Feedback for UG Level Training Program

NATIONAL PROGRAMME ON DIFFERENTIAL EQUATIONS-THEORY, COMPUTATION & APPLICATIONS (NPDE-TCA) National Programme on Differential Equations-Theory, Computation & Applications (NPDE-TCA) was sanctioned by Department of Science & Technology (DST) in Feb, 2012 for a period of five year with a sanctioned outlay of 4.5 crores. The planning and implementation of the training programmes are executed by a local executive committee which is approved from time to time by the National Scientific Organizing Committee. With a mission “To Create Human Resource and Generate Knowledge Source for Academia and Industry in the area of Differential Equations”, The main goal of this programme is to create a work force at the national level in broad areas of Applied Mathematics specifically in Differential Equations, Scientific Computing and Modelling. One of the key components of the proposed activity is to form a national forum on Differential Equations : Theory, Computation & Applications for academia and industry. Under this national programme, the following activities are organised : Undergraduate Training Programme The main objective of this program was to introduce participants to new vistas in the area of differential equations through modelling and expose them to scientific computing lab sessions with hands on computing. 1. 2012-2013: (Participated: 45) Held at IMA, Bhubaneshwar during May 7 – 26, 2012, this programme was coordinated by M.C.Joshi and Swadhin Pattanayak and Seventy Nine (79) candidates from all over India applied for this programme, of which forty five (45) were selected based on their academic records and recommendations. Resource Persons available during this programme were : P.C. Das and N. Parhi (NISER, Bhubaneshwar); P. Dhanumjaya (BITS, Goa); Raju K. George (IIST, Trivandram); M.C. Joshi, Neela Nataraj and Amiya K. Pani (IITB); S. Pattanayak (IMA, Bhubaneshwar); Amit Apte (TIFR, CAM, Bangalore); B. V. Rathish Kumar, P. Shunmugaraj (IITK), (Linear Algebra (LA), Analysis (ANLYS), Metric Space and Fixed Point Theorem (MSFT), Mathematical Modelling (MM), Ordinary Differential Equations – I

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(ODE I), Ordinary Differential Equations – II (ODE II), Boundary Value Problem (BVP), Numerical Analysis-I (NA), Numerical Analysis-II (NA), Control Theory (CT), Scilab (SCI), Scilab Spoken Tutorial (SST)

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2. 2013-2014 : (Participated: 55) This program was held at Birla Institute of Applied Scinces, Bhimtal, during June 3 – 22, 2013 which was coordinated by Anant Pant (BIAS, Bhimtal), M.C.Joshi (IITB), R P Pant and Mahesh Joshi (Kumaun University, Nainital). One hundred thirty five (135) candidates from all over India applied for this program out of which fifty five (55) were selected based on their academic records and recommendations. Resource Persons: Amiya Kumar Pani (IITB), Mohan C. Joshi (IITB), S. Baskar (IITB); Raju K. George (IIST, Thiruvananthapuram), A K Nandkumaran (IISc Bangalore), P. Shunmugraj (IITK), P.S. Datti (TIFR Bangalore), Peeyush Chandra (IITK), R P Pant (Kumaun University, Nainital), Mahesh Joshi (Kumaun University, Nainital) and P. Dhanumjaya (BITS-Pilani, Goa). Feedback of the above program is shown below in the form of a graph :

Feedback for UG Program 2013 16 14 12 10 8 6 4 2 0 1

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Topic 1: Analysis, Topic 2: Linear Algebra, Topic 3: Mathematical Modeling by Differential Equations, Topic 4: Metric Space & Fixed Point Theorem, Topic 5: Mathematical Modeling, Topic 6: Ordinary Differential Equations (I), Topic 7: Ordinary Differential Equations (II), Topic 8: Boundary Value Problems, Topic 9: Numerical Analysis – I, Topic 10: Numerical Analysis – II, Topic 11: Control Theory, Topic 12: Scilab Tutorials, Topic 13: Scientific Labs

Ranking from 0-5 (0 being lowest & 5 being the highest)

3. 2014-2015 : (Participated: 55) This program was held at Maulana Azad National Institute Of Technology, Bhopal, during 26th May to 14th June, 2014 and was coordinated by Professors Peeyush Chandra, B.V. Rathish Kumar (IIT Kanpur) and Kamal Raj Pardasani (MANIT Bhopal). One hundred fifty (150) candidates from all over India applied for this program out of which fifty five (55) were selected based on their academic records and recommendations. Resource Persons: Professors P.S. Datti (TIFR-CAM, Bangalore); K. Sreenadh (IIT Delhi); Peeyush Chandra, B.V. Rathish Kumar (IIT Kanpur); Sunita Gakkhar (IITR); Prashant Srivastava (IIT Patna); A. K. Lal (IITK); Joydip Dhar (IITM); S. Raju (IITM); P. Dhanumjaya (BITS-Pilani, Goa);V. Raghavendra (LNMIIT, Jaipur).

Feedback for UG Program 2014 4.2 4 3.8 3.6 3.4 3.2 1

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Analysis, Linear Algebra, Math Modeling , First Order ODE, Second Order ODE, System of ODE, Mathematical Models using ODE – I, Mathematical Models using ODE – II, Scilab software and Solution of ODE using SCILAB, Introductory SCILAB Sessions

4. 2015-2016: (Participated: 55) This program was held at The LNM Institute Of Information Technology, Jaipur, during May 18 – June 06, 2015 and was coordinated by Professors Akhlaq Husain, Manish Garg and Rasmita Kar (LNMIIT Jaipur); Amiya K. Pani (IIT Bombay). One hundred and five (105) candidates from all over India applied for this program out of which fifty five (55) were selected based on their academic records and recommendations Resource Persons: P. S. Datti (TIFR-CAM, Bangalore); A.K. Lal, Peeyush Chandra, Nandini Nilakantan (IIT Kanpur); Amiya K. Pani (IIT Bombay); R. Vittal Rao, A.K. Nandakumaran (IISc Bangalore); Harish Kumar, K. Sreenadh (IIT Delhi); Ratikant Panda (Delhi University); Raju K. George (IIST Trivandrum); Seema Nanda (TIFR CAM Bangalore); Sanyasiraju (IIT Madras); V. Raghavendra, Ajit Patel, Vikas Gupta, Rasmita Kar, Akhlaq Husain (LNMIIT Jaipur)

Topics : Linear Algebra, Analysis, Mathematical Modelling, Ordinary Differential Equations, Basic Numerical Analysis and Scientific Computation pertaining to Linear Algebra and Ordinary Differential Equations.

Post-Graduate Training Programme The main objective of this programme was to provide linkage between theory and practice through real life problems and generte manpower to support academia, scientific organizations and industry by providing appropriate training and also to expose participants to high end mathematical software like MATLAB. 1. 2012-2013 : (Particpated : 46) This Programme was held at IIT Delhi during May -13 - June 2 nd 2012 which was coordinated by K.Sreenadh with V.V.K. Srinivas Kumar from IITD and S.Baskar with S.Sivaji Ganesh from IITB. Resource Persons: K. Sreenadh , V.V.K.Srinivas Kumar, Girija Jayaraman and Balaji Srinivasan (IITD); M.T. Nair (IITM); R. K. Panda (University of Delhi); V. Raghavendra and B. D.Rathish Kumar (IITK) ; Amiya K. Pani, S. Baskar and S. Sivaji Ganesh (IITB); A. S. Vasudeva Murthy, Shyam sundar Ghoshal, K. Sandeep, P.S. Datti and G. D. Veerappa Gowda (TIFR CAM, Bangalore) and S. Kundu (IITD). Eighty One (81) Candidates appplied for this program and approximately forty six (46) had been selected. Feedback of the above programmeme is shown below in the form of graph :

Ranking Point

Feedback for PG Level Training Program 5 4.8 4.6 4.4 4.2 4 3.8 3.6

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(ODE: Existence & Stability (ODE), Measure Theory & L^2 Space(MT), Multivariable Calculus (MC), Fixed Point Theorem (FPT), Ascoli-Arzela Theorem (AAT), Matlab (ML), Classification of Second Order PDE (SOPDE), Green Functions, Maximum Principles (GF), First Order PDE, Method of Characteristics (FOPDE), Real Analytic Solutions, CK Theorem (RAS), Parabolic Equations, Existence, Maximum Principle(PE), Second Order Wave Equations (SOWE), FDM for Parabolic & Wave Equations (FDM PWE), FDM for Hyperbolic Equations & Conservations Laws (FDM HECL), FDM for elliptic and Matrix Computations (FDM EMC), Mathematical Modelling (MM), Mathematical Models like Heat & Mass Transfer, Fluid Flows (MM HMT), On Application of Functional Analysis to Weak solutions (AFA) 2. 2013-2014 : (Particpated : 44) This Program was held at IIT Madras during 20th May to 8th June, 2013 which was coordinated by S. Sundar and Y.V.S.S. Sanyasiraju (IIT M); S. Baskar and S. Sivaji Ganesh (IIT B). Approximately forty four (44) from all around India particpated in this programme.

R a n kin g fro m 0 -1 0 (0 b e in g lo w e st & 1 0 b e in g th e h ig h e st)

3. 2014-2015 : (Participated : 55) This Program was held at IIT Guwahati during 2 nd to 21st June, 2014 and was coordinated by Professors Rajen K. Sinha, Bhupen Deka (IIT Guwahati); S. Baskar and S. Sivaji Ganesh (IIT Bombay). Fifty five (55) from all around India were selected to attend this programme. Resource Persons: Professors Anjan K. Chakrabarty , P. A. S. Sree Krishna (IIT Guwahati); Phoolan Prasad (IISc, Bangalore); P. Shunmugaraj(IIT Kanpur); V. Sree Hari Rao (JNTU, Hyderabad); P. C. Das (IIT Kanpur (ret’d)); Bhupen Deka (IIT Guwahati); Amiya K. Pani, S. Sivaji Ganesh, S. Baskar (IIT Bombay); R . K. Mohanty (SAU, Delhi); S. Sundar (IIT Madras); B. V. Rathish Kumar (IIT Kanpur).

Feedback for PG Program 2014 10 8 6 4 2 0 1

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Topic 1: Multivariate Calculus, Topic 2: Analysis, Topic 3: First Order PDEs, Topic 4: Measure Theory, Topic 5:Advanced ODEs, Topic 6: Classifications and Methods of Solutions for PDEs, Topic 7: Elliptic PDEs, Topic 8: Heat Equations, Topic 9: Wave Equations, Topic 10: FDM for Heat Equations, Topic 11: FDM for Elliptic and Wave Equations, Topic 12: Mathematical Modeling, Topic 13: Variational Methods

4. 2015-2016: (Participated : 58) This Program was held at Indian Institute Of Technology Kanpur during 18 th May – 5th June, 2015 and was coordinated by Professors B.V. Rathish Kumar (IIT Kanpur) and S.Ghorai (IIT Kanpur). More than 120 candidates appplied for this program and approximately fifty eight (58) had been selected. Resource Persons: Sreenadh (IITD); P. C. Das (IMA Bhubaneswar); Rajen Sinha (IITG); R. K. Mohanty (SAU, Delhi); Phoolan Prasad (IISc Bangalore); C. Praveen (TIFR-CAM, Bangalore); Santhanam (IITK); S. Sundar (IITM); Sanyasiraju (IITM); Shobha Madan (IITK); Rama Rawat (IITK); D. Bahuguna (IITK); Kaushik Bal (IITK); Amiya K. Pani (IITB); M.C.Joshi (IIT Gandhinagar); Thamban Nair (IITM); Sandeep (TIFR-CAM, Bangalore) Topics : Multi-variable Calculus (Implicit and Inverse function theorems, Gauss-Greens theorems), Analysis (Ascoli-Arzela theorem, elements of measure theory, L^2 space); Ordinary Differential Equations (existence theory and stability results); Partial Differential Equations (First order linear and nonlinear hyperbolic PDEs, Second order linear elliptic and parabolic PDEs (Green's function with properties, maximum principles etc.), wave equation (d'Alembert formula, reflection principle etc.)); Mathematical Modeling (basics of modeling with examples from industrial problems); Finite Difference Methods for PDEs with hands on computing (stability, consistency and convergence of numerical schemes for PDEs; iterative methods like Jacobi, Gause-Seidel and SOR).

Advanced Level Training Programme The main aim was to provide a sound mathematical foundation for research and expose participants to frontier areas of research on Differential Equations and to create a pool of trained manpower to support advancement of science and technology in the country. 1. 2012-2013 : (Participants: 41) This program was held at IIT Bombay during 10th – 30th June 2012, which was co-ordinated by A.K.Pani and Neela Nataraj. Around forty one (41) participants were selected to attend this programme. Resource Persons: V. Raghavendra and Pravir Dutt (IIT Kanpur), Amiya Kumar Pani and Neela Nataraj (IIT Bombay) ; R.K.Sinha (IIT Guwahati); A.S. Vasudeva Murthy, K. Sandeep , Rajib Dutt, M. Vanninathan and P.S. Datti (TIFR, Bangalore); A.K. Nandakumaran, M. Ramaswamy and T.Gudi (IISC, Bangalore). Theory of Distribution (TD), Sobolev Spaces (SS), Elliptic PDE (E-PDE), Parabolic PDE (P-PDE), Spectral Theory (ST), Galerkin Formulation (GF), FEM for Heat Equation (FEM-HE), Spectral Methods (SM), FEM for Elliptic Problems (FEM-EP), Semigroup Theory and Linear Evolution Equations (ST&LE), Non-Linear Elliptic PDE (NLE-PDE), Scalar Conservation Lab (SCL), Linear Hyperbolic System (LHS), Matlab Session (MS) 2013-2014 : (Particpated : 59) This program was held at Indian Institute of Science, Bangalore during 24 th June – 19th July 2013, which was co-ordinated by Blanca Ayuso de Dios (Centre de Recerca Matematica (CRM), Spain), Sashikumar Ganesan, A.K. Nandakumaran and Thirupathi Gudi (IISc Bangalore), Amiya K.Pani and Neela Nataraj (IITB). About 59 participants participated in the program. Resource Persons: Blanca Ayuso de Dios (CRM, Barcelona, Spain); Pravir Dutt (IITK); Sashikumar Ganesan, Thirupathi Gudi, A.K. Nandakumaran, Phoolan Prasad (IISc Bangalore); G.D. Veerappa Gowda, Mythily Ramaswamy (TIFR-CAM Bangalore); Neela Nataraj, Amiya K. Pani (IITB).Feedback of the above program is shown below in the form of a graph :

Graph for Advanced Level Training programe - 2013 6 5 Ranking out 5

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4 3 2 1 0 MDT FOPDEs DTSP INMHP

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Motivation on Distribution Theory (MDT), First Order PDEs (FOPDEs), Distribution Theory and Sobolev Spaces (DTSP), Introduction to Numerical Methods for Hyperbolic Problems (INMHP), Weak Formulations (WF), Finite Element Method (FEM), Introduction to Probability (IP), Adaptive FEM (AFEM), Discountinous Galerkin FEM (DGFEM), Mixed FEM (MFEM), Implementing FEM (IFEM).

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2014-2015: (Participated : 61) This program was held at Indian Institute of Science Education And Research, Thiruvananthapuram during May 26th–June 13th 2014 and was co-ordinated by Professors K. R. Arun (IISER, Trivandrum); Raju K. George (IIST Trivandrum); Amiya K. Pani and Neela Nataraj (IIT, Bombay). Sixty one (61) participants attended this programme. Resource Persons: Professors S. Kesavan (IMSc, Chennai); M. Vanninathan, K.T. Joseph, A. Adimurthi, G.D.V. Gowda, Mythily Ramaswamy (TIFR-CAM, Bangalore); Amiya K. Pani, Neela Nataraj (IIT, Bombay); Raju K. George, N. Sabu (IIST, Trivandrum); A.K. Nandakumaran (IISc, Bangalore).

Ranking 1-10 (0 being lowest & 10 being the highest)

Feedback for Advanced Training Program: 2014 10 9 8 7 6 5 4 3 2 1 0 1

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Sobolev spaces, Theory of hyperbolic conservation laws, FD/FV methods for conservation laws, Distribution Theory, Elliptic PDE, Finite dimensional control theory, Heat equation and semigroup theory, Controllability and Observability, FEM for control problems, Optimal control and dynamic programming, Viscocity solutions, Control of heat equation, FEM and approximation theory. 4.

2015-2016 : (Participated: 53) This program was held at Birla Institute of Technology & Science, Pilani – K. K. Birla Goa Campus during May 25th – June 14th, 2015 and was co-ordinated by Professors P. Dhanumajaya, BITS Pilani-K. K. Birla Goa Campus and Amiya Kumar Pani, IIT Bombay. Fifty three (53) participants attended this programme. Resource Persons: M. Vanninathan, K. T. Joseph, A. Adimurthi, G.D.V. Gowda, Mythily Ramaswamy (TIFR-CAM, Bangalore); M.T. Nair (IIT Madras); Amiya K. Pani, Neela Nataraj (IIT Bombay); Mohan C. Joshi (IIT Gandhinagar); K. R. Arun (IISER Trivandrum); Thirupathi Gudi, A.K. Nandakumaran (IISc, Bangalore). Distribution Theory; Sobolev Spaces; Elliptic PDE: weak solution, Lax-Milgram Lemma, regularity results, weak maximum principle, eigenvalue problems; Heat and Wave Equations: existence, uniqueness etc.; Semigroup theory; First Order Hyperbolic PDEs: Existence of weak solution, entropy solution; Finite Difference/Finite Volume Schemes for First Order Equations; Finite Element Methods for Elliptic and Heat Equations; optimal control for elliptic and heat equation & with hands on computation.

Internship Programme I. Summer Internship Programme: (Participated : 67) In order to expose students to research, 15 to 20 internships are offered in a given year. Summer Internship Programme is conducted during April – June. 1. 2012-2013 :(Participated: 04) Thirty Seven Candidates from all over India applied for this Internship Programme. Out of which five candidates from various institutes like Calicut University, ICT Mumbai, SVNIT Surat, IITKGP and IITR had been selected. Four Candidates did their Internship at IIT Bombay and one candidate did the internship at Indian Institute of Space Science and Technology (IIST), Thiruvananthapuram, Kerala. 2. 2013-2014 :(Participated: 14) Fourteen candidates from various institutes were selected. Six Candidates did their Internship at IIT Bombay one candidate did the internship at Indian Institute of Space Science and Technology (IIST), Thiruvananthapuram, Kerala, four did at IIT Kanpur, Two candidates did at Tezpur University and one at IISc Bangalore. 3. 2014-2015:(Participated: 27) Around 345 applications were received out of which 27 applicants were selected, and they did their internship in institutes like IIT Bombay, IIT Kanpur, SAU Delhi, IIT Delhi, IIT Madras, IIT Guwahati, IIT Gandhinagar, IIT Kharagpur, BHU Varanasi, TIFR-CAM Bangalore and IIST Trivandrum, Kerala. 4. 2015-2016 :(Participated: 21) Around 89 applications were received out of which 21 applicants were selected, and they did their internship in institutes like IIT Bombay, IIT Kanpur, SAU Delhi, IIT Delhi, IIT Madras, IIT Guwahati, IIT Gandhinagar, IIT Kharagpur, BHU Varanasi, TIFR-CAM Bangalore and IIST Trivandrum, Kerala.

II. Winternship Programme: (Participated : 48) 1.

2012 -2013 : (Participated: 10) Based on a theme “Learning Mathematics while working on a project'', a few bright participants from both Basic and Advanced Level Programmes are selected to do their winternship with eminent researchers in the month of December 2012. 2. 2013-2014 :(Participated: 08) Two hundred candidates from all over India applied for this Winternship Programme 2013 held in the month of December. Out of which eight (8) candidates from various institutes were selected. Five Candidates did their Winternship at IIT Bombay, two at IIT Kanpur and one candidate at IITB and TIFR-CAM Bangalore. 3. 2014-2015 :(Participated: 12) Two hundred and fifty candidates from all over India applied for this Winternship Programme 2014 held in the month of December, out of which twelve (12) candidates from various institutes were selected. The response was tremendous as compared to last year. 4. 2015-2016:(Participated: 18) 239 candidates from all over India applied for this Winternship Programme 2015 held in the month of December and January, out of which eighteen (18) candidates from various institutes were selected.

Advanced Thematic Programme 1. 2012-2013 : (Total Participants : 206) 1. Advanced Level Workshop on Differential Equations in Ecology & Epidemiology : This workshop was held at IIT Roorkee during 10 th – 14th October, 2012 which was co-ordinated by Sunita Gakkhar. The main objective of this programme was to expose participants to the advanced topics, current trends & future directions in these areas and deliver the state of the art lectures dealing with Mathematical Models in Ecology and Epidemiology by the domain experts. Fifty Four (54) candidates from all over India applied for this programme, of which thirty seven (37) were selected. Resource Persons: Sunita Gakkhar (IITR); Karmeshu (JNU,Delhi); Arni S.R. Srinivasa Rao (ISI,Kolkata); V. Srihari Rao (JNTU); Malay Banerjee (IITK); Vishwesha Guttal (ISC Bangalore); P.D. Srinivasu (Vishakhapatnam); and Ram Naresh (HBTI, Kanpur). 2. Advanced Workshop on Mathematical Theory of Control and Numerics (MTCN-2012): This Programme was held at IIST Thiruvananthapuram during 21st – 30th November, 2012 which is coordinated by Saktivel and Raju K. George. The main objective of this workshop was to explore the concepts of linear and nonlinear control systems mathematically as well as numerically by interacting with a group of eminent scholars from all over India. Resource Persons: Amiya K. Pani, Mohan C. Joshi (IIT Bombay); K. Balachandran (Bharathiyar University, Coimbatore); M.V. Dhekane (VSSC, Thiruvananthapuram); Mrinal K. Ghosh (IISc, Bangalore); A.K. Nandakumaran (IISc, Bangalore); S.S. Sritharan (NPS, Monterey, USA) , N. Sukavanam (IIT Roorkee); M. Thamban Nair (IIT Madras); V. Raghavendra (IITK); N. Parhi (NISER, BBSR) and Sam K. Zachariah (IIST, Thiruvananthapuram) 3. Advanced Workshop on Evolution Equations: Theory, Methods & Applications (AWEETMA-2012): This programme was condcuted at IIT Kanpur during 2nd – 6th December, 2012 which is coordinated by Rathish Kumar and D.Bahuguna. Resource persons: N. Sukavanam (IITR); Amiya K. Pani (IITB); Rajen K. Sinha (IITG); V. Raghavendra, D. Bahuguna, B.V. Rathish Kumar, Pravir Dutt (IITK) and P. Veeramani (IITM). 4. Advanced Workshop on “Non-Standard Finite Element Methods” (AWNSFEM 2013) : This program was held during February 11-15, 2013 at IIT Bombay, co-ordinated by Neela Nataraj and Amiya K Pani. Objective was to expose research scholars to the broad area of non- standard finite element methods, which may be superior to the standard finite element methods in specific applications. Thirty two (32) participants participated in this program. Resource Persons: Susanne C. Brenner (Louisiana State University, Baton Rouge), Carsten Carstensen (Humboldt University, Berlin), Amiya K Pani (IIT Bombay) Thirupathi Gudi (IISc, Bangalore), Li-yeng Sung (Louisiana State University, Baton Rouge). 5. 3rd Indo-German Workshop on “Adaptive Finite Element Methods”(AWAFEM-2013) : IMA Bhubaneshwar hosted this program during February 22 – March 2, 2013. This program was coordinated by C. Carstensen (Humbolt University of Berlin), Amiya K Pani (IITB) and S. Padhy (IMA Bhubaneshwar). The aim of the program was to expose young researchers particularly from India to efficient and reliable algorithms related to adaptivity feed- back and a posteriori error control, to bring together and to provide a common platform for exchanging ideas and results pertaining to the challenges in these front line areas of FEM. 24 participants were selected based on their biodata and recommendation letter.Resource Persons: Ph. Brinkmann (Humboldt University, Berlin), Carsten Carstensen (Humboldt University, Berlin), D. Gallistl (Humboldt University, Berlin), Thirupathi Gudi (IISc, Bangalore), Amiya K. Pani (IITB), Susanne C. Brenner & Li Yeng Sung (Louisiana State University).

6. Workshop on Recent Developments on Numerical Methods for Evolution Equations (RDNMEE-2013) : A four day workshop was held at IIT Bombay during March 18-21, 2013 which was co-ordinated by S. Baskar, Amiya K Pani (IITB) and Phoolan Prasad (IISc Bangalore). More than 30 participants attended this workshop. Resource Persons: K.R. Arun (IISER, Thiruvananthapuram), Maria Lukacova (Johannes Gutenberg University), Phoolan Prasad (IISc, Bangalore), M.K.Kadalbajoo (IIT Kanpur), S.Sundar (IIT Madras), Y.V.S.S. Sanyasiraju (IIT Madras). 2. 2013-2014 : (Total Participants : 369) 1. Advanced Level Workshop on Theoretical and Computational Aspects of Nonlinear Waves (TCANW 2013) : This workshop was held at IIT Bombay during May 27th–31st, 2013 which was co-ordinated by S. Baskar and Amiya K. Pani (IITB). The main objective of this program was to train post-graduate and research students in this field by some experts from India and abroad. Fifty (50) candidates from all over India applied for this program, of which thirty two (32) were selected. Resource Persons: Philip Roe (University of Michigan), P. Prasad (IISC, Bangalore), Veerappa Gowda (TIFR, Bangalore), K. T. Joseph (TIFR, Bangalore), J. C. Mandal (IITB), Raghurama Rao (IISC, Bangalore), Ch. Srinivasa Rao (IITM), S. Baskar (IITB), Harish Kumar (IITD). 2. Advanced Workshop on Mathematical Epidemiology and Differential Equations (AWMEDE-2013): This Program was held at Indian Institute of Technology Patna for six days during July 8th – 13th, 2013 which was coordinated by P. K. Srivastava (IITP) and Peeyush Chandra (IITK). The aim of the workshop was to provide participants an overview of mathematical techniques in ordinary, delay and partial differential equations that allow one to address the challenges in epidemiological modeling. Thirty three (33) participants were selected for this program. Resource Persons: M. Banerjee (IITK), P. Chandra (IITK), Pradeep Das (RMRIMS), B. Dubey (BITS), Anuj Mubayi (NEIU, USA), A. K. Misra (BHU), V. Raghavendra (IITK), A. S. Rao (GRU, USA/ ISIKol), P. K. Srivastava (IITP). 3. Advanced Workshop on “Nonlinear Differential Equations : Dynamics of Complex Systems (NDEDCS-2013): This program was held at University of Calcutta during September 23 rd – 28th, 2013, coordinated by Susmita Sarkar. The main objective of the workshop was to bring together experts working in the field of complex systems and put in focus the essential role of differential equations in determining the collective behavior of the complex systems and acquiring an understanding thereof. More than fifty (50) participants attended this workshop. Resource persons: Jayanta Kumar Bhattacharjee (Director, HRI), V. Balakrishnan (IIT, Chennai), M.Lakshmanan (Bharatidasan University, Tiruchirapally), Govindan Rangarajan (IISc, Bangalore), Deepak Dhar (TIFR, Mumbai), Pranay Goel (IISER, Pune), Sitabhra Sinha (IIMSc, Chennai), Soumitro Banerjee (IISER, Kolkata), B. S. Dandapat (SMIT, Sikkim), K. P. Das (Calcutta University), Anandamohan Ghosh (IISER, Kolkata), M. M. Panja (Viswabharati). 4. Advanced Workshop on “Homogenization” : Department of mathematics at the Indian Institute of Space Science and Technology organized an Advanced level workshop on Homogenization from December 9th – 14th, 2013. This workshop was coordinated by N. Sabu (IIST, Trivandrum). The objective of this workshop was to introduce various techniques of homogenization to the participants. Twenty two (22) participants attended this program. Resource Persons: A. K Nandakumaran (IISc Bangalore), M. Vanninathan (TIFR Bangalore), T. Muthukumar (IITK), Amiya K. Pani (IITB), N. Sabu (IIST, Trivandrum). 5. Advanced Workshop on “Computational Methods for Integral Equations & Applications” (AWCMIEA-2014): IIT Kanpur hosted this workshop with an objective to introduce participants to a number of fundamental mathematical ideas and techniques that lie at the core of integral equation

approach of problem solving. The program was co-ordinated by B.V. Rathish Kumar (IITK) and was held during January 13th – 17th , 2014. The workshop was attended by 29 participants. 6. Advanced Workshop & Symposium on Stability Analysis of Differential Equations with Application to Fluid Flow Problems (SADEAFFP-2014) : A four day workshop & symposium was held at IIT Kanpur during March 20th – 24th, 2014. The aim of the workshop was to introduce participants to the concepts of fluid flow instability. This program was co-ordinated by B.V. Rathish Kumar and S. Ghorai (IITK). 7. Advanced Level Workshop on “Stabilization Methods for Singularly Perturbed Differential Equations” (SPDE-2013). This program was conducted at IISc Bangalore during October 3rd – 5th, 2013 which was coordinated by Dr. Sashikumar Ganesan (IISc Bangalore). The workshop was attended by 37 participants. Resource Persons: Lutz Tobiska (Uni-Magdeburg, Germany), Roddam Narasimha (JNCASR), M. K. Kadalbajoo (IITK), Rama Govindarajan (TIFR-CIS), Sashikumaar Ganesan (IISc Bangalore) 8. Advanced Level Workshop On Orthogonal Spline Collocation Methods (OSCM-2014) For Partial Differential Equations”. South Asian University hosted this four day workshop during March 21st – 24th, 2014. Thirty three participants attended this workshop. The program was coordinated by Kapil K. Sharma (SAU, Delhi). 9. Advanced Workshop on “Nonlinear Functional Analysis & Its Applications” (NFAA-2013) : This program was held during October 21-29, 2013 at University of Kashmir, Srinagar, co-ordinated by N.A. Rather and S. Pirzada. More than 65 candidates applied for this program out of which 45 were selected. Resource Persons: Mohan C Joshi, D V Pai (IIT, Gandhinagar); Amiya K Pani (IITB), P N Srikanth (TIFR, Bangalore), Raju K George (IIST, Thiruvananthpuram), S Kesavan (IMS, Chennai), Amin Sofi (University of Kashmir), N Sukavanam (IIT Roorkee). 10. Advanced Workshop on Mathematical Foundation of Advanced Finite Element Methods (MFAFEM-2013) : A nine day workshop was held at BITS-Pilani, Goa during 26th Dec. 2013 – 3rd Jan 2014 which was co-ordinated by Carsten Carstensen (Humboldt University of Berlin, Germany), P. Dhanumjaya (BITS-Pilani), Neela Nataraj and Amiya K. Pani (IITB). More than 30 participants attended this workshop. Resource Persons: Amiya K. Pani, Neela Nataraj (IIT Bombay) ; P. Dhanumjaya (BITS-Pilani); Thirupati Gudi (IISc Bangalore); Carsten Carstensen, Mira Schedensack , Dietmar Gallistl (Humboldt University of Berlin, Germany); Jay Gopalakrishnan (Portland State University,U.S.). 3. 2014-2015 : (Total Participants : 292) 1. Advanced Level Workshop on “Finite element methods for Navier-Stokes equations: This workshop was held at SERC, IISc Bangalore during September 8th–12th, 2014 which was co-ordinated by Dr. Sashikumar Ganesan (IISc Bangalore). Forty One (41) candidates were selected for this program. Resource Persons: Professors Tanmay Basak (IITM); Sashikumaar Ganesan (IISc Bangalore); John Volker, (WIAS, Germany); B.V. Rathish Kumar (IITK); C. Praveen (TIFR-CAM, Bangalore); Lutz Tobiska, Uni-Magdeburg, Germany. 2. Advanced Workshop on “Variational Analysis And Optimization”: IIT Gandhinagar will be hosting this six days workshop during March 2nd – 7th, 2015 and was coordinated by Professors Amiya Pani (IIT Bombay); Mohan Joshi, Narendra Ladhawala, Chetan Pahlajani, Indranath Sengupta, Jagmohan Tyagi (IIT Gandhinagar). Forty two (42) participants are selected for this program. Resource Persons: Professors Joydeep Dutta (IIT Kanpur); Neela Nataraj, Amiya Pani (IIT Bombay); Mohan Joshi, D V Pai, Jagmohan Tyagi (IIT Gandhinagar); V. Raghavendra

(LNMIIT Jaipur); Mythily Ramaswamy (TIFR-CAM Bengaluru). 3. Advanced Workshop on “Computational Methods For Control Problems”: This program will be held at Mar Ivanios College, Trivandrum (Autonomous) during March 16th – 21st, 2015, and was coordinated by Dr. Sarvesh Kumar (IIST, Trivandrum) and Prof. Mary George (Mar Ivanios College, Trivandrum). Resource persons: Professors Amiya Kumar Pani, Neela Nataraj (IIT Bombay); Raju. K. George, Harsha Simha M.S., Priyadarshnam, Sarvesh Kumar. (IIST Trivandrum); Mohan C. Joshi (IIT Gandhinagar); A. K. Nandakumaran (IISc Bangalore); Mythily Ramaswamy (TIFR Bangalore); K. Balachandran (Bharathiar University, Coimbatore), N. Sukavanam (IIT Roorkee); Anil Kumar, P. Dhanumjaya (BITS-Goa) 4. Advanced Workshop on “Finite Difference Methods For Differential Equations”: Department of Mathematics, South Asian University will be hosting this advanced workshop during March 13th – 17th , 2015. The program is coordinated by Prof. Kapil Sharma, Prof. R.K.Mohanty and Prof. Navnit Jha (SAU, Delhi). Resource persons: Professors M.K.Kadalbajoo, B.V. Rathish Kumar (IIT Kanpur); Amiya K. Pani (IIT Bombay); YVSS Sanyasiraju (IIT Madras); SCS Rao (IIT Delhi); V.S.Hari Rao (JNTU, Hyderabad); Sirj-ul-islam (UET Pakistan); Kapil Sharma, R.K.Mohanty, Navnit Jha (SAU, Delhi). 5. Advanced Workshop on “Mimetic Spectral Element Methods”: The one week long workshop is coordinated by Profs. Pravir Dutt and B.V.Rathish Kumar (IIT Kanpur) and is scheduled to be held at IIT Kanpur in the end of March 2015. Resource persons: Professors Marc Gerristma, TU/Delft; M. K. Kadalbajoo, Pravir Dutt, C.S. Upadyay, B.V. Rathish Kumar, M.K.Verma (IIT Kanpur); Aklaq Hussain (LNMIIT Jaipur), Subhashree Mohapatra, Kishore Kumar, Subir Singh Lamba, Arbaz Khan, Lokendra Bilaiyan, Pankaj Biswas, Nagaraju 6. Advanced Workshop on “Biomathematics”: The workshop will be held at Banaras Hindu University, Varanasi in the month of March 2015. The aim of this workshop is to initiate an interdisciplinary dialogue and motivate young researchers to tackle the challenges arising in the modeling of the biological and medical systems. This program is coordinated by Professors Peeyush Chandra (IITK) and Arvind K. Mishra (BHU, Varanasi). 7. Advanced Workshop on “Hyperbolic PDEs: Theory, Numerics and Applications” (HPTNA-2014): The LNM Institute of Information Technology, Jaipur organised this workshop from December 1st – 9th, 2015. Resource persons: Professors P. S. Datti, C. Praveen, Imran Biswas (TIFR-CAM, Bangalore); Prof. V. Raghavendra, (LNMIIT Jaipur); Prof. Amiya K. Pani, Sivaji Ganesh (IIT Bombay); Harish Kumar (IIT Kanpur); K. R. Arun (ISER, Trivandrum). 4. 2015-2016 : (Total Participants : 201) 1. Advanced Level Workshop on “Integral Eqations – Solvability, Analysis and Applications”: This workshop was held at Jaypee University of Information Technology, Waknaghat, Solan during October, 19-25, 2015 which was co-ordinated by Prof. Rakesh Bajaj. Thirty One (31) candidates were selected for this program. Resource Persons: Mohan Joshi (IIT Gandhinagar); N Sukavanam (IIT Roorkee); A K Nandakumaram (IISc Banglore); K Balachandran (Bharthiar University, Combatoire); Raju K George (IIST Thiruvananthapuram); Sree Hari Rao (JNT Hyderabad); Amiya K Pani (IIT Bombay); Rathish Kumar (IIT Kanpur); Anil Kumar (BITS – Goa Campus, Goa) 2. Advanced Workshop on “Controllability of Heat and Wave equations” : Held at Indian Institute Of Technology Mandi during November 16 - 20, 2015 and was coordinated by Muslim Malik (IIT Mandi ) and A. K. Nandakumaran (IISc Bangalore ). Eighteen (18) participants are selected for this program. Resource Persons: Amiya Kumar Pani (IIT Bombay); Raju. K. George

(IIST); N. Sukavanam (IIT Roorkee); Sheetal Dharmadhikari (IISER,Trivandrum); Nandakumaran (IISc); D. Bahuguna (IIT Kanpur)

A. K.

3. Advanced Workshop on “Variational Inequality (VI) & Applications”: This program was Sharda University, Knowledge Park-III, Greater Noida during January 24-28, 2016, and was coordinated by A.H. Siddiqi and P. Manchanda. Resource persons: Mohan C Joshi (IIT Gandhinagar); S Kesavan (IMSC Chennai); Amiya K Pani (IIT Bombay); Neela Nataraj (IIT Bombay); T. Gudi (IISc Bangalore); A.A. Khan (Rochester Institute of technology, USA); Barbara Lee Keyfitz (Ohio State University, USA) 4. Advanced Workshop on “Homogenization and Control: Theory & Application” (AWHCTA-2016): Indian Institute of Technology Kanpur hosted this advanced workshop during February 27-March 03, 2016. The program was coordinated by Prof. T.Muthukumar & Prof. B.V.Rathish Kumar. Resource persons: Kesavan (IMSC); Nandakumaran (IISc); Mythily (TIFR-CAM); Vanninathan (TIFR-CAM); Amiya Pani (IIT Bombay); Sivaji Ganesha (IIT Bombay); Sabu (IIST, Trivendrum); T.MuthuKumar; Pravir Dutt; BVRKumar (IIT Kanpur); Shirshendu (IISER, Kolkata). 5. Advanced Workshop on Dynamical Models in Ecological, Epidemiological Sciences and Engineering – Theory, Computations, and Real World Applications: The one week long workshop is coordinated by A. Kanaka Durga and K.L.Vasundhara and held at Stanley college of Engineering and Technology for Women, Hyderabad during 14- 19 March, 2016. Forty (40) students from various institutes attended the programme. Resource persons: Ranjith Kumar Upadhayay(ISM, Dhanbad); Sumitha Ghakkar (IIT Roorkee); V.Sree Hari Rao (JNTUH Hyderabad) ; Saroj Sahani(SAU Delhi); Peeyush Chandra(IIT Kanpur);PDN. Srinivasu (Andhra University) and M.A.S.Srinivas (JNTUH Hyderabad). 6. Advanced Level Workshop On Singularly Perturbed PDEs: Theory, Computation And Applications: The workshop was held at Indian Institute of Technology Kanpur during March 24-28, 2016. This program was coordinated by Mohan K Kadalbajoo and B.V.Rathish Kumar. Resource persons: R.K.Mohanty (SAU, Delhi); Natesan Srinivasan (IIT Guwahati); Kapil Sharma (SAU, Delhi); Mohan K Kadalbajoo (IITK); BVRKumar (IITK); Kailash Patidar (UWC, Cape Town) and Relja Vulanovic (Kent State Univ, USA).

Modeling Week and Study Group Meeting on Industrial Problems 1. 2012-2013 : (Participants: 68) Indo-European Modeling Week and Study Group Meeting on Industrial Problems (IEMWSGMIP-2012): This program was held at M.S. University of Baroda, (MSU) Vadodara in collaboration with Industrial Mathematics Group at IITB and Lapeenranta University of Technology of Technology, Finland (Modeling Week: 3rd – 8th, December 2012, Study Group Meeting – 10th – 15th, December 2012) which is coordinated by Dhanesh Patel from M.S. University of Baroda and Amiya K. Pani from IITB. Resource Persons: M.K.Abeyratne (University of Ruhuna, Sri Lanka); Andrew Lacey (Heriot-Watt University, United Kingdom); Dhanesh Patel, D.C.Vakaskar, V.D.Pathak, S.Ramamohan (M.S.University of Baroda); Ewald H. Lindner (Johannes Kepler University, Austria); Francisco Manuel Bernal Martinez (Instituto Superior Tecnico, Portugal); Hilary Ockendon (University of Oxford, United Kingdom); Mads Peter Sorense (Technical University of Denmark, Denmark); Matti Heilio, Tuomo Kauranne (University of Technology, Finland); C.W. Mehra (University of Dar es Salaam, Tanzania); Mohan C. Joshi (IITB); Morten Willatzen (University of Southern Denmark, Denmark); S.Panda (NIT, Calicut); Passi Franti (University of Eastern Finland School of Computing, Finland); Peregrina Quintela (Santiago De Compostela, Spain); B.V.Ratish Kumar (IITK); Russell Davies (Cardiff University, United Kingdom); Sergey Lupuleac (Saint Petersburg State Polytechnic University, Russia); S.Sundar (IITM); Susana Serna (Universitat Autonoma De Barcelona,Spain); A.S.Vasudeva Murthy (TIFR Bangalore); Wil H.A. Schilders (Eindhoven University of Technology, Netherlands). Sixty Eight participants covering all overing India and some from Srilanka are selected for this programme. 2. 2013-2014 : (Participants: 50) Modeling Week and Study Group Meeting on Industrial Problems (MWSGMIP-2013) This program was hosted at NIT Calicut in collaboration with Industrial Mathematics Group at IITB (Modeling Week: 2nd – 7th, December 2013, Study Group Meeting: 9th – 14th, December 2013) which was coordinated by Satyananda Panda and Suresh Kumar Nadupuri (NIT Calicut) and Amiya K. Pani (IITB). One of the objectives of the MW & SGM wass to give exposure to research scholars and young faculty members to study industrial problems requiring mathematical solutions. Resource Persons: Keijo Ruotsalainen (University of Oulu, Finland), N.G.A. Karunathilake (University of Kelaniya, Sri Lanka), A Grm (C3M, Slovenia), S. Perera (University of Colombo, SriLanka), Amiya Kumar Pani (IITB ), N G A Karunathilake (University of Kelaniya,Srilanka), Neela Nataraj (IITB), Mohan C Joshi (IITB), S Sundar (IITM), Raju K George (IIST, Trivandrum), L Chandra (IIT, Rajasthan), Dhanesh Patel (MS University,Baroda), S Panda (NIT, Calicut), Jagadeesha T (NIT Calicut ), Suresh Kumar Nadupuri (NIT, Calicut). 3. 2014-2015 : (Participants : 62) Modeling Week and Study Group Meeting on Industrial Problems (MWSGMIP-2015) Department of Applied Mathematics at MSU in collaboration with industrial Mathematics Group at IITB, Powai-Mumbai, hosted Study Group Meeting (SGM) during March, 23 rd - 27th , 2015 and as a precursor to SGM a Modeling Week (MW) has been organized during March 17 th - 21st 2015. One of the objectives of the SGM & MW is to give exposure to Research Scholars and young faculty members to live industrial problems requiring mathematical solutions. The program is coordinated by Professors D. C.Vakaskar and B.M. Shah (MSU, Baroda). Resource Persons: Professors M. C. Joshi (IITB), A. K. Pani (IITB), V. D. Pathak (MSU), S. Ramamohan (MSU), Sukavanam (IITR), R. K. George (IIST - Trivendrum), B. V. Ratish Kumar (IITK), A. S. Vasudeva Murthy (TIFR - CAM Bangalore), Nandakumar (IISc - Bangalore), S. Sundar (IITM), J. Tyagi (IITGn), Shree Hari Rao (JNTU - Hyderabad), J. J. Patel (Consultant), Mahajani (Deputy General Manager, Amtech Electronics), S. Panda (NIT Kalicut), M. N. Mehta (NIT - Surat), V. H. Pradhan (NIT - Surat), D. C. Vakaskar (MSU), D. P. Patel (MSU), B. M. Shah (MSU), Nitin Bhate (MSU), Milind Koranne (MSU).

4. 2015-2016 : (Participants : 42) Modeling Week and Study Group Meeting on Industrial Problems (MWSGMIP-2016) The Institute of Technology & Management Universe, Vadodara, in collaboration with the Department of Applied Mathematics, M. S. University of Baroda, Vadodara and Industrial Mathematics Group at IITB hosted Modelling Week (MW) during 10 - 14 March 2016 and Study Group Meeting (SGM) during 15 –19 March, 2016 at ITM Universe, Vadodara under the National Programme On Differential Equations :Theory, Computation & Applications. (NPDE-TCA 2016). Forty Two (42) candidates from all over India from various institutes were selected and attended the progarmme. Objective of Modelling Week and Study Group Meeting is to give exposure to Research Scholars and young faculty members to live industrial problems requiring mathematical solutions. The program is coordinated by Professors V. D. Pathak and Sanjay kumar Vij. Visitor Programme 1. 2012-2013 : (Total visitors : 5) I. Not Supported by NPDE-TCA 1. Prof. Carsten Carstensen, Department of Mathematics from Humboldt University of Berlin visited Department of Mathematics, IIT Bombay as a distinguished professor (supported by the Department) for a period of one month from Feb. - March, 2012 for the on-going research collaboration. During his visit, we had organised an advanced level workshop on Adaptive finite element methods in IIST, Trivandrum with full financial support from IIST, for the workshop. C. Carstensen, A. Dond, Neela Nataraj and A.K. Pani have worked on “Aposteriori mixed finite element error analysis for non-symmetric and indefinite elliptic problems”. 2. Vidar Thomee from Chalmers University of Technology, Sweden was been invited in the month of Jan. – Feb. 2012 under “Visitor's Programme” and he gave a series of talks in the Department of Mathematics, IIT Bombay. 3. Jin Yun Yuan, Oishi and Pedro Jamazio from Federal University of Parana, Brazil visited Department of Mathematics, IIT Bombay for the on-going research collaboration. During their visit we had worked on spectral finite element methods for Kelvin-Voigt fluid flow problems. II. Partially Supported by NPDE-TCA 1. Dr. Samir Karaa, Department of Mathematics and Statistics from Sultan Qaboos University, Sultanate of Omen, Omen visited IIT Bombay for the NPDE-TCA Programme from June 03 – 09, 2012 and only a partial support in terms of honorarium is provided by NPDE-TCA. During his visit he was collaborated with our on-going research programme in Department of Mathematics, IIT Bombay. A.Karaa, A.K.Pani and S.Yadav have worked on “An hp-estimates for linear hyperbolic integral differential equations”. 2. Dietmar Gallistl, Institute of Mathematics from Humboldt-Universitat of Berlin had been invited to Department of Mathematics, IIT Bombay during the period 7 th -13th October, 2012 and collaborated with our on-going research program under National Program on Differential Equations – Theory, Methods & Applications (NPDE-TCA). A nominal support was provided through NPDE-TCA. C.Carstensen, D. Gallistl and Neela Nataraj worked on “Comparison result of non-standard P2 Finite element Methods for the Biharmonic Problems”.

2. 2013-2014 : (Total visitors : 14) 1. Prof. Philip L. Roe (University of Michigan): visited India during 15th May to 14th June (roughly), 2013 as an INSA visiting professor. His visit was funded by INSA, whereas the local hospitality for his stay in IIT Bombay during the period of 22nd May to 1st June was taken care by NPDE-TCA (with partial support from NPDE-TCA). During this period, Prof. Roe took part as a resource person in the advanced level workshop on Theoretical and Computational Aspects of Nonlinear Waves and gave 5 lectures each of 90 minutes duration. 2. Prof. Daniele Boffi (University of Pavia, Italy) visited the Department of Mathematics, IISc Bangalore during the period July 6th-20th, 2013 (with a partial support from NPDE-TCA). Prof. Boffi is one of the resource persons in the CIMPA-NPDE-NBHM research school on “Current Trends in Computatonal Methods for PDEs" which held during July 8-19, 2013 at the Department of Mathemaitcs, IISc Bangalore. Prof. Boffi delivered a series of lectures on mixed finite element formulations and eigen value problems. The research school has been a great success because of the renowned speakers like Prof. Boffi. There were several discussions and interactions between the participants and Prof. Boffi. Prof. Chandrasekhar S. Jog from the Department of Mechanical Engineering, IISc Bangalore had discussed some of his research problems with Prof. Boffi. 3. Prof. Lucia Gastaldi (University of Brescia, Italy) visited the Department of Mathematics, IISc Bangalroe during July 6th-20th, 2013 (with a partial support from NPDE-TCA ). Prof. Gastaldi devilered a series of lectures on mixed variatioanl problems and mixed eigen problems in the CIMPA-NPDe-NBHM research school on ``Current Trends in Computational Methods for PDEs" held at the Department of Mathematics, IISc Banglaore during July 8th-19th, 0213. There were a total of 60 participants in the research school out of which 40 are from India. All the participants have benefitted by the lecutures of Prof. Gastaldi. 4. Prof. C. Carstensen visited BITS, Goa to give a series of lectures in the Advanced Workshop on “Mathematical Foundation of Advanced Finite Element Methods” (MFAFEM-2013) and IITB for research collaboration during 28th Dec. - 6th Jan, 2014. 5. Prof. Gudo Kanschat (University of Heidelberg) visited IITB during 24th Feb to 6th March, 2014. He was here for research collaboration and to give a series of lectures in the workshop on “FEM using Deai II”. 6. Prof. Luca Pavarino (Department of Mathematics, Univ. Milano, Italy) visited IIT Kanpur from February 14th-23rd, 2014 (with full support from NPDE-TCA) . 7. Prof. Daniele Boffi (Department of Mathematics, Univ. Pavia, Italy) visited IIT Kanpur from February 23rd to March 3rd, 2014 (with full support from NPDE-TCA). 8. Prof. D.A.S.Rees (University of Bath, UK) visited IIT Kanpur during March 18 th – 26th , 2014 (with full support from NPDE-TCA). The lectures were attended by 60 faculty/Ph.D. students of SADEAFFP-2014 and IITK. 9. Prof. Matin Bees (York University, UK) visited IIT Kanpur during March 19- April 4, 2014 (with full support from NPDE-TCA). He has given a series of Four 90 minute talks in IIT Kanpur. 10. Prof. Graeme fairweather (Colorado School of Mines USA) visited IIT Bombay, LNMIIT Jaipur and SAU, Delhi for “ Advanced Level Workshop On Orthogonal Spline Collocation Methods for Partial Differential Equations” (OSCM-2014) . During his visit, he gave two lectures in IITB and two lectures in LNMIIT Jaipur. Prof. Graeme visited SAU, Delhi during March 21st – 24th , 2014 (with a partial support from NPDE-TCA).to give series of lectures in OSCM-2014 workshop.

11. Prof. Jacques Henry visited SAU Delhi during March 9th – 24th , 2014 (with full support from NPDE-TCA). During his visit at SAU, he has given four lectures at different Indian Universities . 12. Prof. Samir Kaara from Sultan Qaboos University, Sultanate of Oman has visited IIT Bombay during 1st – 10th June, 2014 (with a partial support from NPDE-TCA).for research collaboration and discussions. 13. Dr. Soumaya Bajpai visited IITB from March 3rd – 10th , 2014. She was here for research discussion and collaboration. 14. Dr. Anil Kumar Pundir visited SAU Delhi from February 10 th – 17th , 2014 for a research collaboration and discussion on Controllability of PDE (under preparation) with Prof. AK Pani. 3. 2014-2015 : (Total visitors : 8) 1. Prof. Rakesh from Department of Mathematical Sciences, University of Delaware, Newark, DE19808, USA had been invited at Tata Institute of Fundamental Research, Centre for Applicable Mathematics, Bangalore, (TIFR-CAM) India. An advanced instructional school on the theoretical and numerical aspects of Inverse Problems was organized from June 16 – 28, 2014 at TIFR-CAM, Bangalore. Prof. Rakesh gave a series of lectures in the workshop held in TIFR-CAM and had discussed with Prof. Venky Krishnan on Inverse Problems. The lecture & research topics included were Electrical impedance tomography (EIT), Cloaking, Hybrid imaging, Tensor tomography, Spherical Radon transform, Inverse problems for Einstein equations. 2. Prof. Lutz Tobiska from Uni-Magdeburg, Germany was invited for the advanced workshop on “Finite element methods for Navier-Stokes eqautions” during September 8 th – 12 th 2014 at SERC, IISc Bangalore to give a series of lectures in the workshop. Professor Tobiska is collaborating with Sashikumar Ganesh, the host in IISc on an ongoing research programme on stabilized methods. 3. Prof. Jeffrey Ovall, Portland State University visited to the Department of Mathematics and Statistics at the Indian Institute of Technology Kanpur during November - December, 2014. During his visit, he gave a series of research talks on a posteriori error estimation for finite element methods and interacted with departmental faculty members and research scholars working in the broad areas of Computational Mathematics so as to explore joint collaborative research projects. 4. Prof. Roberta Musina visited IIT Delhi during January 13th – 26th , 2015. During the visit at the Mathematics Department of the Indian Institute of Technology Delhi, some open problems in a research field of current and international interest were discussed. In particular, they dealt with classes of variational problems driven by nonlocal differential. During her visit she also gave two seminars in the department. In the first one she surveyed the classical theory of variational inequalities driven by the conventional Laplace operator. In the second one she reported about some recent results about the Dirichlet and the Navier Laplace operators. Those include noncompact Dirichlet problems of Brezis-Nirenber type for the fractional Laplace operator, Kirchoff equations, and singular problems involving the Heaviside functions. 5. Prof. Samir Karaa visited IIT Bombay during February 2nd – 10th , 2015 for a research discussion and collaboration with Prof. Amiya K. Pani. He had also visited South Asian University for their gave a talk. During his visit, they worked on an ongoing research project on Finite volume methods for fractional-diffusion problems and also on posteriori analysis for a second order wave equation.

6. Professor G. Fairweather from Colorado School of Mines, Golden is presently visiting IIT Bombay and later on will be visiting BITS, Goa for few days. During his visit ( 14th Feb-28th Feb,2015), he will be collaborating with Professor Pani from IITB on an ongoing project Orthogonal spline collocation methods for Schrodinger equations and also on qualocation method. At BITS, Goa, he will be collaborating with Professor P. Dhanumjaya and his group on numerical solution to Helmohltz equation. 7. Professor C. Carstensen from Humboldt University, Berlin is presently visiting IIT B and subsequently he also visited IISc, Bangalore. During his visit ( Feb 14- March 3, 2015), he will be collaborating with the research gorup in IITB and the research group in IISc, Bangalore on adaptive finite element methods. He will give a Departmental Colloquium in IITB. 8. Professor Vidar Thomee from Chalmerse Univ. Technology, Sweden will be visiting TIFR (CAM) and also IITB. During his visit ( Feb 18- March 4,2015), he will collaborate on an on going project with Professor Vasudeva Murthy on nonlocal parabolic problems and in IIT B, a part from collaborating on mixed finite element methods for parabolic problem in nonconvex polygonal domain, Professor Thomee will give a Departmental colloquium. 4. 2015-2016: (Total visitors : 8) 1. Prof. Sangita Yadav had visited Indian Institute of Technology Bombay under the auspices of National Programme on Differential Equations: Theory, Computations And Applications (NPDE-TCA). She has been invited through the visitors program of NPDE-TCA for research collaboration and discussion. 2. Prof. Ricardo Ruiz- Baier from University of Lausanne, Switzerland had visited IIST from 22nd September to 3rd October, 2015 under the auspices of National Programme on Differential Equations: Theory, Computations And Applications (NPDE-TCA). During his visit, he focused on the numerical approximations of optimal control problems governed by specific partial differnetial equations, which have various applications in scientific and engineering problems. 3.Prof. Andreas Veeser from Department of Mathematics' F. Enriques' University of Milan has visited IIT Bombay from 4 July, 2015 to 18th July, 2015 for the CIMPA School on Current Research in Finite Elements held during 6th July, 2015 to 17th July, 2015 at Indian Institute of Technology, Bombay. He was here for research collaboration and discussion. 4. Prof. Marcus Gerritsma had visited IIT Kanpur during 20th March - 24th March, 2015. 5. Prof. Srikumar Panda had visited Department of Mathematics, IIT Kharagpur for collaborative research work with Dr. R. Gayen under NPDE-TCA visitors program for the period April 22, 2015May 20, 2015. 6. Prof. Sheetal Dharmatti has visited Indian Institute of Technology Bombay from 2nd May, 2015 under the auspices of National Programme on Differential Equations: Theory, Computations And Applications (NPDE-TCA). She has been invited through the visitors program of NPDE-TCA for research collaboration and discussion. 7. Prof. Pankaj Mishra from South Asian University, Delhi had visited Department of Mathematics, IIT Bombay for collaborative research work with Prof. Amiya K Pani under NPDE-TCA visitors program for the period 28th February, 2016 – 15th March, 2016.

8. Prof. Graeme Fairwhether visited IIT Bombay during 26th February – 14th March, 2016 for research collaboration work with Prof. Amiya K Pani and his group to continue their earlier collaborations on orthogonal collocation methods for the nonlinear Schrodinger equations. Prof. Fairwhether will also visit Panjab University to interact with Prof. Kapil Sharma, Prof. Pankaj Misra and Prof. A K Pani. During his visit, they plan to continue their investigations on singularly perturbed convection-diffusion-reaction problem and parabolic equations.