.m-2:00 p.m
Lecture 3, 2:00 p.m-3:00 p.m: Trace Class Operators and Duality- Dr. G. Ramesh
Tea break: 3:00 p.m-3:30 p.m
Lecture 4, 3:30 p.m-4:30 p.m: Some Applications of spectral Theorem-                                            

Discussion: 4:30 p.m.-5:00 p.m. Dr. Rajarama Bhat

Resource persons & Speakers





Dr. B. V. Rajarama Bhat

Indian Statistical Institute


Indian Statistical Institute, R. V. College(PO) Bangalore-560059

Dr. G. Ramesh

Indian Statistical Institute

Post-doctoral Fellow

Indian Statistical Institute, R. V. College(PO)

Dr. Vijayarajan A. K.

Kerala School of Mathematics

Associate Professor

Kerala School of Mathematics

@2010 Kerala School of Mathematics