Prof. Santosh Kumar Upadhyay
Professor
Department of Mathematical Sciences,IIT BHU.
skupadhyay.apm@iitbhu.ac.in
9450112714
Area of Interest:
Wavelet Analysis, Distribution Theory, Pseudo differential operator
Education:
 D. Sc. Mathematics: B.R.A. Bihar University, Muzaffarpur (2006)
Title of Research: A study of Pseudodifferential Operators.
 Ph. D. Mathematics: Banaras Hindu University, Varanasi (1993)
Title of Research: On Certain Weighted L_{p}
spaces and Fourier and Hankel Transforms of Distribution.
 M. A. Mathematics: Banaras Hindu University, Varanasi(1988).
 B.A. Mathematics(Hon), Economics, Statistics: Banaras Hindu University, Varanasi (1985).
Current Position:
 Professor in Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi.
Experience: Teaching
 Lecturer, Department of Mathematics, B.R.A. Bihar University, Muzaffarpur, 18 Nov. 1996 to 26 Dec. 2002.
 Senior Lecturer, Department of Mathematics, Vir Kunwar Singh University, Ara, 27 Dec. 2002 to 5 Dec. 2005.
 Reader, Department of Mathematics and Statistics, D.D.U. Gorakhpur University, Gorakhpur, 6 Dec. 2005 to 29 Jan. 2008.
 Associate Professor, Department of Applied Mathematics, IT BHU, Varanasi, 30 Jan. 2008 to .
 Functional analysis
 Distribution theory
 Wavelet analysis and its applications
 Mathematical method
 Pathak R.S. and Upadhyay S.K., Wpspaces and Fourier transform. Proceedings of the American Mathematical Society, 121(3), 733–738, 1994.
 Pathak R. S. and Upadhyay S. K., U_{µ}^{p}spaces and Hankel transform, Integr Transf. Spec. F. 3(4), 285–300, 1995.
 Upadhyay S. K., H_{µ}^{p}spaces and Hankel transform, Proc. Math. Soc. 11, 71–76, 1996.
 Pathak R. S. and Upadhyay S. K., Pseudodifferential operators involving Hankel transforms, J. Math. Anal. Appl, 213(1), 133–147, 1997.
 Pathak R. S. and Upadhyay S. K., Convolution in W^{p}_{M,a} space, Rend. Sem. Mat. Univ. Padova, 98, 57–65, 1997.
 Upadhyay S.K., Convolution in K_{r}(M_{p}) space, J. Int. Acad. Phys. Sci, 3, 8187, 1999.
 Upadhyay S. K., Uniqueness class of a Cauchy problem in W_{M}_{1,1/b}^{Ω1,1/a,m} space, Progr. Math. (Varanasi), 34 (12), 31–38, 2000.
 Upadhyay S. K., Pseudodifferential operator on Gelʹfand and Shilov spaces, Indian J. Pure Appl. Math., 32(5), 765–772, 2001.
 Pathak R. S. and Upadhyay S. K., L_{µ}^{p} boundedness of the pseudodifferential operator associated with the Bessel operator. J. Math. Anal. Appl., 257 (1), 141–153, 2001.
 Upadhyay S. K., Asymptotic series of general symbol and pseudodifferential operators, Integr Transf. Spec. F., 14 (1), 87–95, 2003.
 Upadhyay S. K., Wspaces and pseudodifferential operators, Appl. Anal., 82 (4), 381–397, 2003.
 Upadhyay S. K., The Hankel transformation of the Banachspacevalued ultradistributions, Integral Transf. Spec. F., 14 (5), 459–467, 2003.
 Upadhyay S. K., L_{µ}^{p} Boundedness of localization operators associated to Bessel left regular representations, J. Math. Anal. Appl., 311 (1), 76–91, 2005.
 Upadhyay S. K., L^{p} norm inequality of the product of pseudodifferential operators involving Hankel transformation, Appl. Anal., 85(4), 415–428, 2006.
 Upadhyay S. K. and Yadav R. N., Generalized Hankel convolution on Banach space valued Gevery ultradistribution [Generalized Hankel convolution on Banach space valued Gevrey ultradistributions], J. Nat. Acad. Math. India, 21, 65–78, 2007.
 Upadhyay S.K., Minimal and Maximal Pseudodifferential Operators on Gel’fandShilov Space, Progr.Math, (Varanasi), 41 &42, 89102, 2008.
 Upadhyay S. K., Yadav, R. N. and Debnath L., The ndimensional continuous wavelet transformation on Gelfand and Shilov type spaces, Surv. Math. Appl., 4, 239–252, 2009.
 Upadhyay S.K. Pseudodifferential operators on W^{Ω}(C^{n})space, J. Int. Acad. Phys. Sci., 14 (1), 53–60, 2010.
 Upadhyay S.K., Pseudo Differential Operator on H_{µ}(A)  type space, Progr.Math, (Varanasi), 43, 44 & 45, 2936, 2009, 2010 & 2011.
 Upadhyay S.K., Hankel Convolution of Ultradistribution of Exponential Growth, J. Com. Math. Sci., 2(1),145152, 2011.
 Pathak R.S, Upadhyay S.K., and Pandey R.S., Bessel Convolution Product, Rend. Sem. Mat. Politec.Torino., 69(3), 2011.
 Upadhyay S.K. and Pandey R.S., Properties of Hausdorff Operator on a Subspace of L^{p}(R) , Investigation in Mathematical Sciences, 1,127135, 2011.
 Upadhyay S.K, Pandey R.S, The H^{p}(R) Boundedness of Hausdorff Operator Involving Wavelet Transformation, Journal of wavelet theory and application, 5 (1), 17, 2011.
 Upadhyay S.K, Some Characterization of H_{µ}Type Spaces, J. Int. Acad. Phys. Sci., 15 (1), 25–32, 2011.
 Upadhyay S.K., Pandey R.S. and Tripathi Alok, Some Properties of Bessel wavelet convolution product, Proc. of Jammu Mathematical Society, 2011.
 Upadhyay S.K., Yadav R.N. and Debnath L., On Continuous Bessel wavelet transformation associated with the Hankel Hausdorff Operator, Integr Transf. Spec. F., 23(5),315323,2012.
 Upadhyay S. K. and Tripathi Alok, Continuous Watson Wavelet Transform, Integr Transf. Spec. F., 23(9),639647, 2012.
 Upadhyay S.K., Yadav R.N. and Debnath L., Infinite Pseudo Differential Operators on W_{M} (R^{n} ) space, Analysis, 32(2), 10011012, 2012.
 Upadhyay S.K., Yadav R.N. and Debnath L., Properties of Hankel Housdroff Operator on Hardy space H^{1}(0, infinity), Analysis, 32, 221230, 2012.
 Upadhyay S.K., Pandey Ravi Shankar and Tripathi Alok, The Spectrum of Housdroff Operator on a subspace of L^{2}( R^{n}) , Analysis 33, 2533, 2013.
 Upadhyay S.K., Kumar Anuj and Dubey Kumar Jitendra, Asymptotic Series of General Symbol of PseudoDifferential Operator Involving Fractional Fourier Transform, ISRN Mathematical Analysis, 2013, 2013, DOI 10.1155/2013/501382.
 Upadhyay S.K., Kumar Anuj and Dubey Kumar Jitendra, Characterization of space of type W and pseudodifferential operator of infinite order involving fractional Fourier transform, J. PseudoDifferential Operator Application, 5, 215230, 2014.
 Upadhyay S.K., Pseudo Differential Operators on W^{Ω}(C^{n}) space, Palestinian Journal of Mathematics, 3(2), 256268, 2014.
 Upadhyay S.K., Pandey Ravi Shankar and Mohapatra R.N. H^{p} Boundedness of Hankel Hausdroff Operator involving Hankel Transform, Dynamics of Continuous, Discrete and Impulsive Systems,243258 2014.
 Upadhyay S.K., Kumar Anuj, Characterrization of W ptype of spaces involving fractional Fourier transform, Journal of Inequalities and Applications, 2015, DOI 10.1186/s1366001405449.
 Upadhyay Prateep, Upadhyay S.K., Colour Image Encryption  A Wavelet Transformation Associated with Artificial Neural Network Approach, International Journal of Computer Applications (0975  8887),124(7), 2015.
 Upadhyay S.K., Tripathi Alok, Calderon’s Reproducing Formula for Watson Wavelet Transform, Indian J. Pure Appl. Math., 46(3), 269277, 2015.
 Pandey J.N. and Upadhyay S.K., The Continuous Wavelet Transform and Window Functions, Proceedings of the American Mathematical Society, 143(11), 47594773, 2015.
 Pathak, R.S. and Upadhyay, S.K., Cauchy Wavelet transform of ultra –distributions in tube domains, Complex variables and Elliptic Equations , 60 (11), 15531566, 2015.
 Upadhyay S.K., Tripathi Alok and Kumar Anuj, Approximation in Watson wavelet Transform, Southeast Asian Bulletin of Mathematics, 39,149162, 2015.
 Dubey, Jitendra Kumar, Kumar Anuj and Upadhyay S.K., “Pseudo Differential Operators and Localization Operators on S_{v}^{µ}(R) Space Involving Fractional Fourier Transform”, Novi Sad J. Math. , 45(1), 285301, 2015.
 Upadhyay, S.K. and Dubey, Jitendra Kumar, “Pseudo–differential operators of infinite order on W^{Ω}_{M}(C^{n}) space involving fractional Fourier transform”, J. PseudoDiffer. Oper. Appl., 6(1), 113133, 2015.
 Upadhyay, S.K. and Singh, Reshma, “Integrability of the continuum Bessel wavelet kernel”, International Journal of Wavelets, Multiresolution and Information Processing,13(5), 2015, DOI: 101142/S0219691315500320.
 Upadhyay S.K. Dubey Jitendra Kumar, “Calderon’s formula for fractional wavelet transform”, ProceedingsInternational conference on Fractional Differentiation and its Applications, Novi Sad, Serbia, July 1820, 2016, 745752.
 Upadhyay, S.K. and Singh, Manmohan Chauhan, L^{p} Norm Inequality of the Product of PseudoDifferential Operator of Homogeneous Symbol involving Hankel Transformation, Investigation in Mathematical Sciences, vol. 5, 2016, 5570.
 Upadhyay, S.K. and Dubey, Jitendra Kumar, Wavelet Convolution Product involving Fractional Fourier Transform, J. Frac. Cal. Appl. Analysis , Vol 20 (1), 173189, 2017.
 Upadhyay, S.K. and Singh, Reshma, Bessel Wavelet Transform on the Spaces with Exponential Growth”, FILOMAT 31:8 (2017),24592466.
 Upadhyay, S.K., Singh, Reshma and Tripathi Alok, “The relation between Bessel wavelet convolution product and Hankel convolution product involving Hankel transform”, International Journal of Wavelets, Multiresolution and Information Processing, Vol. 15 No.3(2017).
 Upadhyay, S.K., Singh, Reshma “Abelian theorems for the Bessel wavelet transform”, The Journal of Analysis (Proceedings: ICMAA 2016), 112.
 SrivastavaH. M, Upadhyay, S.K, KhatterwaniK., “A Family of Pseudo Differential Operators on the Schwartz Space Associated With the Fractional Fourier Transform” , Russian Journal of Mathematical Physics, Vol 24 No. 4 (2017), 534543.
 Upadhyay, S.K, Khatterwani K., “Continuous Fractional Wavelet Transform”, Journal of International Academy of Physical Sciences, Vol. 21 No. 1 (2017), 5561.
 Upadhyay, S.K, Kumar, Anuj, “Pseudo Differential Operators and Wavelet Transform Associated With Fractional Fourier Transform”, GANITA, Proceedings of NCMAA, Vol 67(3), 2017,7995.
 Upadhyay, S.K. and Singh, Manmohan Chauhan, “Pseudo Differential Operators of Homogenous Symbol Associated With nDimensional Hankel Transformation”, Journal of the Indian Soc 85, (34), 2018.
 Upadhyay, Prateep, Upadhyay, S.K, Shukla, K.K. ,”Denoising 1D Signal Using Wavelets”, Springer CCIS Series (Accepted),2017.
 Upadhyay, Prateep, Upadhyay, S.K, Shukla, K.K., “Heat Equation Based ECG Signal Denoising in The Presence of White, Coloured and Muscle Artifact Noises”, Springer AISC Series (Accepted),2018.
 Upadhyay, Prateep, Upadhyay, S.K, Shukla, K.K,”A Mathematical Model of Consumers’ Buying Behaviour Based On Multiresolution Analysis”, Procedia Computer Science, Vol 122(2017), 564571.
 Upadhyay, S.K., Singh, Reshma, “Linear Time Invariant Filter associated with Bessel Wavelet Transform”, J. Anal. (2018) 26: 323332.
 Upadhyay, S.K, Kumar, Anuj, “The continuous fractional wavelet transform on Wtype spaces”, Journal of the Indian Soc. 85, (34), 2018
 Upadhyay, S.K, Khatterwani K., “Characterizations of certain Hankel transform involving RiemannLiouville fractional derivatives”, Computational and Applied Mathematics (2019) 38:24.
 Srivastava H. M., Khatterwani K., Upadhyay, S.K., “A certain family of fractional wavelet transformations”, Math Meth Appl Sci.2019; 42, 31033122.
 Pandey J.N., Maurya J.S., Upadhyay S.K.and Srivastava H.M., “Continuous Wavelet Transform of Schwartz Tempered Distributions in .” Symmetry 2019, 11, 235.
Projects  Details of Projects 
Major Projects amount mobilized with grants above 5.00 Lakhs  up to 30.00 Lakhs  Wavelet and its Application, Amount 16 Lakhs ,CIMS (DST), Coinvestigator 
Minor Research Project for new faculty, IT BHU, Varanasi  Amount 1 Lakh 
Name of Student  Year of Completion  Title of Thesis  Coguides (if any)  
R.N.Yadav  2010  Pseudodifferential operators on certain distribution spaces  Nil  
Alok Tripathi  2013  Watson Wavelet and related wavelet transforms  Nil  
Anuj Kumar  2015  A study of pseudodifferential operators involving fractional Fourier transform  Nil  
Jitendra Kumar Dubey  2017  Pseudo Differential Operators associated with Fractional Fourier Transform  Nil  
Reshma Singh  2017  Study on the Bessel Wavelet Transform  Nil  
Manmohan Singh Chauhan  2019  Some Observations on Certain Class of Pseudo Differential Operators.  Nil  
Komal Khatterwani  2019 (Submitted) 
Some Observations of PseudoDifferential Operators and Wavelet Transform Involving Fractional Calculus  Nil  
Prateep Upadhyay  2019 (Submitted) 
Wavelet Transformation Based Denoising of PWC Signals, ECG Signals and MR Images 
Shukla


Pragya Shukla  In Progress (July 2017) 
Spectral analysis of Pseudodifferential operator and its applications  Nil  
Jay Singh Maurya  In Progress (July 2017) 
Wavelet transform of distribution on various spaces  Nil  
Kush Kumar Mishra  In Progress (July 2018) 
Nil  
Mohd. Sartaj  In Progress (January 2019) 
Nil  
Amit  In Progress (July 2019) 
Nil  
Babita  In Progress (July 2019) 
Nil  
Sitaram Yadav  In Progress (July 2019) 
Nil 
M. Tech. Produced:
Name of Student  Year of Completion  Title of Thesis 
Shishir Kumar  20122013  
Priyanka Baban  20132014  Color image encoding using fractional wavelet transform associated with wavelet transform 
Abhishek Mani  201516  Construction of Orthogonal wavelets and it’s Relation with Filter Banks 
Nikhil Sharma  201617  Study of Lossless Compression of Medical Image Data Based on Different Algorithms and Techniques 
Life Members of Various Academic Bodies:
1.Academy of Progress of Mathematics.
2.BHU Mathematical Society, BHU.
3.National Academy of Mathematics.
4.International Academy of Physical Sciences.
5.Jammu Mathematical Society, Jammu.
6.Society of Special functions.
7.Indian Society of Mathematics and Mathematical Sciences.
2.BHU Mathematical Society, BHU.
3.National Academy of Mathematics.
4.International Academy of Physical Sciences.
5.Jammu Mathematical Society, Jammu.
6.Society of Special functions.
7.Indian Society of Mathematics and Mathematical Sciences.
Reviewer/ Member of the Editorial Board in Various Journals:
1. Assistant Editor, Progress of Mathematics, BHU.
2. Member of the editorial board, Journal of special function and Its Applications.
1. Assistant Editor, Progress of Mathematics, BHU.
2. Member of the editorial board, Journal of special function and Its Applications.
Organized Conference / Workshop:
 Academic Secretary, Recent Trends in Pure and Applied Mathematics, Department Applied Mathematics, IT (BHU), 2009.
 Member of organizing committee in the Conference of Modeling and Simulation, Department Applied Mathematics, IT (BHU), 2010.
 Training Program on Integral Transform, Wavelets, Distribution theory and their Applications, DSTCIMS, (BHU), from 12^{th} July 21^{th} July 2012.
 Organized a Symposia in 78^{th} Annual Conference of Indian Mathematical Society, Wavelet Transform and Its Applications, Department of Mathematics and DSTCIMS, Banaras Hindu University, 22^{th} January 25^{th} January, 2013.
 Member of Organizing Committee in Conference of Indian Mathematical Society, Department of Mathematics and DSTCIMS, Banaras Hindu University, 22^{th} January 25^{th} January, 2013.
 Member of Organizing Committee in International Conference of The Indian Mathematics Consortium (TIMC) in cooperation with American Mathematical Society (AMS). During 1417 Dec, 2016. DSTCentre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi221005.
 Organized a Short Term Course on “Algebra, Analysis & Applications2017 in the Department of Mathematical Sciences, IIT(BHU), Varanasi from 3^{rd} July 9^{th} July, 2017.
Attended Conference of International Academy of Physical Sciences:
 Paper (“Convolution in K_{r}(M_{p}) space”) presented in the first conference of International Academy of Physical Sciences which was held in Mahatma Gandhi Kashi Vidyapeeth, Varanasi in 1996.
 Paper presented in the conference of International Academy of Physical Sciences which was held in DDU Gorakhpur University in the department of mathematics and statistics, Gorakhpur in 2004
 Presented a paper (“Pseudo Differential operator on W^{Ω}(C^{n}) space “)in the conference of International Academy of Physical Sciences which was held in University of Allahabad, Allahabad in 2010.
 Presented a paper (“The H^{p}(ℝ) Boundedness of Hausdorff Operator Involving Wavelet Transformation”) in the conference of International Academy of Physical Sciences which was held in University of Petroleum and Energy Dehradun, Dehradun in the year 2011.
 Delivered a talk on “Pseudo Differntial Operator on W^{Ω} space”in the conference of International Academy of Physical Sciences which was held in Guru Ghasidas University Bilaspur, Bilaspur in 2008.
 Delivered a talk on “Pseudo Differential operator on W^{Ω}(C^{n}) space” in the conference of International Academy of Physical Sciences which was held in S.V.N.I.T. Surat, Surat in 2011.
 Delivered a talk on “A construction of Wavelet Transform”, was given in the conference of International Academy of Physical Sciences. IIIT Jabalpur, March 2022, 2014.
 Delivered a talk in 17th International Conference of Physical Sciences on Recent Trends in Physical Sciences, January 1618, 2015, Department of Mathematics, University of Rajasthan.
 Delivered a talk on “Cauchy Wavelet Transform on Tube Domains” in International Academy of Physical Sciences which was held in Guru Jambeshwar University Hisaar, Haryana in 2017.
Invited Talk:
 Invited talk on “Properties of Watson Wavelet Transform”, was given in the International Conference of Special Function and its Applications, SVNIT Surat, June 2729, 2012.
 Invited talk on “Watson Wavelet Transform” was given in “78^{th} Annual Conference of Indian Mathematical Society”, January 2225, 2013, in the Department of Mathematics, B.H.U., Varanasi
 Invited talk on “Product of Distribution” was given in “Non Linear Functional Analysis and Applications”, March 410, 2013 in DSTCIMS (B.H.U.), Varanasi.
 Presented talk on “L^(p)boundedness of localization operators involving Watson Transform associated to regular representations and wavelet multipliers”, was given in ICRPAM 69 November, 2014, Antalya Turkey.
 Invited talk on “Wavelets and application” was given in NIT Surat on 13^{th} February 2015.
 Short Term Advanced Training Programme on Integral Transformations, Distributions and Wavelet Analysis, December 1418, 2015, Department of Applied Mathematics, ISM, Dhanbad.
 Invited talk on “Calderon’s formula for fractional wavelet transform”, was given in International Conference on Fraction Differentiation and its Applications, Novi Sad, Serbia, July 1820, 2016.
 Presented talk on “Abelian Theorems of the Bessel Wavelet Transform”, was given in International Conference on Mathematical Analysis& its Applications, November 28December 02, 2016.
 Invited talk on “Relation between Bessel Wavelet Convolution Product & Hankel Convolution Product” was given in “Silver Jubilee Conference of the Jammu Mathematical Society and a National Seminar on Recent Developments in complex Analysis, Operator Theory and Related Areas”, October 2022, 2016.
 Expert guest speaker in “Advanced Numerical and Analytical Methods for Engineers and Scientists”, organized by Department of Mathematical Sciences, IIT(B.H.U.), from January 1218, 2017.
 Expert guest speaker in “Transform Methods in Sciences and Engineering” organized by Sardar Vallabhbhai National Institute of Technology, Surat from March 0610,2017.
 Presented talk on “Wavelet Transform on Schwartz space” was given in “ International Conference on Fourier Analysis and Wavelets”, organized by Ramanujan Institute for Advance study in Mathematics, University of Madras from March 2125,2017.
 Delivered a lecture on “Wavelet Transform on Window Function” in Short Term Course on “Algebra, Analysis & Applications2017 in the Department of Mathematical Sciences, IIT (BHU), Varanasi from 3^{rd} July 9^{th} July, 2017.
Session Chaired in Various Conferences:
 Chaired the Paper Presenting Session of Mathematical Modelling, Analysis and Geometry in the 11^{th} International Conference of International Academy of Physical Sciences on Mathematical Modelling, Analysis and Geometry, University of Allahabad, 2022 February,2010.
 Chaired the Paper Presenting Session in the International Conference on Special Functions and their Applications (ICSFA2012), SVNIT, Surat, 2729 June, 2012.
 Chaired the session of Symposia of Wavelets and their Applications in 78^{th} Conference of Indian Mathematical Society, Department of Mathematics and DSTCIMS, BHU, 22 25 January, 2013.
 Chaired the Paper Presenting Session in the International Conference of International Academy of Physical Sciences, IIIT, Jabalpur,2022, March, 2014.
 Chaired the Paper Presenting Session and other Sessions in the International Conference of International Academy of Physical Sciences, Department of Mathematics, University of Rajasthan, 1618, January, 2015.
 Session chaired in the paper presenting session on wavelet analysis in the International Conference of The Indian Mathematics Consortium (TIMC) in cooperation withAmerican Mathematical Society(AMS) During 1417 Dec, 2016.
 Session chaired in the paper presenting session in the annual conference of Mathematical Society of Banaras Hindu University on Recent trends in Mathematical analysis and its applications, Feb 1718, 2017.
Training Programs and Refresher/ Orientation Courses:
1. 42 Day Research Training Programme on Generalized Special Function of matrix Arguments, Trivandrum, 1995.
2. Orientation Course, BRA Bihar Univ., Muzaffarpur, 1997.
3. 3Weeks Refresher Course on Linear Algebra, Linear Programming and Dynamical System, Academic Staff College, BRA Bihar Univ., Muzaffarpur, 1999.
4. 3Weeks Refresher Course, Univ. of Allahabad, Allahabad, 2005.
1. 42 Day Research Training Programme on Generalized Special Function of matrix Arguments, Trivandrum, 1995.
2. Orientation Course, BRA Bihar Univ., Muzaffarpur, 1997.
3. 3Weeks Refresher Course on Linear Algebra, Linear Programming and Dynamical System, Academic Staff College, BRA Bihar Univ., Muzaffarpur, 1999.
4. 3Weeks Refresher Course, Univ. of Allahabad, Allahabad, 2005.
Attended National Conferences:
Name  Place/Year  Contribution 
Indian Mathematical Society  Pune University, Pune, 1994  Paper Presented 
Ramanujan Mathematical Society  Rishikesh (India), 1995  Paper Presented 
Conference of BHU Mathematical Society  Banaras Hindu Univ., Varanasi, 1995  Paper Presented 
VI Annual Conference on Mathematical Society  Banaras Hindu Univ., Varanasi, 2000 
Paper Presented 
A Conference of Society of Special Fucntion and Application  Banaras Hindu Univ., Varanasi, 2002. 
Paper Presented 
A Symposium on Wavelet,  Banaras Hindu Univ., Varanasi, 2002  Attended 
XVII Annual Conference of Ramanujan Mathematical Society  Institute of Technology, Banaras Hindu Univ., Varanasi, 2002. 
Paper Presented 
Conference of Molecular Physics  BRA Bihar Univ., Muzaffarpur,2003  Paper Presented 
Annual Conference on Mathematical Scoiety  Banaras Hindu Univ., Varanasi, 2006  Paper Presented 
Annual conference of Jammu Mathematical Society  Univ. Of Jammu, Jammu, 2010  Invited Talk 
Annual conference of Indian Mathematical Society  NIT, Surat, 2010  Invited Talk 
Annual conference of Indian Mathematical Society, 
University of Jammu, 2011.  Invited Talk 
Attended International Conferences:
International Symposium of Generalized Functions and their Applications.  Banaras Hindu Univ, Varanasi, 1991 

Conference of International Academy of Physical Science.  Mahatma Gandhi Kashi Vidyapeeth, Varanasi, 1996  Paper Presented 
International Conference on Functional Spaces and Application in Differential Equation.  Delhi Univ., Delhi, 1997  Paper Presented 
International Conference 
Banaras Hindu Univ., Varanasi, 1998  Paper Presented 
International Conference on Analysis, Algebra and Geometry.  Banaras Hindu Univ., Varanasi, 2000  Paper Presented 
Conference of International Academy of Physical Sciences,  Gorakhpur Univ., Gorakhpur, 2004. 
Paper Presented 
International Academy of Physical Sciences in the Department of Physics and Mathematics,  Guru Ghasidas Univ., Bilaspur, 2008.  Invited Talk 
11^{th} International Conference of International Academy of Physical Sciences on Mathematical Modelling, Analysis and Geometry,  Univ. Of Allahabad, 2010 
Paper Presented and chaired the session in Analysis and Mathematical Modeling 
14^{th} International Conference of International Academy of Physical Sciences (Physical Sciences Interface with Humanity)  NIT, Surat, 2011  Invited Talk 
Attended Workshop:
International Instructional Workshop on Wavelets and Application,  Univ. of Delhi, Delhi, 1999  Attended 
Workshop on Technical Words in Hindi  BRA Bihar Univ., Muzaffarpur, 2003  Attended 
Instructional Workshop on Wavelet Analysis

Banaras Hindu Univ., Varanasi, 2007

Attended 
Major awards, Fellowships of Academies Professional Societies and other honours and distinctions:
 BHU Fellowship from 1989 to 1992.
 Post Doctoral Fellowship NBHM (DAE) from 1994 to 1996.
 Academy awards as an Associate Fellow for his valuable contributions to Mathematical Sciences on November 16, 2018 during CONIAPS XXIII at Nepal Academy of Science and Technology, Kathmandu,Nepal.
 Delivered Professor Tribikram Pati Memorial Lecture 2018 during CONIAPS XXIII, November 1618, 2018 held at Nepal Academy of Science and Technology, Kathmandu, Nepal.