**Department
of Mathematics**

**Annual
Report (2007-08)**

The year witnessed
excellent contributions and achievements of faculty and students in
research; interaction with industry and noted national and international
institutes, universities and organizations; and extended educational
activities beyond the departmental academic programmes.

Some of the
notable events include : * Prof. Gopal K. Srinivasan* being selected to receive the Excellence
in Teaching Award 2007,* Prof. U. K. Anandavardhanan* being selected as an Associate of
the Indian Academy of Sciences, Bangalore, and *Amiya K. Pani * representing South Asia at the ICIAM
2007 Round Table Discussion on `Developing Mathematics in the Developing
World'. In 2007-08, six faculty members in the Department served as
members of the editorial board of national and international journals.

As a part of
Golden Jubilee celebrations, many distinguished visitors like *Prof.
David Mumford* (Field medallist, Brown University), *Prof. S.-T.
Yau* (Field medallist, Harvard University), *Prof. Richard Hamilton*
(Columbia University), *Prof. Manjul Bhargava* (Princeton University),
Prof. John Whiteman (FRSA, Brunel University), visited the Department.

Besides the
teaching of B. Tech. courses, the Department offers M.Sc. and Ph.D.
programmes. It has two distinct M.Sc. programmes: M.Sc. in Mathematics
and M.Sc. in Applied Statistics and Informatics (ASI). In addition,
the Department has a research programme leading to Ph.D. degree.
This year, the Ph.D. programme is thoroughly revised with the feature
that it has a broad-based course work with a number of advanced level
topics courses to provide a good background to Ph.D. students and a
system of qualifying examinations.

Continuing
with its tradition, the Department has further augmented its basic research,
focusing in contemporary areas of fundamental, developmental and strategic
importance, applied and interdisciplinary research and productive collaboration
with industries and reputed R & D departments. The collaborating
R & D institutions/organizations include: TIFR, IISc, ISI, ONGC,
Institute of Mathematical Sciences etc., and foreign universities like
Brunel University (U.K), Florida Technical University (USA), Colorado
School of Mines (US), Humboldt University (Germany), CNRS-IML, Marseille
(France), INSA, Toulouse (France), Univ. St-Etienne (France), l'Université
Pierre et Marie Curie, Paris (France), Vilnius University, Lithuania, etc.
and nodal organizations such as CSIR, DAE, DBT, DST, etc., for scientific
exchange of ideas of national importance. In 2007-08, the Department
has constituted a committee for promotion of research to boost its research
activities. In order to fulfill the broad objectives of research activities,
steps are taken to ensure that, the theoretical bases 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 by evolving a pool of trained manpower in
thrust areas. During this year, the department organized two year- long
programmes, few distinguished lecture series, two international conferences,
one national conference, one CIMPA workshop, two international workshops,
several study group meetings in Statistics, several CEP courses and
one instructional school. This year, three NBHM post-docs joined the
Department and the Department has witnessed a steady increase in the
number of quality publications.

Algebraic methods
in multivariable operator theory, IRCC.

Factorization of period integrals,
IRCC.

A fast marching method for monotonically propagating fronts in an inhomogeneous moving fluid, IRCC.

Homogenization and defects
in network structures, IRCC.

Establishing the analytic properties
of automorphic L-functions, IRCC.

Obstruction theory for projective
modules, IRCC.

Accelerated
refinement schemes for computation of eigen elements of integral operators
with singular kernels using wavelet Galerkin methods, Dept. of Science
& Technology, Govt. of India.

Adaptive mixed finite element
methods and applications, Dept. of Science & Technology, Govt. of
India and DAAD, Germany.

Analytical and numerical study
of non-linear gas dynamic waves, ISRO-IITB Space Technology Cell.

Quantum groups and topological
quantum field theory, Dept. of Science & Technology, Govt.
of India.

Design of component reliability
test plans, their software development and a centre for quality and
reliability (CQR), Dept. of Science & Technology, Govt. of India.

Extension and web implementation
of PROPAINOR for ab-initio prediction and computational function-elucidation
of 3-D structure of proteins, Dept.
of Biotechnology, Govt. of India.

Instrumentation assisted decision support system deploying data mining techniques for pulse examination and diagnostics, Ministry of Information Technology, Govt. of India.

Data Mining of Petroleum Exploration, BHP Billiton, Melborne, Australia.

Co-Investigator: Prof G. Mohan,
Dept. of Earth Sciences

Selection of forecasting granularity
to maximize benefits of scheduling in service industries,
Tata Consultancy Services, Mumbai.

**Activities
of Mathematics Association**

**Mathematics
Olympiad**

The annual Mathematics Olympiad is a mathematical talent search examination to bring out the mathematical skills among students. This year, it was organized by 70 Volunteers of M.Sc. & Ph.D. students on Feb 3, 2008. There were three levels in which first level is for class 8-10 students, second level is for class 11-12 and third one is for U.G students (IIT & NON-IIT). 780 students from about six hundred schools and colleges from all over Mumbai participated in this event. Separate Prizes were given to the winners of each level and participation certificate was given to each and every student.

During 2007-08, the Department
organized 4 talks under the *popular lecture series.*

“An application of p-adic
numbers”, **V. Srinivas**, Tata Institute of Fundamental Research,
Mumbai.

“List-decoding reed-Solomon
codes”, **Jaikumar Radhakrishnan**, TIFR, Mumbai.

“An Investor's Martingale
Walk”, **M. G. Nadkarni**, University of Mumbai, Mumbai.

“On Some Statistical Aspects
of Agreement Among Measurements”,** Bikas Kumar Sinha,** ISI, Kolkata.

**Conferences,
Workshops, CEP Courses, **

**Study Group
Meetings Organized by the Department**

**Baskar S.; Natraj Neela;
Pani Amiya K.**

“Instructional School on
Partial Differential Equations”, May 28 -- June 23, 2007.

**Kulkarni, Rekha P**.

“International workshop on
Approximate Solutions of Operator Equations and Eigenvalue Problems",
February 25--29, 2008.

**Puthenpurakal, Tony J.;
Verma, Jugal K.**

“CIMPA Workshop and International
Conference in Commutative Algebra", January 1-11, 2008.

**Rana, Inder K.**

“TIME 2007, Second national Conference on Technology and Innovation in Math Education”, December 1--4, 2007.

CEP courses organized: Math
for ECM, 2007, April 16--28, 2007. Professional Development for Mathematics
Teachers, 24 February 2008.

**Sabnis,
Sanjeev V**.

Initiated Statistics-Study
group activity by involving statistics faculty from various colleges
affiliated to University of Mumbai.

**Shastri, Anant R.**

“Golden Jubilee International
Workshop and Conference in Geometry and Topology”, August 17--26,
2007.

**Publications**

**Books/Chapters
in Books**

**Joshi, K.
D**.

Revised edition
of “Calculus for Scientists and Engineers – An Analytical Approach”,
Narosa Publishing House, New Delhi.

**Kulkarni,
Rekha P., Kulkarni, S. R. and Pani A. K.**

Editor of the
Proceedings of the International Conference on “Topics in Functional
and Numerical Analysis” held at I.I.T. Bombay during December 7 --
9, 2005. The Proceedings were published as a special issue of `The Journal
of Analysis', Volume 14 (2006).

**Pai, D.
V. **

**“**An
Introduction to Wavelet Analysis”, Chapter 2 in:** **
Lecture Notes of the 5th S.E.R.C. School on Special Functions and Functions
of Matrix Argument: Recent Advances and Applications in Stochastic Processes,
Statistics, Wavelet Analysis and Astrophysics, Centre for Mathematical
Sciences, Pala Campus, Publication No.34. Edited by A.M. Mathai, CMS,
Pala, Kerala, 55--80.

**Pai, D.
V.**

“Wavelet
Analysis: An Introduction", in: Applied Mathematics, Instructional
Lectures delivered in DST sponsored Instructional Workshop on Applied
Mathematics, Edited by Uma Basu and B.N. Mandal, Narosa Publishing House,
244--261 (2008).

**Papers in
Proceedings**

**International:**

**Ahues, M.;
Largillier, A.; Limaye, Balmohan V.**

"On the
acceleration of spectral computations for integral operators with weakly
singular kernels", Proceedings of the Ninth International Conference
on `Integral Methods in Science and Engineering: Techniques and Applications'
held at Niagara falls (Canada), Birkhauser, Boston,

9--16 (2007).

**Kumar,
Sarvesh; Nataraj, Neela; Pani,** **Amiya. K.**

Finite volume element method for incompressible miscible displacements in porous media, Proc. Appl. Math. Mech., 7, 2020015--2020016 (2007).

**International:**

**Abreu, A.; Elias, A.; Loza,
M. A.; Mukhopadhyay, Siuli; Rueggeberg, F.**

“Effect of metal type and
surface treatment on in vitro tensile strength of copings cemented to
minimally retentive preparations”, The Journal of Prosthetic Dentistry,
98, 199--207 (2007).

**Athavale, Ameer; Chavan,
S. **

"Sectorial forms and unbounded
subnormals", Math. Proc. Cambridge Philos. Soc., 143, 685--702
(2007).

**Agnihotram, G.; Sabnis,
Sanjeev V.; **

“Reliability test plan for
series systems in the presence of covariates”, Economic Quality Control,
22, No. 2, 197--209 (2007).

**Bhattacharya, Amitava; Peled,
Uri N.; Srinivasan, Murali K.**

“Cones of closed alternating
walks and trails”, Linear Algebra and its Applications, 423, 351--365
(2007).

**Das, Ashish;
De Los Reyes J. P.; Midha, C. K.**

A matrix approach to construct magic rectangles of even order.

Australasian
Jour. of Comb. (2008), 40, 293-300.

**Dharmadhikari, A. D.; Sabnis,
Sanjeev V.; Sinha, B. K. **

“Construction of bounds in
prototype testing”, Journal of Statistical Theory and Applications,
6, No. 3, 302--312 (2007).

**Fairweather, G. ; Fernandes**,**
R. I.; Pani Amiya K.**

“Alternating direction implicit
orthogonal spline collocation methods for an evolution with a positive–type
memory term”, SIAM J. Numer. Anal., 46, 344--364 (2008).

**Gnana, Bhaskar, T.; Hariharan,
S. ; Nataraj, Neela**

“Heatlet approach to diffusion
equation on unbounded domains”, Applied Mathematics and Computation,
197, 891--903 (2008).

**Gudi, T. ; Nataraj, Neela;
Pani, Amiya K.**

“hp-discontinuous Galerkin
methods for strongly nonlinear elliptic boundary value problems”,
Numer. Math., 109 (2008).

**Gudi, T. ; Natraj, Neela;
Pani,** **Amiya K.**

“An hp-local discontinuous
Galerkin method for some quasi-linear elliptic boundary value problems
of non-monotone type”, Math.Comp., 77, 731--756 (2008).

**Iyengar, S.; Puthenpurakal,
Tony J.**

"Hilbert-Samuel functions
of modules over Cohen-Macaulay rings" Proceedings of American Mathematical
Society, 135, 637--648 (2007).

**Jayanthan, A. V.; Puthenpurakal,
Tony J. ; Verma, Jugal K.**

"On fiber cones of m-primary
ideals." Canadian Journal of Math, 59, 109--126 (2007).

**Jena, J.; Sharma, Vishnu
D.**

"Interaction of a characteristic
shock with a weak discontinuity in a relaxing gas", J. Engrg. Math.,
60, No. 1, 43--53 (2008).

**Joshi, Rajani R.**

“Peptide vaccine models using
statistical data mining” Protein Peptide Letters, 14, No. 6, 536--542
(2007).

**Joshi, Rajani R.**

“A decade of computing to
traverse the labyrinth of protein domains”, Current Bioinformatics,
2, 113--131 (2007).

**Joshi, Rajani R.;
Manda, C.**

“Statistics of catalytic
domain sequences in protein kinases vs non-kinases” Protein
Peptide Letters, 14, No. 6, 518--527 (2007).

**Joshi, Rajani R.**; **
Samant, V. V. **

“Bayesian data mining of
protein domains gives efficient predictive algorithm and new insight”,** **
J. Molecular Model,** **13, No.** **
1, 275--282 (2007).

**Kumar, S.; Nataraj, Neela;
Pani, Amiya K. **

“Finite volume element method
for second order hyperbolic equations”, Int. J. Numer. Anal. and Modeling,
5, 132--151 (2008).

**Mantri, P.; Nataraj, Neela;
Pani,** **Amiya K. **

“A quolocation method for
Burgers' equation”, J. Comp. Math. Appl., 21, No. 3, 1--13 (2008).

**Mukhopadhyay, Siuli; Khuri,
A. I.**

“Comparison of designs for
multivariate generalized linear models”, Journal of Statistical Planning
and Inference*, *138, 169--183 (2008).

**Pai, D. V.**

“Strong unicity of restricted
p-centers”, Numerical Functional Analysis & Optimization, 29,
No. 5-6, 638--659 (2008).

**Puthenpurakal, Tony J.**

"Ratliff-Rush filtration,
regularity and depth of higher associated graded modules. I.",
Journal of Pure and Applied Algebra, 208, 159--176 (2007).

**Puthenpurakal, Tony J. ;
Zulfeqarr, Fahed**

"Ratliff-Rush filtrations
associated with ideals and modules over a Noetherian ring", Journal
of Algebra, 311, 551--583 (2007).

**Raja, Sekhar T.; Sharma,
Vishnu D. **

"Similarity solutions
for three dimensional Euler equations using Lie group analysis",
Appl. Math. Comput., 196, No. 1, 147--157 (2008).

**Rana, Inder K.; Sinha V.**

“Fubini Type Theorems for
BV integrals”, Real Analysis Exchange, 33, No. 1, 109--214 (2008).

**Sinha, K.; Sinha N.; Vellaisamy,
P.**

“Kronecker sum of binary
orthogonal arrays”, Utilitas Mathematica, 75, 249--257 (2008).

**Trung, N. V.; Verma, Jugal
K.**

“Mixed volumes versus mixed
multiplicities”, Trans. Amer. Math. Soc., 359, 4711--4727 (2007).

**Vellaisamy, P.; Vijay, V.**

“Some collapsibility results
for n-dimensional contingency tables”, Annals of the Institute of
Statistical Mathematics, 59, 557--576 (2007).

**Vellaisamy, P.; Vijay, V. **

“Collapsibility of regression
coefficients and its extensions”, Journal of Statistical Planning
and Inference, 138, 982--994 (2008).

**National:**

**Ahues, M.; Largillier, A.;
Limaye, Balmohan V. **

"A singularity subtraction
iterative refinement scheme for spectral subspaces of weakly singular
integral operators", J. Analysis, 14, 111--133 (2006).

**Kulkarni Ravi, S.**

Review of “Collected Works
of V. Patodi”, edited by M.F. Atiyah and M.S. Narasimhan, Mathematics
Student, Indian Mathematical Society (2007).

“Dynamical types and conjugacy
classes of centralizers in groups”, J. Ramanujan Math. Soc. 22 (2007),
no. 1, 35-36.

“Some curvature functions
and their arithmetic properties”, J. Ramanujan Math Soc. 22 (2007),
no. 1, 57-74.

**Mukhopadhyay, Siuli; Khuri,
A.I**.

“Bias in multivariate generalized
linear models”, Calcutta Statistical Association Bulletin, 59, 87--105
(2007).

**Parcha, S. K.; Sabnis, Sanjeev
V.; Saraswati, P. K. **

“Taxanomic application of classification and regression tree (CART) and random forest (RF):

A case study of middle cambrian
trilobites”, Journal of The Geological Society of India, 70, No. 6,
1033--1038 (2007).

**Shastri, Anant, R.**

“Complex Numbers and Plane Geometry”, Resonance, 35--53 (2008).

**Participation
in Conferences/Symposia**

**Anandavardhanan,
U. K.**

"Root
numbers of Asai L-functions", Summer School and Conference on Automorphic
Forms and Shimura Varieties, The Abdus Salam International Centre for
Theoretical Physics, Trieste, July 9--27, 2007.

**Garge, Shripad
M.**

Buildings and Groups, Ghent, Belgium, May 20--26, 2007.

Quadratic forms, triangulated
categories and valuations, Lens, France, June 11--15, 2007.

International Conference on Automorphic Forms and Shimura Varieties,
ICTP, Italy, July 9--27,

2007.

Motives of projective homogeneous
varieties, Mainz, Germany, September 17--21, 2007.

Buildings 2007, Münster,
Germany, October 8--11, 2007.

**Ghorpade,
Sudhir R**.

First Symposium
on Algebraic Geometry and its Applications (SAGA 2007), in honour of
the 60th birthday of Gilles Lachaud, Papeete, Tahiti, French Polynesia,
May 2007. Presented a paper entitled: “On the weight hierarchy of
Grassmann codes”.

Eleventh International Conference on
Arithmetic, Geometry, Cryptography and Coding Theory (AGCT - 11), Centre International de Rencontres
Mathématiques (CIRM),
Luminy, France, November 2007. Presented an invited talk entitled “Decomposable
subspaces, linear sections of Grassmann varieties, and higher weights
of Grassmann codes”.

**Kulkarni,
Ravi S.**

Delivered one
of the New world lectures at the 4^{th} International Congress
of Chinese Mathematicians, Hong-zhou, China, December 2007 entitled
"Dynamical types and conjugacy classes of centralisers in groups".

**Mukhopadhyay,** **
Siuli**

Design and
Analysis of Experiments DAE 2007 Conference, Tennessee, USA October
2007. Presented: “Optimization in a Multivariate Generalized Linear
Model Situation”

**Pani, Amiya
K.**

International Congress of Industrial and Applied Mathematics (ICIAM-2007), ETH Zurich, Switzerland July 16--20, 2007 gave a talk on “Oldroyd Viscoelastic Model : Theoretical and Computational issues”.

**Raghunathan,
Ravi**

International
Conference on automorphic forms and Shimura varieties, International
Centre for Theoretical Physics, Trieste, Italy, July 23--27, 2007.

**Rana, Inder
K**.

ATCM 2007 Asia
Technology Conference in Mathematics, Taiwan December 16--20, 2007.
Gave invited talk: Role of Technology in Math Education, Indian perspective.

**Sabnis,
Sanjeev V**.

International
Conference on Mathematical Methods on Reliability (MMR 2007), Glasgow,
Scotland, July 1--4, 2007. Presented a talk on “Reliability Test Plans
for Systems with Dependent Components”.

**Sharma,
Vishnu D**.

International
Congress of Industrial and Applied (ICIAM-2007), ETH Zurich, Switzerland
July 16--20, 2007.

**Verma, Jugal
K.**

Invited international distinguished talk on “Hilbert functions of multigraded algebras, mixed multiplicities of ideals and their applications”, in the Fourth International Congress of Chinese Mathematicians, Hangzhou, China, December 2007.

**Anandavardhanan,
U.K**.

Galois Representations and Modular Forms, Chennai Mathematical Institute, Chennai, September 24 -- October 4, 2007.

73rd Annual Meeting of
the Indian Academy of Sciences, Thiruvananthapuram, November 1--4,
2007.

Arithmetic Geometry, NCBS,
Bangalore, March 23--29, 2008.

**Das, Ashish**

10th Conference of the Society of Statistics, Computer and Applications held at St. Thomas College, Pala, Cochi during 16-18, November 2007.

Presented an
invited talk on “Some statistics of cheque collections in India”.

**Garge, Shripad
M.**

K-theory and
algebraic cycles, Chennai, January 15--17, 2008.

**Ghorpade,
Sudhir R**.

Golden Jubilee
Meeting on Geometry and Topology, Indian Institute of Technology Bombay,
Mumbai, August 2007. Member of the Organising Committee.

International
Conference on Recent Advances in Mathematics and its Applications, Belgaum,
Karnataka, September 2007. Presented an invited plenary lecture entitled
“Geometric, combinatorial and coding theoretic aspects of subspaces
of a vector space”.

Eleventh International Conference on
Arithmetic, Geometry, Cryptography and Coding Theory (AGCT - 11), Centre International de Rencontres
Mathématiques (CIRM),
Luminy, France, November 2007. Presented an invited talk entitled “Decomposable
subspaces, linear sections of Grassmann varieties, and higher weights
of Grassmann codes”.

Seventeenth Symposium on Applied algebra,
Algebraic algorithms, and Error Correcting Codes
(AAECC-17), Indian Institute of Science, Bangalore, December 2007. Chaired
a session.

CIMPA School on Commutative Algebra, Indian Institute of Technology Bombay,
January 2008. Chaired a session.

Seventy third
Annual Conference and the Centenrary Celebrations of the Indian Mathematical Society, Pune, December 2007. Presented an
invited talk entitled “Higher weights of Grassmann codes” in the
Symposium on Coding Theory at this conference.

**Joshi, Rajani
R.**

Nonparametric
Statistics in Computational Biology. Invited talk at *All India Symposium
on Computational Biology. *Maulana Azad National Inst. Tech., Bhopal
(April 06--08, 2007).

**Keshari,
Manoj Kumar**

CAAG VII, ISI
Bangalore, July 2007. Invited talk on " Projective modules over
Discrete Hodge algebras".

**Keshari,
Manoj Kumar**

Gave an invited
talk on " Projective modules over Discrete Hodge algebras"
in CAAG VII, ISI Bangalore, July 2007.

**Kulkarni,
Rekha P**.

Invited lecture
"Approximate solution of the second kind integral equations with
Green's kernel" in the International Conference on Functional Analysis
and its Applications held at Scott Christian College, Nagercoil, November
28 -- December 1, 2007.

**Limaye,
Balmohan V**.

Gave a talk
on "Integral Operators with Weakly Singular Kernels" in the
International Conference on `Functional Analysis and its Applications'
held at Scott Christian College, Nagercoil, Kerala, November 28 -- December
1, 2007.

**Limaye,
Balmohan V**.

Gave a talk
on "Uniformly Well-Conditioned Bases for Spectral Subspaces"
in the International Workshop on `Approximate Soulutions of Operator
Equations and Eigenvalue Problems", held at IIT Bombay from February
25--29, 2008.

**Puthenpurakal,
Tony J.**

CIMPA workshop and International Conference in Commutative Algebra, IIT Bombay, Jan 1--11, 2008.

Invited talk on "Upper
bound of Multiplicity conjecture" in Commutative Algebra and Algebraic
Geometry Conference; held at ISI Bangalore, July 16--20 (2007)

**Rana, Inder
K.**

Conference
in Mathematics Education and Technology 2007, Delhi Public School, Delhi.
Invited talk on “Teaching with Technology”

**Sabnis,
Sanjeev V**.

International
Conference on Reliability, Safety and Quality Engineering, BARC, Mumbai,
January 5--7, 2008. Presented: An Overview of Construction of Optimal
Reliability Test Plans.

International
Conference on Present Practices and Future Trends in Quality and Reliability
(ICONQR08), Indian Statistical Institute, Kolkata, Jan.22-25, 2008.
Presented: Construction of Optimal Reliability Test Plans for Coherent
Systems with Independent and Non-identical Components.

National Conference
on Industrial Statistics, Dept. of Statistics, Univ. of Pune, August
4-6, 2008. Presented: Modeling of Panel Data using Hierarchical Bayesian
Methodology and Metropolis-Hastings Algorithm

National Seminar
on Statistical Methods and Reliability Analysis, Cochin University of
Science and Technology, Cochin, January 28--30, 2008. Presented: Reliability
Test Plans for k-out-of-n and Bridge systems.

**Verma, Jugal
K.**

Mixed Multiplicities,
mixed volumes of polytopes and a new proof of Bernstein's theorem, Symposium
on geometry and topology, 74th annual meeting of the Indian Mathematical
Society, University of Pune, December 2007.

Hilbert-Samuel polynomials, six lectures, Workshop in Commutative Algebra and Algebraic Geometry IIT Madras, June 2007.

"Hilbert functions and powers of ideals", CAAG VII, ISI Bangalore, July 2007.

**Garge, Shripad
M.**

"Gelfand
models for finite Coxeter groups", Buildings 2007, Münster, Germany,
October 8--11, 2007.

**Kulkarni,
Ravi S.**

"Poincare Conjecture", University of Mumbai

"Subgroups
of the Modular group", University of Mumbai,

**Kulkarni,
Rekha, P.**

Invited lecture
series of 6 lectures on "approximate solutions of operator equations"
in the Indo-French Spring school held at Jean Monet University, Saint
Etienne, France, June 11--15, 2007.

**Limaye,
Balmohan V**.

Gave seven invited lectures on `Functional Analysis' in the Indo-French Spring School held at Saint-Etienne, France, June 11--15, 2007.

**Mukhopadhyay,
Siuli**

Optimization
in multivariate generalized linear models, design and analysis of experiments
DAE 2007 Conference, Tennessee, USA, October 2007.

**Pani, Amiya.
K.**

Oldroyd model of viscoelastic flow : theoretical and computational issues, in the International Congress of Industrial and Applied Mathematics (ICIAM-2007), ETH Zurich, Switzerland July 16--20, 2007.

Discontinuous Galerkin
methods : An Old Wine in a New Bottle, in the Graduate Seminar held
in Humboldt University, Berlin, June 2007.

Finite element approximation
of the equations of motion arising in the Oldroyd model, Colloquium
talk, Berlin, June 2007.

**Sharma,
Vishnu D**.

Delivered a
lecture on nonlinear resonantly interacting waves in a Special Session
of the American Mathematical Society (AMS) on Wave Propagation from
Numerical and Analytical View Points held at DePaul University, Chicago,
USA, October 5, 2007.

Delivered a lecture on the evolutionary behavior of shocks in a relaxing fluid in AMS-special session on Mathematical/Computational Aspects of Compressible Flow Problems held at the University of New Mexico, Albuquerque, USA, October 13, 2007.

Delivered a lecture on weakly nonlinear waves to the Applied Mathematics Group, Department of Mathematics, Stanford University, USA, January 11, 2008.

**Anandavardhanan,
U. K.**

Serre's Conjecture
(3 lectures), Galois Representations and Modular Forms, Chennai Mathematical
Institute, Chennai, September 24 -- October 4, 2007.

**Baskar,
S.**

“Numerical
Methods to Scalar Conservation Laws” (4 lectures), Instructional
School in PDEs, IIT Bombay, May 28 – June 23, 2007.

**Ghorpade,
Sudhir R.**

“Introduction
to algebraic geometry”, Short Term Training Programme on Advances
in Control Theory, Veermata Jijabai Technological Institute (VJTI),
Mumbai, October 2007.

“Development
of calculus and real analysis”, Annual Mathematics Day of the Harish-Chandra
Mathematics Society, Deen Dayal Upadhyaya College (University of Delhi),
New Delhi, November 2007.

“Complex
problems in coding theory*”*, Scientific Analysis Group, Defence
Research and Development Organisation, Delhi, November 2007.

“Some aspects
of coding theory*”*, Jamia Millia Islamia, New Delhi, November
2007.

“On the development
of calculus and real analysis*”*, Karnataka University, Dharwad,
December 2007.

“Introduction
to coding theory*”*, Workshop on Mathematics for Engineers, D.
J. Sanghvi College of Engineering, Vile Parle, Mumbai, February 2008.

**Joshi, Kapil
D.**

Gave a series of lectures at the ATML school by NBHM at the Bhaskaracharya Pratishthan, Pune, May 2007

Gave a series of lectures
at Banasthali University, Rajasthan, March 2008.

**Joshi, Rajani
R**.

Nonparametric
Statistics in computational biology. Invited Talk at National Workshop
on Advanced Methods for Protein Bioinformatics. Bose Instiute, Kolkata,
March 3--5, 2008.

New paradigms
of holistic health care — Role of information technology. Series of
three Talks at Tata Consultancy Services, Pune.

ANN applications
in molecular recognitions. Invited Talk at SERC School on Machine Learning
and Pattern Evolution Methods for Chemo and Bioinformatics. C-DAC, Pune,
June 29--30, 2007.

**Kulkarni,
Rekha, P.**

"Improvement
by iteration" in the International workshop on "Approximate
solutions of operator equations and Eigenvalue problems",
I.I.T. Bombay, February 25--29, 2008.

**Limaye,
Balmohan V**.

Gave an invited
lecture on `Zabreiko's result on the continuity of countably subadditive
seminorms' at the Cochin University of Science and Technology, December
3, 2007.

**Neela, Nataraj**

A series of
lectures on Finite element
methods for elliptic PDEs in the Instructional School on Modern PDEs
held during May 28 - June 23, 2007.

**Pai, Devidas
V**.

One hour, “On
strong uniqueness of best simultaneous approximation” (Colloquium
Lecture), Department of Mathematics, Sardar Patel University, Vallabh
Vidyanagar, Gujarat, September, 2007.

One hour, “Strong
unicity of restricted Chebyshev centers” (Departmental Colloquium),
Department of Mathematics, IIT Bombay, August 23, 2007.

One hour, “On
well-posedness and regularization in variational analysis” (Special
Colloquim Lecture), Instructional School on Modern PDE's, Department
of Mathematics, IIT Bombay, June 2007.

A compact instructional lecture course series consisting of 4 lectures of duration 2 hours each and 3 problem sessions of duration 2 hours each for two consecutive days on Wavelet Analysis in: DST sponsored 5th S.E.R.C School on Special Functions and Functions of Matrix Argument held at Centre For Mathematical Sciences (CMS), Pala Campus, Pala, Kerala-686574, India, May 2007.

**Pani, Amiya
K.**

Two hour talk
on “How to compute fair price in an American option: A case study
from finance.” Institute of Mathematics and its Applications,
Bhubaneswar, February 2008.

Navier-Stokes
Equation : A million dollar open problem, in IIT Kharagpur, March 2008.

A series of
lectures on Finite Element Methods for Parabolic Problems: in the Instructional
School of Modern PDE held during May-June 2007.

**Ranjan,
Akhil**

A set of 6
lectures on Differential Geometry at Vanasthali Vidyapeeth.

**Shastri,
Anant R**.

Attended an
International Workshop/Conference on Recent Advances in Mathematics
at Kittur Chennamma Post Graguate Center, Karnatak Univerity, Belgaum,
September 24--29, 2007 and gave an invited talk on “3- dimensional
Poincare Conjecture”.

Attended Annual
Meeting (Conference) of Ramanujan Mathematical Society and presented
a survey type talk on “Topology of Algebraic Varieties”.

**Sista, Sivaji
Ganesh**

Delivered lectures
on Complex Analysis at Mathematics Training & Talent Search programme,
Mumbai, May--June, 2007.

Delivered lectures
on Ordinary Differential Equations in Annual Foundation School - I,
IIT Kanpur, December 2007.

A series of
lectures on ‘Theory of Homogenization’ in the Instructional School
on Modern PDEs during May 28 – June 23. 2008.

**Srinivasan
Murali K.**

“Vershik-Okouukov
approach to the representation theory of the symmetric groups” in
Advanced instructional school on representation theory and its applications,
July 2007.

**Verma, Jugal
K. **

Reforms in
the Ph. D. Programme and establishment of a Center for Mathematical
Sciences at IISER, Mohali. For a rapid transformation of Ph.D. programmes
in universities in Punjab, Workshop on Education and Research in Punjab,
IISER, Mohali, Feb 2008.

**Anandavardhanan, U.
K.**

Reviewer for MathSciNet and
Zentralblatt MATH

**Athavale,** **Ameer**

Reviewed 2 papers for Mathematical
Reviews.

**Garge, Shripad M.**

Reviewer for Zentralblatt MATH.

**Ghorpade, Sudhir R**.

Referee for the IEEE Transactions
of Information Theory, Resonance and the International Journal of Information
and Coding Theory.

Member, Faculty Selection Committee
of a NIT and the Assessment Committee of the Directorate of Technical
Education, Maharasthra State.

**Joshi, Rajani R**.

Reviewed Papers submitted to
“Proteins – Structure, Function, Bioinformatics”, “BioMed Central
Structural Biology”, “Protein Peptide Letters” and “Royal Society
Journal – Interface”.

Reviewed Research Project Proposals
(in Biostatistics, Computational Biology, or in Statistical and Mathematical
Modeliling in Biology & Medicine) submitted to DBT/DST and Indo-French
Centre for the Promotion of Advanced Research.

**Kulkarni, Ravi S.**

Editor in chief of RMS Lecture
Notes series.

A member of the Programme Advisory
Committee - Mathematical Sciences (DST).

A member of the Guidelines
Committee for Distinguished Ramanujan Chairs, (DST).

**Kulkarni, Rekha P.**

Refereed a thesis.

**Mukhopadhyay, Siuli**

Reviewed papers submitted to
“Computational Statistics and Data Analysis”.

**Nataraj, Neela**

Member of Organizing Team of
Olympiad conducted by Mathematics Association, IIT Bombay.

**Pai, Devidas V**.

Member, DST appointed subgroup
for C.R. Rao Advanced Institute of Mathematics, Statistics and Computer
Science (AIMSC), Hyderabad, India.

Member,(UGC nominee), Advisory
Committee for Special Assistance Programme (SAP) DRS for Department
of Mathematics, Sardar Patel University, Gujarat.

Member, Project Management
and Monitoring Committee(PMMC) for the DST sponsored 5-year project
entitled ``Evolving Core Group Research Facilities at Banaras Hindu
University".

**Pani, Amiya K.**

Continued to work as a member
of five international journals, reviewed manuscripts in SIAM J. Numer.
Anal., IMA J. Numer. Anal. etc.,

Member of selection committee
of NITs and universities.

Project evaluation for DST,
Indo- French Collaborations etc., and Examiner of one thesis from IIT
and three theses from Universities.

**Puthenpurakal, Tony J.**

Refereed papers for Mathematische
Zeitschrift, Journal of Algebra, Communications in Algebra, Proceedings
for Indian Acad. Sci, Indian Journal of Pure and Applied Mathematics

Reviewer for Math Reviews and Zentralblatt Math.

**Raghunathan, Ravi**

Reviewer for Mathematical Reviews.

**Ranjan, Akhil**

Member selection committee
at NIT Kurukshetra.

**Sabnis, Sanjeev V**.

Evaluated two Ph.D. theses
from the University of Calcutta and Shivaji University, Kolhapur.

**Sharma, Vishnu D**.

Appointed Member of the Following National Committees:

- CSIR-Committee for recommending nominees for the Bhatnagar Award (2007).
- INSA- Committee for recommending nominees for the Young Scientist Award (2007).
- INSA Sectional Committees (On Mathematical Sciences-I, and Multidisciplinary Sciences-M1) for recommending nominees to the Election of INSA Fellows (2007).

**Verma, Jugal K.**

Secretary, Advanced Training
in Mathematics Schools, National Board for Higher Mathematics.

Trustee, Bhaskaracharya Institute
of Mathematics.

Member, Scientific Committee
and Organizing Committee, CIMPA School and International Conference
in Comm utative Algebra, IIT Bombay, January 2008.

**Significant
Awards and Distinctions**

**Anandavardhanan, U. K.**

Selected as an Associate of
the Indian Academy of Sciences, Bangalore.

**Puthenpurakal, Tony J.**

Recieved BOYSCAST fellowship
from DST.

**Mukhopadhyay, Siuli**

Junior Researcher Award, Design
and Analysis of Experiments DAE 2007 Conference, Tennessee, USA.

**Srinivasan, Gopal**

Excellence in Teaching Award
2007.

**Ghorpade, Sudhir R**.

Member, Editorial Board, International
Journal of Information and Coding Theory, Interscience Publishers, U.K.

Member, Council of Editors,
Resonance, Indian Academy of Sciences, Bangalore and Springer, New York.

**Joshi, Rajani R.**

Selected as editor of international
journal *Protein Peptide Letters* for the special issues on “Protein
Informatics and Drug Designing”.

**Pai, Devidas V**.

Member, Editorial Board, Asian-European
Journal of Mathematics, World Scientific, Singapore and Imperial College
Press, UK.

**Pani, Amiya K.**

Panel member representing the
South Asian Countries in the panel discussion on `Developing Mathematics
in Developing World' on July 19, 2008 in the International Congress
of Industrial and Applied Mathematics (ICIAM-2007), ETH Zurich, Switzerland.

Member of the Editorial
Board of five national and international journals.

**Visitors**

**Golden Jubilee Distinguished
Lecture Series**

“Linguistics, Drumming and
Mathematics”, **Manjul Bhargava**, Department of Mathematics, Princeton
University, USA.

Discovering the same things
in two such different ways: Indian and Western Calculus”, **David
Mumford**, Division of Applied Mathematics, Brown University, USA.

“Geometry, Nonlinear Analysis
and Theoretical Physics”, **S.-T. Yau**, Departemet of Mathematics,
Harvard University, USA.

**Institute Colloquia**

“P. R. Halmos: My Teacher
– The best in the business”, **V. S. Sunder**, Institute of Mathematical
Science, Chennai.

“Playing with cards and hats
- data transmission and coding theory”, **Michel Waldschmidt**,
Universite Pierre et Marie Curie, Paris.

**Department Colloquia and
Seminars**

“Strong unicity of restricted
Chebyshev centers”, **D. V. Pai**.

“Geometric, combinatorial
and coding theoretic aspects of subspaces of a vector space”, **S.
R. Ghorpade**.

**By Other Visitors**

“Spectral stochastic methods”
(A series of lectures), **Dr. Didier Lucor**, UPMC Universite de
Paris-6.

“Quillen’s proof of Serre’s
conjecture” (A series of lectures), **S. M. Bhatwadekar**,
TIFR, Mumbai.

“Convergence of orbital measures”, **
S. Shrihari**, Institute of Mathematical Science, Chennai.

“On volichenko algebras”, **
Uma Iyer**, Bronx Community College, USA.

“Elasticity of elasticity”, **
K. Rajagopal**, University of Texas, USA.

“Optimization in multivariate
generalized linear models”, **Siuli Mukhopadhyay**, Department
of Biostatistics, Medical College of Georgia, USA.

“Bayesian inference for
zero-inflated count data”, **Archan Bhattacharya**, Department
of Statistics, University of Georgia, USA.

“Quantum field theory as
an aid to geometers”, **Katrin Wendland**, University of Augsburg,
Germany.

“A brief review of tight
closure theory”, **Rajasekhar Bhattacharyya, **
.

“Phantom exactness, flatness
and phantom homology”, **Rajasekhar Bhattacharyya, **
.

“The Birch and Swinnerton-Dyer
conjecture”, **Amod Agashe**.

“What is logical consequence?”, **
Rohit Parikh**, City University of New York, USA.

“Ramanujan graphs and optimal
expander graphs from algebraic geometric codes”, **Heeralal Janwa**,
University of Puerto Rico, San Juan, Puerto Rico.

“Nonparametric Bayesian
estimation – Some challenges”, **Eswar Phadia**, William Paterson
University of New Jersey, USA.

“Maximin universally optimal
designs in the presence of a trend”, **Dibyen Majumdar**, University
of Illionois at Chicago, USA.

“Componentwise linear and
integrally closed ideals”, **M. E. Rossi**, Universita di Genova,
Genova, Italy.

“Evolutionarily robust strategies:
Two nontrivial examples and a theorem”, **A. J. Shaiju**, University
of New Southwales, Australian Defence Force Academ, Canberra.

“Learning functions on the
sphere”, **H. N. Mhaskar**, California state university, Los Angeles,
USA.

“Real elements in spin groups”, **
Anupam Kumar Singh**, Institute of Mathematical Science, Chennai.

“Spectrum and Arithmetic”, **
C. S. Rajan**, TIFR, Mumbai.

“Riemann and his zeta function”, **
Peter Zvengrowski**, University of Calgary, Canada.

“Design of Factorial experiments”
(A series of lectures), **Aloke Dey**, Indian Statistical Institute,
New Delhi.

“Combinatorial representation
theory”, **A. Joseph Kennedy**. Pondicherry University.

“Partition algebras”, **
A. Joseph Kennedy**. Pondicherry University.

“Early history of irrational
and transcendental numbers”, **Michel Waldschmidt**, Universite
Pierre et Marie Curie, Paris.

“Perelman's noncollapsible
estimate on Ricci Flow”, **Richard Hamilton**, Columbia University,
USA.

“Spacetime with Torsion”, **
S.-T. Yau**, Harvard University, USA.

“All About "Statistics"
You Wanted to Know”, **B. L. S. Prakasa Rao**, University of Hyderabad.

“Gauss Composition Laws and
their applications”, **Manjul Bhargava**, Department of Mathematics,
Princeton University, USA.

“What's an infinite dimensional
manifold and how can it be useful in hospitals?”, **David Mumford**,
Division of Applied Mathematics, Brown University, USA.

“Navier-Stokes Equations:
Solvability, Control and Stochastic Analysis” (A series of lectures), **
Sivaguru S. Sritharan**, University of Wyoming, USA during Dec.2007
– Jan. 2008 under year long programme on New Trends in PDEs : Theory
and Computations.

“Statistical Surveillance :
Issues, models and methods with applications”, **Bikas Kumar Sinha**,
Indian Statistical Institute, Kolkata.

“Temperley-Lieb Algebras”, **
V. S. Sunder**, Institute of Mathematical Sciences, Chennai.

“An introduction to II_{1}
factors and subfactors”, **V. S. Sunder**, Institute of Mathematical
Science, Chennai.

“Lectures on inference for
stochastic processes”, **B. L. S. Prakasa Rao**, University of
Hyderabad, Hyderabad.

“An evolution operator (in
integral form) for the solution of a Cauchy problem for the wave equation”, **
Phoolan Prasad**, IISc. Bangalore.

“The method of moving planes”, **
S. Kesavan**, Institute of Mathematical Science, Chennai.

“Factorization principle
in homogenization”, **M. Vanninathan**, TIFR, Bangalore.

“Navier Stokes Equations:
A million dollar open problem”, **Amiya Kumar Pani**, IIT Bombay,
Mumbai.

“Far field boundary conditions
and its numerical approximation”, **A. S. Vasudeva Murthy**, TIFR
Bangalore.

“Homogenization of low cost
control problems in perforated domain”, **A.
K. Nandakumaran**, IISc, Bangalore.

“Wellposedness and regularization
in variational analysis”, **D. V. Pai**, IIT Bombay, Mumbai.

“How to compute a fair price
for an option derivatives: A case study”, **Amiya Kumar Pani**,
IIT Bombay, Mumbai.

“On quasilinear hyperbolic
equations and systems”, **V. D. Sharma**, IIT Bombay, Mumbai.

“Nonlinear Fuchsian equations”, **
Gopal K. Srinivasan**, IIT Bombay, Mumbai.

“Some remarks on the convergence
of adaptive finite element methods”, **Carsten Carstensen**, Humboldt
University, Germany.

“Computational Modelling
of Thermoforming Processes for Viscoelastic Polymer Sheets, with Applications
to thermo-plastic starch”, **John R. Whiteman** (FRSA), Brunel
University (UK) during January 2008.

Under this year long programme four-weeks long Instructional School on Modern PDEs was also

organized during May – June
2007 and the following talks were given by experts :

“Theory of
Distributions”, **S. Kesavan,** IMS, Chennai

“Sobolev
Spaces”, **M. Vanninathan, **TIFR, Bangalore

“Scalar Conservation
Laws”, **Phoolan Prasad, **IISc Bangalore

“Elliptic
PDEs”, **A. K. Nanadakumaran**, IISc Bangalore

“Evolution
Equations”, ** A. S. Vasudevamurthy,** TIFR, Bangalore

“Semigroup
Theoretic Approach to PDEs”, **N. Sabu,** IIT Bombay

“Numerical
Solutions to Scalar Conservation Laws”, **S. Baskar**, IIT Bombay

“System of
Hyperbolic Equations”, **Gopal K. Srinivasan**, IIT Bombay

“Viscosity
Methods”, **K. S. Mallikarjun**, IIT Bombay

“Theory of
Homogenization”, **Sivaji Ganesh Sista **
and **N. Sabu,** IIT Bombay

“Financial
Modelling”, ** N. Hemachandra**, IIT Bombay

“Stochastic
Process and Option Derivatives”, **Suresh Kumar, **
IIT Bombay

“Finite Element Methods ( Elliptic PDEs, Mixed Methods), MATLAB session”,

**Neela Nataraj**,
IIT Bombay

Finite Element
Methods (Evolution Equations), Discontinuous Galerkin Methods, Problem
Solving Sessions, **Amiya Kumar Pani**, IIT Bombay

Lecture series on “Group
Cohomology”, **A. R. Shastri**.

Lecture series on “3-Manifolds”, **
A. R. Shastri**.

Lecture series on “Vector
bundles, flag manifolds and Stiefel manifolds”, **Peter Zvengrowski,
University Calgary, Canada.**

Lecture series of five lectures on " Topological methods in the study of bilinear forms",

**K. Y. Lam, University of
British Columbia, Canada.**

Lecture series of five lectures
on: "Wall obstructions", **K. Varadarajan, University Calgary,
Canada,**

Lecture series of five lectures on: "Group theoretic methods in fixed point theoy".

**Peter Wong, Bates College,
USA.**

Lecture series of five lectures on: "Introduction to L2 cohomology".

**Peter Zvengrowski, University
Calgary, Canada.**

Under this programme International Workshop and International Conference were also organized during August 2007.

This year,
a statistic study group activity was initiated by evolving faculty members
from various colleges in Mumbai. The group focused on reading research
articles dealing with concepts and results taught at undergraduate level.
The following talks were presented under this study group meeting. .

“The inequality
between the coefficient of determination and the sum of squared simple
correlation coefficients”, **K. G. Rajan**, M. V. L. U, College,
Andheri, Mumbai.

“Moments
of discrete probability distributions derived using finite difference
operators”, **Shailaja Deshmukh**, K. C. College, Churchgate, Mumbai.

“Alternative
proofs for properties of correlation coefficient”, **Amrit Rajwadkar**,
Mithibai College, Vile Parle, Mumbai.

“A note on
the best linear unbiased estimation based on order statistics”, **
Shailaja Deshmukh**, KC College, Mumbai.

“Reliability
test plans for systems with dependent components”, **Sanjeev Sabnis**,
IIT Bombay, Mumbai.

“Small sample
interval estimation of Bernoullli and Possion parameters”, **Alok
Dabade**, Mithibai College, Mumbai.

“A delta
method for obtaining asymptotic distribution”, **Sanjeev Sabnis**,
IIT Bombay, Mumbai.

“The two-sample
T test with one variance unknown”, **Amrit Rajwadkar**, Mithibai
College, Mumbai.

“An overview
of resampling methods”, **Ashish Das**, IIT Bombay, Mumbai.

“Bootstrap
test of stochastic equality of two populations”, **Alok Dabade**,
Mithibai College, Mumbai.

“Approximate
median regression via box-cox transformation”, **Sanjeev Sabnis**,
IIT Bombay, Mumbai.

**1.
Athavale, Ameer*** - *Indiana University - *Functional
Analysis*

**Anandavardhanan, U.K**. - University of Hyderabad -*Number Theory***Das, Ashish –***Design of Experiments***Baskar, S.**– IISc Bangalore -*Hyperbolic Conservation Laws: Theory, Numeric and Applications***Garge, Shripad M. –**HRI Allahabad -*Number Theory, Linear Algebraic Groups***Ghorpade, Sudhir R**. - Purdue University -*Algebraic Geometry, Combinatorics***Joshi, Kapil D**. - Indiana University -*Topology, Discrete Mathematics***Joshi, Rajani R**. - IIT Bombay; UTC, Compiegne -*Computational Biology*,*Biostatistics*and*Bioinformatics***Keshari, Manoj Kumar -**TIFR Mumbai -*Commutative Algebra (Projective modules)***Kulkarni, Rekha P**. - IIT Bombay; JFU, Grenoble -*Numerical Functional Analysis, Spline Theory***Limaye, Balmohan V**. - University of Rochester -*Functional Analysis, Numerical Analysis, Spectral Approximation***Mahajan, Swapneel -**Cornell University –*Geometry and Topology***Mukhopadhyay, Siuli -**University of Florida -*Statistics***Nataraj, Neela -**IIT Delhi -*Finite Element Methods***Pai, Devidas V**. - IIT Bombay -*Functional Analysis, Approximation Theory, Set-valued Analysis***Pani, Amiya K**. - IIT Kanpur -*Numerical Analysis, Partial Differential Equations, Industrial Mathematics***Puthenpurakal, Tony J. -**Purdue University -*Commutative Algebra***Raghunathan, Ravi**- Yale University -*Automorphic forms, Number Theory***Raman, Preeti –**TIFR Mumbai -*Number Theory***Rana, Inder K**. - ISI Delhi -*Harmonic Analysis, Mathematics Education***Ranjan, Akhil**- TIFR Mumbai -*Differential Geometry***Kulkarni, Ravi S. –**Harvard University -*Differential Geometry***Sabnis, Sanjeev V**. - Old Dominion University -*Reliability Theory, Industrial Statistics***Sharma, Vishnu D**. - BHU Varanasi -*Quasilinear Hyperbolic Systems of PDEs/ Nonlinear Waves***Shastri, Anant R**. - TIFR Mumbai -*Algebraic Geometry, Algebraic Topology***Singh, Balwant –***Commutative Algebra***Sista, Sivaji Ganesh –**IISc Bangalore -*Partial Differential Equations***Sivasubramanian, S. –**TIFR Mumbai -*Combinatorics***Srinivasan, Gopal K**. - University of Minnesota -*Partial Differential Equations***Srinivasan, Murali K**. - Univ. of Illinois at Chicago -*Combinatorics***Subramanyam, A.**- University of Pune -*Statistical Inference, Geostatistics***Sureshkumar, K**. – IISc Bangalore -*Stochastic Differential Game Theory, Mathematical Finance.***Vellaisamy, P**. - IIT Kanpur -*Applied Probability, Statistical Inference, Industrial Statistics***Verma, Jugal K.***– Purdue University – Commutative Algebra*