**IIT ****BOMBAY**

**DEPARTMENT OF MATHEMATICS**

**ANNUAL REPORT (YEAR 2004-2005)**

The Department has continued with its tradition of excellence in teaching with synergistic augmentation of research in Fundamental and Applied areas. The department is celebrating the year 2005 as "Year of Popularizing Mathematics". The major Academic and R & D activities of the current academic year include the following:

**Industrial Mathematics Group:**

Industrial Mathematics Group (IMG) of the department aims to develop a long term partnership with industry via Study Group Meetings, Workshops, Inhouse Programme and Industry - IIT Meets.

Apart from an ongoing European Union Funded ASIA IT project on WEBOPT (Web Enabled Optimization Tools and Industrial Deployment) with partners from CARISMA, Brunel University, UK, University of Vienna (Austria), Jadavpur University, Kolkata and IITB, IMG is also a partner of an ONGC sponsored project titled `Physical and Numerical Models for Unconventional Flood Patterns' of amount 2.16 crores.

During the Year 2004-05 the group had a few rounds of
discussion with RBI, Govt. of India and HDFC on a possible interaction in the
areas of quantitative finance, with Managing Director from Countrywide Security
Corporation and with CEO and its group from Zafin
Labs on possible collaboration in terms of joint projects. IMG had a brain
storming session with the President-Worldwide Research and Technology and its
group from Michelin Tyre Company (France) for
possible sponsorship on research and also for hiring mathematicians from

During the academic year 2004-2005, IMG in collaboration
with

As a part of IMG activity, a year long programme on Computational Partial Differential Equations (CPDE-05) with an objective of bringing together experts working in this area and of developing awareness in the Mathematics Departments in the country is presently going on.

**Year Long Programme on Computational Partial Differential Equations
(CPDE- 05):**

Industrial Mathematics Group (IMG) in the Department of
Mathematics, IIT Bombay is presently hosting a year-long programme
on ``Computational Partial Differential Equations'' starting from January,
2005. The focus of this programme is to bring
together experts working on this area, to develop awareness amongst the
mathematical community in our country, to train campus community in effective
use of public domain computational tools and to encourage young researchers and students from
our country to participate in the year long activities. Main emphasis is on the
recent advances in the development of new methodologies and solution strategies
employed in Computational PDEs in solving physically
relevant and mathematically hard problems. The list of speakers included Prof.
S. Kesavan, IMT, Chennai; Prof. C. Carstensen,

**Year long Programme on Homological Methods in Commutative Algebra:**

During the academic year 2004-05, the members of the research group in commutative algebra organized several activities. Distinguished lecture series were organized. The following mathematicians visited the department and delivered series of lectures: Prof. S. M. Bhatwadekar, TIFR, Mumbai, Dr. V. Trivedi, TIFR, Mumbai, Prof. R. A. Rao, TIFR, Mumbai, Prof. B. Singh, IIT Bombay, Prof. T. Puthenpurakal, IIT Bombay, Prof. A. R. Shastri, IIT Bombay, Mr. A. Bhattacharya, TIFR, Mumbai, Dr. A. V. Jayanthan, HRI, Allahabad, Dr. Clare D'Cruz, CMI, Chennai, Prof. J. Herzog, University of Essen-Duisberg, Germany.

**Year long Programme
on Mathematics Education and Awareness:**

During the period
January 2005- March 2005 the following activities were organized: Lecture by
Prof. M.S. Raghunathan titled “Mathematics, the Queen
of Sciences”, “Mathematica in Math Education” by R. Knopp, Wolfram Labs**.**

**Academic Programmes:**

Besides the teaching of
B. Tech. Courses, the department offers M.Sc. and
Ph.D. programmes along with its research
activity. It has two distinct M.Sc. programmes. M.Sc. in Mathematics (intended for those who wish to pursue research
and/or teaching as their career) and M.Sc. in Applied
Statistics and Informatics (ASI). This job oriented programme
that began in 1997, has been a success and a trend setter for some other IITs.

In addition, the Department has a research programme leading to Ph.D. degree. This programme has a broad based course work and specialization in Pure Mathematics, Applied Mathematics, Scientific Computing and Statistics.

** R & D Activities**

The key objectives of the research and development
activities of the department are: **Basic
Research, **focusing in contemporary areas of fundamental, developmental and strategical importance and **Interdisciplinary Research, **aiming at** **development of multidisciplinary research teams involving
mathematicians and scientists/engineers in frontier areas of Mathematics and
Statistics. Academic & Research Interaction of the Department has further
expanded with leading R & D institutions like** **TIFR, IISc, ISI, ISRO, DRDO, ONGC,
Indian Meteorological Centers, etc., and Foreign Universities like Brunel (U.K), Humboldt University, Berlin, Technical
University, Dresden, INSA, Toulouse (France) and nodal organizations such as
CSIR, DAE, DBT, DST, etc., for scientific exchange of ideas of national
importance. In order to fulfill the
broad objectives of research activities, steps are taken to ensure that the
theoretical base in emerging areas are strengthened, interdisciplinary problems
requiring mathematical solutions are identified, interaction between Indian and
overseas scientists are facilitated, local talents are well nurtured through
lecture series and instructional workshops and by evolving a pool of trained
manpower in thrust areas.

The Department has 25 core and 2 adjunct faculty members.

The research interests of the faculty members cover a wide range of fields:

v Algebraic Geometry

v Algebraic Topology

v Applied Probability,

v Approximation Algorithms

v Bio-Statistics Combinatorial Optimization

v Combinatorics

v Commutative Algebra

v Computational Biology. & Bio-informatics

v Functional Analysis

v Geo-Statistics

v Harmonic Analysis

v Image Processing & Pattern Recognition

v Industrial Mathematics & Financial Mathematics

v Inference of Stochastic processes & Statistical Inference

v Mechanics of Solids and Fluids

v Number Theory

v Numerical Analysis & Scientific Computing

v Optimization & Control

v Partial Differential Equation

v Quasilinear Hyperbolic Systems of PDE’s and Non-Linear waves.

v Reliability theory and Industrial Statistics

v Riemannian Geometry

v Statistical Signal Processing

v Stochastic Differential Game Theory

Faculty members undertake projects sponsored by organizations such as National Board for Higher Mathematics (NBHM), Indian National Science Academy (INSA), Board of Research in Nuclear Science (BRNS), Council of Scientific & Industrial Research (CSIR), Department of Science & Technology (DST), Department of Bio-Technology (DBT), and Indian Council of Medical Research (ICMR). Some

of the important ongoing and
recently completed projects are listed below:

**Joshi R.R.**

Project Title: Software Development for Ab-initio Prediction of 3D structure of Proteins using
Knowledge-Based Nonparametric Regression.

Sponsoring Agency: Dept. of Biotechnology, Govt. of

Amount generated: Rs.11.76 lakhs

Beginning Year:
2003

End Year: 2006

**Natraj****, N.**

Project Title: A parallel mixed finite
element implementation of* *IV order
elliptic source/ eigenvalue problems in distributed
memory environments.

Sponsoring Agency: IRCC

Amount generated: Rs.
3 lakhs

Beginning Year: 2003

End Year: 2005

**Pani**** A.K. and Patkar Sachin**

Project Title: WebOPT

Sponsoring Agency: European Union ASIA-ITC

Amount generated: Rs.
40 lakhs

Beginning Year: 2003

End Year: 2005

**Pani**** A. K., Mitra S.K
and Vinjamur M.**

Project Title: Physical and Numerical Models for Un-conventional Flood Patterns

Sponsoring Agency:

Amount generated: Rs.2.16 crores

Beginning Year: 2004

End Year: 2007

Project Title: Stochastic Modelling, Analysis and Optimization of resource allocation.

Sponsoring Agency: ISPC

Amount generated: Rs.
5.7 lakhs

Beginning Year: 2003

End Year: 2005

Project Title: Preparation of E-Modules.

Sponsoring Agency: MHRD

Amount generated: Rs.
1.6 lakhs

Beginning Year: 2003

End Year: 2005

Project Title: 10^{th} Workshop in Mathematics

Sponsoring Agency: DST

Amount generated:
Rs.1.5 lakhs

Beginning Year: 2004

End Year: 2005

Project Title: NPTEL. (jointly with CDEEP)

Sponsoring Agency: MHRD

Amount generated:
Rs.

Beginning Year: 2003

End Year: 2006

**Sabnis**** S.V.**

Project Title: Study of Optimal Reliability Test Plans

Sponsoring Agency: DST

Amount generated: Rs. 6.43 lakhs

Beginning Year: 2002

End Year: 2005

**Sharma V.D.**

Project Title: Analytical and numerical methods for hyperbolic conservation laws with applications.

Sponsoring Agency:
CSIR

Amount generated: ~ Rs.7 Lakhs

Beginning Year:2003

End Year: 2005

**Consultancies**

**Pani**** A.K.**

Project Title: Enhanced Oil Recovery

Sponsoring Agency: ONGC

Amount generated: Rs. 4,50,000/-

Beginning Year: 2004

End Year: 2007

**Patkar**** Sachin**

Project Title: Issues in VLSI Partitioning

Sponsoring Agency: SoftJin

Amount generated: Rs. 5,50,000/-

Beginning Year: 2004

End Year: 2005

Project Title: Algorithmic Investigation of Simulator Accelerator

Sponsoring Agency: Powai labs

Amount generated: Rs. 1,50,000/-

Beginning Year: 2004

End Year: 2005

**Sabnis**** S.V.**

Project Title: Statistical modelling of
Airline Data.

Sponsoring Agency: Kale Consultancy, Mumbai

Amount generated: Rs. 49,986/-

Beginning Year: 2003

End Year: 2005

Project Title: Development of Design of Experiments related subroutine.

Sponsoring Agency: Asian PPG Industries Limited

Amount generated: Rs. 15,000/-

Beginning Year: 2004

End Year: 2005

Project Title: Discrete Choice Modelling

Sponsoring Agency: TNS India Pvt. Limited

Amount generated: Rs.95,000/-

Beginning Year: 2004

End Year: Ongoing

**Extension Activities**** **

**POPULAR LECTURE SERIES**

The faculty is actively involved in various programmes of popularizing of mathematics and training in Mathematics such as NBHM sponsored nurture programme, Ganit Utsav organized by Bombay Mathematical Colloquium and popular lectures at Nehru Science Centre, to name a few.

Another important activity in
this direction is the Popular Lecture Series in Mathematics a joint activity of
Mathematics Association of IIT,

This was started in 1997 by the
Mathematics Association of IIT,

The lectures are aimed at a wide spectrum of audience. Besides mathematicians, we also invite scientists and engineers who apply mathematics in research and development in their areas. The speakers are instructed to start from the basics and build their lectures so that beginners as well as experts can benefit. The series has become extremely popular among students and faculty at IIT and college teachers in Mumbai.

**Workshops and
Conferences Organized by the Department:**

**Organizer: Prof. Inder K. Rana**

10^{th} Workshop in Mathematics sponsored by DST.
The Workshop aims to motivate Young Students for higher studies in Mathematics.
About 40 students participated in the Workshop.

**Organizer: Prof. A.K. Pani**

Indo-Uk Study Group Meeting on Industrial Problems:

IMG and

sponsored by DST and Royal Society (UK).

International Conference on Recent
Trends in Nonlinear Analysis and
Its Applications,

**CEP Workshops**

**Prof. Sabnis S.V**.

Conducted a two-day in-house CEP
workshop on "Statistical Process Control- Basic Awareness Programme" for Crompton
Greaves during

Acted as one of the resource
persons for a workshop on “Design of Experiments” conducted for a group of
scientists from

Acted as
one of the resource persons for a SAS Workshop held at Department of
Statistics,

**Workshops and Conferences Organized outside the Department.**

**Organizer: Prof. J.K. Verma**

Conducted a
3 week long workshop and an international conference, “School on Commutative
Algebra and Interactions with Algebraic Geometry and Combinatorics”
in International Centre for Theoretical Physics, ^{th} May to ^{th} June 2004

**VISITORS TO OUR DEPARTMENT**

**Prof. Upendra Kulkarni**,

Modular and Integral representations of GLn

**Dr. Vrushali A Bokil**,

A Computational and statistical framework for multidimensional domain acoustooptic interrogation.

**Dr. Ravi Raghunathan**, TIFR

Converse theorems, Zero and poles of L-functions

**Dr. Urmie Ray**,

Bocherds-Kac-Moody Lie algebras and denominator formulas

**Dr.
Swagata Nandi**,

Sinusoidal Frequency Model and chirp signal model

**Dr. Radha Mohan**,

Inetgrally Closed Modules, reductions and cores.

**Professor Kishore Sinha**, Birla Agricultural University,

Balanced and Partially Balanced Designs

**Prof. Arun Bagchi**,

Stochastic system Theory.

**Dr. V.V.K.Srinivas Kumar**, IIT Knapur

Web-Spline method for the Navier Stokes Problem.

**Bruno Poizat**, Universite Claude
Bernard- Lyon

Computations over an Arbitary Structure.

**Prof. P.N.Kaloni**,

Stability Problems in Magnetic Fluids

**Prof. Anand Srivastav**, Universitaet zu

Geometric Discrepancies in High Dimensional Integration.

**Prof. Jitesh Gajjar**,

Numerical Solutions of the Navier- Stokes equations for the flow in a Cylindrical Cascade.

**Dr. Rama Misra**, IIT

Polynomial Knots and their Degree Sequence.

**Dr. M.N.N. Namboodiri**,

Spectral Gaps of Self-Adjoint Operators.

**Prof. N. Rao Chaganty**,

Bivariate Models for identifying Differentially Expressed Genes in Micro array Experiments

**Prof. Gerard Ioose**, Institut Non LinÃ©aire

Existence of standing gravity waves in deep water.

**Prof. S. Kesavan**, Institute of Mathematical Sciences, Chennai

Saint Venant Revisited

**Prof. S. Kabadi**,

Multipath Flows: Analysis, Realizability and Network Synthesis problems

**Prof. Shreeram S. Abhyankar**,

Resolution of Singularities and Modular Galois Theory.

**Prof. R.L. Karandikar**, ISI,

An Invitation to Cryptography

**Professor Vidar Thomee**, Chalmers

Parabolic finite Element Equations in Nonconvex Polygonal Domains

**Mr. Amitava Bhattacharya**, TIFR Mumbai

Introduction to Polytopes

**Prof. J. Herzog**,

Grobner bases in Commutative Algebra and Combinatorics

**Dr. A.V. Jayanthan**, HRI,

Grobner bases and Initial Ideals

**Prof. P.N. Rathie**,

Renyi’s entropy and Tail Probabilities.

**Dr. Clare D’Cruz**, CMI, Chennai

Regularity of Ideals I

**Prof. Francois
Coulouvrat**, Universit
Pierre et Marie

Diffraction of nonlinear waves : numerical simulation and applications

**List of Faculty and Specializations**

** Athavale Ameer** (Professor-
VF)

* Functional Analysis*

**Ghorpade**** Sudhir R**.
(Professor)

*Algebraic
Geometry, Combinatorics*

**Joshi K. D**.
(Professor)

*Topology,
Discrete Mathematics*

**Joshi R. R**. (Professor)

*Computational
Biology and Biostatistics, Bioinformatics*

**Kulkarni**** Rekha P**. (Professor)

*Numerical
Functional Analysis, Spline Theory*

**Limaye**** Balmohan V**.
(Professor)

*Functional
Analysis, Numerical Analysis, Spectral Approximation*

**Mitra**** Amit (**Assistant
Professor)

*Statistical
Signal Processing*

**Nataraj**** Neela **(Assistant Professor)

*Finite Element
methods*

**Pai**** Devidas V**.
(Adjunct Professor)

*Functional
Analysis, Approximation Theory, Set-valued Analysis*

**Pani**** Amiya K**. (Professor)

*Numerical
Analysis, Partial Differential Equations, Industrial Mathematics*

**Patkar**** Sachin B**.
(Associate Professor)

*Combinatorial
Optimization, Algorithms*

**Prakash**** J**.
(Professor)

*Tribology*

**Puthenpurakal**** T.J (**Senior Lecturer)

*Commutative
Algebra*

**Rana**** Inder K**. (Professor)

*Harmonic
Analysis, Mathematics Education*

**Ranjan**** Akhil** (Professor)

*Differential
Geometry *

**Raghunathan** **Ravi**** **(Assistant
Professor)

*Automorphic** forms,
Number Theory*

**Sabnis**** S. V**.
(Associate Professor)

*Reliability
Theory, Industrial Statistics*

* ***Saikia**** Anupam**
(Assistant Professor)

* Number Theory*

**Sharma V.D**. (Professor)

*Quasilinear** Hyperbolic
Systems of PDEs/ Nonlinear Waves*

**Shastri**** A. R**.
(Professor)

*Algebraic
Geometry, Algebraic Topology *

** Sivaramakrishnan
Sivasubramanian** (Senior Lecturer)

* Polyhedral Combinatorics,
Approximation Algorithms*

**Srinivasan**** Anitha** (Senior Lecturer)

*Number Theory*

**Srinivasan**** G. K**.
(Assistant Professor)

*Partial
Differential Equations *

**Srinivasan**** M. K**.
(Professor)

*Combinatorics*

**Subramanyam**** A**. (Associate Professor)

*Statistical
Inference, Geostatistics*

**Sureshkumar**** K**. (Assistant Professor)

*Stochastic
Differential Game Theory, Mathematical Finance.*

**Vellaisamy**** P**. (Professor)

*Applied
Probability, Statistical Inference, Industrial Statistics*

**Verma**** J. K.** (Professor)

*Commutative Algebra*

**Publications in Books **

**Pai**** D.V.**

Haussdorff Strong Uniqueness in Simultaneos Approximation. Part I, in " Approximation Theory XI Gatlinburg 2004", C. K. Chui, M. Neamtu and L. L. Schumaker(eds.),101 118, Nashboro Press, Brentwood, TN, USA, 2005.

(with Indira K.)

On Well-Posedness of Some Problems in Approximation Theory, in "Advances in Constructive Approximation", M. Neamtu and E. B. Saff(eds.), Nashboro Press

(wirh Indira
K.)

**Srinivasan**** M.K.**

A Polytope in Hypergraph Theory, in
Combinatorial Optimization, Narosa publishing House,
2004, 139-150

**Publication in Journals**

**(International)**

**Athavale**** Ameer**

On a class of
alternatingly hyperexpansive
subnormal weighted shifts, Irish Math. Soc. Bulletin 53 (2004), pp. 35-52.

(with A. Ranjekar,
V.M. Sholapurkar)

**Joshi R.R.**

Yagyopathic Herbal
treatment of Pulmonary Tuberculosis symptoms – A clinical Trial.
Alt. Compl. Therap. 2004, Vol. 10(2),
pp. 101-105.

(with M. Raghuvanshi,
P. Pandya)

A Biostatistical Approach to Ayurveda
– Qunatifying the Tridosha,
Jnl. Alt. Comp. med. 2004, Vol. 10(5), pp. 879-889.

**Kulkarni**** R.P.**

Approximate
Solution of Multivariable Integral Equations of the Second Kind, Journal of Integral
Equations and Applications, 16(2004), 343-374.

Spectral Refinement using a New Projection
Method, ANZIAM J, 46(2004), 343-374.

(with

**Limaye**** B.V.**

Computation of Spectral Subspaces for Weakly Singular Operators, Numerical Functional Analysis and Optimization, Vol.25, pp 1-14 (2004).

(with M. Ahues)

**Mitra**** Amit**

"Time series lag selection
using genetic algorithms", Advances and Applications in Statistics, Vol.
4(2), 233-251, 2004**.**

(with Ashok K. Nag**) **

"Forecasting business cycle
movements using wavelet filtering and neural networks",
, Finance

(with Sharmishtha Mitra)

"Detecting multidimensional outliers from large datasets using self-organizing maps", , Computational Statistics, 2, 2005.

(with Ashok K. Nag, Sharmishtha Mitra)

**Nataraj**** Neela**

A parallel mixed finite element implementation of fourth order
plate bending problems in distributed memory environments. Applied Mathematics and Computation, 163,
253-274 (2005).

(with Kshitij
Kulsreshtha, Michael Jung)

Performance of a parallel mixed finite element implemenatation for fourth
order clamped anisotropic plate bending problems in distributed memory
environments, Applied Mathematics and Computation, 155, 753-777 (2004).

(with Kshitij
Kulsreshtha, Michael Jung)

**Pai**** D.V.**

On well-Posedness of some problems in
approximation, Journal of Indian Math. Soc. 70 (2003), 1-16.

**Pani**** A.K.**

An
H^1-Galerkin mixed method for second order hyperbolic equations, International J. Numer. Anal & Modeling, 1 (2004) pp.111-130.

(with Rajen
K. Sinha, Ajaya K. Otta).

Higher order fully discrete scheme combined with H^1-Galerkin
mixed finite element method for semilinear
reaction-diffusion equations, J. Applied Mathematics and Computing, 15, (2004),
pp. 1-28

(with S. Arul
Veda Manickam,
Kannan M. Moudgalya)

Sliding motion and stability of a class of discontinuous
dynamical systems,** **Nonlinear
Dynamics, 37 (2004), pp. 151-168.

(with Jyoti Agrawal, Kannan M. Moudgalya)

A second
order splitting lumped mass finite element method for the Rosenau
equation, Differential Equations and Dynamical Systems, 12 (2004), pp.
331-351.

(with Sang K. Chung)

Orthogonal
cubic spline collocation method for the extended
Fisher-Kolmogorov equation, Journal of Computational
and Applied Mathematics, 174 (2005), pp. 101-117

(with** **P.Dhanumjaya)

A qualocation method for unidimensional
single phase Stefan problem, IMA J. Numer. Anal. 25 (2005), pp.139-159

(with L. Jones Doss)

**Rana**** Inder K.**

On the
continuity of the associated
interval function, Journal
of Real Analysis Exchange, (29) 2003/04, No.2

**Sharma V.D.**

Energy
dissipated across shocks in weak solutions of conservation laws, Studies in
Applied Mathematics (

(with G.K. Srininvasan)

Imploding
cylindrical and spherical shock waves in a non-ideal medium, Journal of
Hyperbolic Differential Equations, (World Scientific;

(with Madhumita G)

**Sivaramakrishnan**** S.**

“On approximating the isoperimetric number of strongly regular
Graphs” to appear in the Electronic journal of Linear Algebra.

**Srinivasan**** Anitha**

Solutions of
some Generalized Ramanujan- Nagell
Equations, to appear in Indagationes Mathematicae

(with

**Srinivasan**** G.K.**

Implosion
time for converging
Cylindrical and Spherical shells, Z. Angew.
Math. Phy. , Vol 55, (2004), pp. 974-982.

**(**with V.D. Sharma)

**Srinivasan**** M.K.**

On the quotients of posets,
with an application to the q- analog of the Hypercube, European Journal of Combinatorics 25 (2004) 675-683.

**Subramanyam**** A**

On the equivalence of the Cokriging
and Kriging systems, Journal of the Mathematical
Geology, 36 (4), 2004, pp. 504-523.

(with Pandalai
H.S)

Tests of

(with Usha A.
Kumar)

**Suresh Kumar K.**

A nonzero-sum
Stochastic differential game in the orthant, Journal
of Mathematical Analysis and Applications, Vol. 305, Issue 1, 2005, pp.158-174

(with M.K Ghosh)

**Vellaisamy**** P.V**.

Poisson
Approximation for (K1,

**Verma**** J.K.**

Cohen-Macaulay fiber cones of almost minimal multiplicity,
Nagoya J. Math. 177(2005), 155-179.

(with
A. V. Jayanthan)

**Papers in Proceedings**

**(International)**

**Mitra**** Amit**

"Frequency
estimation of signal processing models using genetic algorithms",

Proceedings
of the International Conference on Recent Advances in Statsiitcs,
IIT

(with Debasis Kundu)

"Relationship
between money, output and price: revisited using wavelet filtering", Proceedings of the
International Conference on Recent Advances in Statsiitcs,
IIT Kanpur, January 2005**.**

(with Sharmishtha Mitra)

**Neela**** Natraj**

A Mixed
Finite Element Method for Fourth Order Eigenvalue
Problems PAMM, Volume 4, Issue 1, Date: December 2004, Pages: 358-359.

**Pani**** A.K.**

Industrial Mathematics, Proceedings of the International
Conference on Industrial Mathematics, 2002 (toappear).

* *(with Mohan C. Joshi, Sanjeev Sabnis)

**Sivaramkrishnan**

On complete Partitions of Graphs, “Symposium on Discrete
Algorithms”, 2005.

(with Jaikumar
Radhakrishnan, Magnus Halldorsson,
Guy Kortsarz)

**Presentation / Participation in
Conferences/ Symposia.**

**(National)**

**Athavale**** Ameer**

Title: Functional Analysis and its Applications

Organizer:

Duration:

Details:
Presented an invited talk on “Sectorial Forms and
Unbounded Subnormals”.

**Ghorpade**** S.R.**

Title: S. K Malik Memorial

Organizer:

Duration:

Details:
Delivered Lecture on “Geometric and Combinatorial Aspects of Coding Theory”.

Title:
Symposium on Algebraic Groups in honour of V.Lakshmibai.

Organizer:
Chennai Mathematical Institute, Chennai

Duration:

Details:
Participated

**Joshi K.D.**

Duration:

Details:
Delivered 2 lectures on “Quaternionic Approach to
SU_2” at Karnatak Vishwavidyalaya,
Dharwad

Title: Recent Trends in Analysis

Organizer: Karnatak Vishwavidyalaya, Dharwad

Duration:

Details: Presented
an invited talk on “Fibonacci Numbers in Analysis”.

**Joshi R.R.**

Title:
National Symposium on Recent Trends in Molecular and Medical Biophysics

Organizer:
IBS, Pune

Duration:
22-25 Feb, 2005

Details: Talked on Statistical Computational Approach to
Function-Elucidation Predicted Structure of an EF-hand Ca2+ Binding Protein.

**Limaye**** B.V.**

Title: Conference on Functional Analysis and its
Applications.

Organizer:

Duration:

Details:
Delivered lecture on Continuity and Countable Subadditivity
of a Seminorm.

**Pani**** A.K.**

Title: Scientific Computing: Linear Solvers

Organizer:

Duration:

Details:
Delivered 2 hours talk on `Scientific Computing: Linear Solvers.

Title: Surprises in
Mathematics and Their Applications

Organizer: UGC

Duration:

Details:
Industrial Mathematics: A Key to Key Technologies

**Sharma V.D.**

Title**: **Workshop on
Optical Communications

Organizer: Department of Electronics and Telecommunication
Engineering, VES Institute of Technology, Mumbai

Details:
Delivered the Inaugral address.

**Shastri**** A.R.**

Title:

Organizer:
NBHM

Duration: May 2004

Details: Delivered 6 Lectures
in Differential Topology.

Title:

Organizer:
NBHM

Duration:
December, 2004

Details:
Delivered 9 Lectures on Algebraic Topology..

**Srinivasan**** M.K.**

Title: Workshop on Algebraic Graph theory.

Organizer:
IIT Guwahati

Duration:
December, 2004

**Suresh Kumar K.**

Title: 19^{th } Annual Conference of Ramanujan Mathematical Society

Organizer: Dept. of Mathematics, Dr. B.R.Ambedkar
University,

Duration:

Details:
Delivered Lectures on Portfolio Optimization problems.

**Verma**** J.K.**

Title: R. P.
Stanley's solution of the ADG conjecture, National symposium in memory of Hans-Raj Gupta,

Organizer:

Duration:
19-20 November, 2004

Title: Annual
Foundation School II, HRI

Organizer:
NBHM

Duration:
3-15 December, 2004.

Details:
Delivered Six lectures on Noetherian
rings and modules

Title: Hilbert functions and magic squares

Organizer:
IIT

Duration:

Title:

Organizer:
NBHM

Duration:
17-22 May, 2004

Details:
Delivered lectures on Topics in Galois theory,

**(International)**

**Joshi K.D.**

Title: Conference on Discrete Mathematics and its Applications

Organizer: Devi Amritha Vidyapeetham,

Duration:
9-11 December, 2004.

Details:
Chaired a panel discussion on Discrete Mathematics.

**Pai**** D.V.**

Title: 11^{th
}International Conference in Approximation Theory .

Organizer: NSF, Army
Research office and

Duration:

Details: Delivered Research talk entitled Hausdorff
strong uniqueness in simultaneous approximation of 20 minutes duration.

**Pani**** A.K.**

Title:
Conference on Complex Systems, Control and Optimizations .

Organizer: Northeastern University,

Duration:

Details: Plenary Talk on Oldroyd
Model in Viscoelestic Fluid Flow Problems:

Some
Theoretical and computational Issues

Title: Indo-French Workshop on Partial Differential
Equations and Applications

Organizer: IISc Bangalore

Duration:

Details: Delivered 45 minutes invited talk entitled ` A New Mixed
Finite Element Method for Evolution Equations: An Old Wine in a New Bottle'

**Patkar**** Sachin B.**

Title: APMOD 2004 (at

Organizer:

Duration:
June 2004

Details:
Presented paper on Multidimensional Scheduling.

**Rana**** Inder K.**

Title: 10^{th }International Congress on Mathematics
Education

Organizer:
International Mathematics

Duration:
July 2004.

Details: Made
a presentation on the development of E-course.

**Sabnis**** S.V.**

Title: International Conference on the Future of Statistical
Theory, Practice and Education

Organizer:
Indian

Duration:

Details: Gave
an invited talk on Estimation and Construction of Bounds using r th Best Prototype

**Shastri**** A.R.**

Title: International AMS-India meeting, I.I.Sc.

Organizer:

Duration: May
2004.

Details:
Presented a paper on Topology of Matrix Varieties.

Title:
International workshop on Low Dimensional Topology, I.S.I,

Organizer:
I.S.I Bangalore.

Duration:
September 2004

Details:
Delivered 4 lectures on Topology of open Algebraic Surfaces.

**Joseph Tony**

Title:
Commutative Algebra and Interactions with Algebraic Geometry and Combinatorics

Organizer: ICTP,

Duration:

**Vellaisamy**** P.**

Title: International Conference on Reliability
Statistics and Related areas.

Organizer:
IIM,

Duration:

**Invited lectures**

**Ghorpade**** S.R.**

"On the number of solutions of equations over finite fields'',
Colloquium talk,

"Linear Codes, Schubert
Varieties and Enumerative Combinatorics'', Colloquium talk, State University of New
York at

"Rational points of varieties over finite fields'', Algebra
Seminar,

"Linear codes, Schubert
varieties and enumerative combinatorics'', Geometry -
Algebra - Singularities - Combinatorics (GSAC)
Seminar,

"Varieties, codes and combinatorics'',

"Coding Theory'', A series of three lectures, Workshop on Coding Theory, Mathematical Sciences Institute, Postgraduate Centre of Karnataka University, Belgaum, November 2004.

"Algebraic Geometry for Scientists and
Engineers'',

"Codes, enumeration and
varieties over finite fields'', Indian Statistical Institute,

**Kulkarni**** R.P.**

Approximate
Solution of Operator Equations, Max Planck Institute for Mathematics in
Sciences,

A Superconvergence Result for Solutions of Compact Operator
Equations,

A Superconvergence Result for Solutions of Second Kind
Integral Equations, Technische Universitat,

Approximate
Solution of Integral Equations,

**Limaye**** B.V.**

Invited
lecture at the ^{th}, 2004

Mathematics
Colloquium at ^{th} , 2004

**Pai**** D.V.**

Colloquium
lecture entitled “Strong unicity in Simultaneous
Approximations at Facultaat Mathematische,
Catholische Universitaet,

**Pani**** A.K.**

A series of
eight Lectures (each one and half hours) on Mathematical Theory of Finite
Element Methods in the Department of Mathematics , Dr.
Babasaheb Ambedkar Marathwada University,

Gave a talk
to B.Sc. students on `Why should Industry Hire Mathematicians' in the

Gave a talk
on `Industrial Mathematics: A Case Study' under lecture series on Development
in Graduate Level Masthematics, held in Jawaharlal
Nehru Enginering College, Aurangabad, on February 25,2005,organised by Marathwada
Mathematical Society.

**Sabnis**** S.V.**

Acted as one of the Resource Persons for a workshop on "Design of Experiments" conducted for a group of scientists from Onida research Center in April,2004.

Acted
as one of the resource persons for a SAS workshop held at Dept. of Statistics,

Delivered
8 lectures on "Sample Size Methodology" in the DST sponsored Workshop
during

Gave
one invited talk at

**Sharma V.D.**

Delivered an invited lecture at the Fourth World Congress of Nonlinear Analysts – 2004, organized by the Florida Institute of Technology held at Orlando, Florida (July 3, 2004).

Delivered an invited lecture at the International Conference on Mathematical Fluid Dynamics held at the Department of Mathematics and Statistics, University of Hyderabad, Hyderabad (December 3, 2004).

**PATENTS**

**Patkar**** Sachin B.**

Patent filed based on R & D work at Powai Labs, Mumbai. Simulator Accelerator “IMAGE”.

**Honorary work**

**Athavale**** Ameer**

Reviewer for “Mathematical Reviews”

**Ghorpade**** S.R.**

Member,
Council of Editors, Resonance, A Journal of Science Education published by the

Co-opted
Member, Board of Studies in Mathematics:

Editor (with J. K. Verma and H. Srinivasan), Contemporary Mathematics volume on Commutative Algebra and Algebraic Geometry, American Mathematical Society.

Reviewer for Zentralblatt MATH

**Joshi R.R.**

Referee for
papers submitted to "Nucleic Acid Research" and "BioSilico"

Reviewer for
projects submitted to DBT and DST.

Member of the selection committee in

**Limaye**** B.V.**

Member of the Selection committees for
faculty recruitment at various IIT’s.

**Pai**** D.V.**

Appointed
as a Member, Programme Advisory Committee(PAC)-
Mathematical Sciences, SERC, DST, Govt. of

Appointed as a Member, Scientific Committee-Indian side of Indo-French Institute of Mathematics(IFIM) by DST, Govt. of India.

Examined a Ph.D. thesis from IIT Madras.

**Pani**** A.K.**

Referee job
for IMA J. Numer. Anal, Numer. Meth. PDEs, Journal of Computational
and Applied Mathematics,
Indian J. Pure and Applied

Examined Ph. D. Theses: one from

**Patkar**** Sachin B.**

Member of Expert Committee for deigning Curriculum at IGNOU

Refree for Maths of OR, IPL.

**Nataraj**** Neela**

Reviewer for Calcolo, Journal of The
Indian Institute of
Science

**Sabnis**** S.V.**

Acted as one of the Resource Persons for a workshop on "Design of Experiments" conducted for a group of scientists from Onida research Center in April,2004.

Acted
as one of the resource persons for a SAS workshop held at Dept. of Statistics,

Examined one Ph.D. thesis from

Evaluated one research proposal for DST.

**Sharma V.D.**

Reviewer for
Mathematical Reviews (

Examined Ph.D. Thesis submitted to ISI Calcutta and IIT Kharagpur.

Served as a
member of the Selection Committee for faculty recruitment at University of
Hyderabad and NIT Jalandhar (Punjab)

**Shastri**** A.R.**

Reviewer for Mathematical Reviews

**Srinivasan**** M.K.**

Referee for research papers

**Verma**** J.K.**

Reviewer for Mathematical Reviews

Editor (with S.R. Ghorpade and H. Srinivasan), Contemporary Mathematics volume on Commutative Algebra and Algebraic Geometry, American Mathematical Society.

Secretary for the NBHM supported Advanced Training in Mathematics
Schools

Member of the Nurture Programme
committee of the NBHM.

Member of Board of studies of

Member, Council of Editors, Resonance, A Journal of Science Education published
by the

Member, Coordinating committee for
China-India-Vietnam network for Commutative Algebra of ICTP,

**Significant Awards and Distinctions**

**Pani**** A.K.**

Plenary Speaker in the International Conference on Complex
Systems and Optimization, held in
Northeastern University, Shenyang (China) during August, 2004.

Member of the Editorial Board: Differential Equations and
Dynamical Systems :
An International Journal; International J. Numer.
Anal & Modeling.

Inagaurated the UGC sponsored conferences on
`Surprises in Mathematics and Their Applications, held in Vivekananda College, Chembur during January 17, 2005**.**

**Sharma V.D.**

Nominated as a Member of the Editorial Board of the Indian Journal of Pure and Applied Mathematics.

Nominated as a
Member of the Sectional Committee of INSA (

Nominated as a
Member of Technical Advisory Committee for the Physics and Earth Sciences Divisions,
ISI