Manoj Kumar Yadav Assistant Professor Department of Mathematics

Dr. Manoj kumar Yadav is an Assistant Professor at the Department of Mathematics, School of Natural Sciences, Mahindra University École Centrale School of Engineering. He obtained his PhD from the Department of Mathematics, IIT Madras followed by postdoctoral positions at IISc Bangalore and Czech Technical University in Prague and a visiting position at the Czech Academy of Sciences. His expertise, experience and research interests span across several domains of Applied Mathematics such as Asymptotic analysis and computation of nonlinear partial differential equations describing evolution processes. Homogenization of PDE models describing composite material properties and fluid flows in heterogeneous media. Stochastic modeling and computation of problems in Mathematical Finance. Data driven modeling and analysis of real world problems. He has published research papers in peer reviewed international journals along with contributing in various talks in India and abroad.

  • Education
    • 1998-2001 : B.Sc. (H) in Mathematics, Kalyani University, WB
    • 2001-2003 : M.Sc. Mathematics, Kalyani University, WB
    • 2005-2010 : Ph.D. Mathematics, IIT Madras, Chennai
    • 2010-2012 : Post Doctoral Researcher,  IISc Bangalore
    • 2014-2015 : Post Doctoral Researcher, Czech Technical University, Paragu
  • Research

    Areas of Expertise :

    Analysis of evolutionary PDEs. Homogenization of PDE models describing composite material properties and fluid flows in heterogeneous media. Mathematical theory of compressible Navier-Stokes flows. Stochastic modeling and computation of problems in Mathematical Finance. Data driven modeling and analysis of real world problems.

    Current Research Interests :

    • PDE and Monte Carlo simulations based numerical techniques for option pricing problems in finance.
    • Analysis and application of various Reinforcement Learning algorithms in optimal stopping problems in finance. Search for optimal early exercise policy in American option pricing.
    • Mathematical and data driven modeling of various intervention strategies impact on epidemic evolution and control.

    Real world problems :

    Optimization of large portfolios using factor models. Model based and model free VaR estimation of portfolios.

  • Awards
    • Project Assistant, DRDO Project,  Nonlinear Studies Group, Department of Mathematics, IISc Bangalore, March 2004 to December 2004.
    • Junior Research Fellowship, Council of Scientific and Industrial Research (CSIR), January 2005 to January 2007.
    • Senior Research Fellowship, Council of Scientific and Industrial Research (CSIR), February 2007 to January 2010.
    • Post Doctoral Fellowship, National Board for Higher Mathematics (NBHM), August 2010 to July 2011.
    • Dr. D. S. Kothari Post Doctoral Fellowship, UGC, August 2011 to July 2012.
    • NBHM grant for participation in ICM 2010 held in Hyderabad, India, August 2010.
    • Travel grant awarded  by NBHM for participation and paper presentation  in ICIAM 2011 held in Vancouver, Canada, July 2011.
    • European Social Fund for the project Support for intersectoral mobility and quality enhancement of research teams at Czech Technical University in Prague Reg No. CZ.1.07/2.3.00/30.0034, March 2014.
       
  • Publications

    Peer Reviewed Journals

    • Manoj K. Yadav, Initial boundary value problems for some damped nonlinear conservation laws, Electronic J. Qualitative Theory of Differential Equation, No. 86, 1-11, 2015.
    • Michal Benes, Ales Nekvinda, Manoj K. Yadav, Multi-time step domain decomposition method with non-matching grids for parabolic problems, Appl. Math. Comp. 267, 571-582, 2015.
    • Manoj K. Yadav, Solutions of a system of forced Burgers equation in terms of generalized Laguerre polynomials, Acta Math. Sci. Ser. B, 34(5), 1461-1472, 2014.
    • Manoj K. Yadav, Solutions of a system of forced Burgers equation, Appl. Math. Comp. 225, 151-157, 2013.
    • Ch. Srinivasa Rao, Manoj K. Yadav, Large time behaviour of solutions of the inviscid non-planar Burgers equation, J. Engrg. Math. 69, 345-357, 2011.
    • Ch. Srinivasa Rao, Manoj K. Yadav, Solutions of a nonhomogeneous Burgers equation, Stud. Appl. Math. 124 (4), 411-422, 2010.
    • Ch. Srinivasa Rao, Manoj K. Yadav, Solution of an initial boundary value problem for non-planar Burgers equation using Hermite interpolants, Int. J. Nonlinear Sci., 9 (2), 159-164, 2010.
    • Ch. Srinivasa Rao, Manoj K. Yadav, Large time asymptotics for solutions of a nonhomogeneous Burgers equation, Appl. Math. Mech., 31 (9), 1189-1196, 2010.
    • Ch. Srinivasa Rao, Manoj K. Yadav, On the solution of a nonhomogeneous Burgers equation, Int. J. Nonlinear Sci., 10 (2), 141-145, 2010.

    Conference Proceedings

    • P. L. Sachdev and Manoj K. Yadav, Nonplanar Burgers equation - An overveiw. Proceedings of the International Symposium on Recent Advances in Fluid Mechanics, Bangalore University, 2004.
    • Manoj K. Yadav, Large time behaviour of solutions of an inviscid generalized Burgers equation with linear damping. Proceedings of ICIAM 2011, Vancouver, Canada.
  • Experience
    • Ad hoc Faculty at National Institute of Technology, Warangal, July 2013-December 2013.
    • Assistant Professor at Jaypee University of Information Technology, Solan, July 2012-January 2013.
    • Teaching Assistantships for the courses Ordinary Differential Equations, Partial Differential Equations, Dynamical Systems, Numerical Analysis of Differential Equations, Linear Algebra and Numerical Analysis at the Department of Mathematics, IIT Madras.
    • Tutor at the Third Annual Foundation School - Part I held at IMSc Chennai during December 4-30, 2006.
    • Tutor at QIP-STTP on Harmonic Analysis and Partial Differential Equations held at the Department of Mathematics, IIT Madras during January 1-12, 2007.

    Courses Taught @ MEC :

    • Complex Analysis and Integral Transforms - Tutor (Fall 2015, Fall 2016)
    • Linear Algebra and Multivariable Calculus - Instructor and Tutor (Spring 2016)
    • Partial Differential Equations - Instructor (Spring 2017, Spring 2018)
    • Numerical Analysis & Scientific Computing - Lab Instructor (Spring 2017)
    • Probability and Queuing Models - Instructor (Fall 2017)
    • Probability Theory - Instructor (Fall 2017)
    • Computer Graphics - Lab Instructor (Fall 2017)
    • Signals & Systems - Lab Instructor (Spring 2018, Fall 2018)
    • Probability and Statistics - Instructor (Fall 2018, Fall 2019)
    • Financial Mathematics - Instructor (Spring 2019, Spring 2020)
    • Numerical Analysis & Scientific Computing - Lab Instructor (Spring 2019, Spring 2020)
  • Others

    INVITED and CONTRIBUTED TALKS

    • Contributed Talk : Large Time Behaviour of Solutions of an Inviscid Generalized Burgers Equation with Linear Damping. ICIAM 2011, Vancouver, Canada (July 19, 2011).
    • Invited Talk : Approximate Solutions of PDEs using Hermite Interpolation. National Workshop on Computational Methods in Sciences and Engineering, National Institute of Technology, Warangal, India (November 25, 2013).
    • Contributed Talk : Domain Decomposition Methods and Asynchronous Time Integration for Parabolic PDEs, Applied Analysis for Materials, BMS Summer School 2014,  TU Berlin, Germany.
    • Seminar Talk : Multi-time-step Domain Decomposition Method with Non-matching Grids for Parabolic Problems, Department of Mathematics, Czech Technical University, Prague, Czech Republic (November 19, 2014).
    • Seminar Talk : Solutions of a system of Forced Burgers equation, Department of Numerical Mathematics, Charles University, Prague, Czech Republic (December 11, 2014).
    • Contributed Talk : Modelling effective slip law at thin porous interface via two scale homogenization techniques, ICMM 2015, Cite Internationale Universitaire de Paris, France (April 27, 2015).
    • Contributed Talk : Homogenization of Heterogeneous Materials, Summer School at Brno, Czech Republic (September 16, 2015).
    • Invited Talk : Mathematical Models for Real World Problems, National Seminar on Recent Trends in Applied Mathematics, Govt. College Madappally, Vatakara, Kerala (December 7, 2016).
    • Contributed Talk : Multi-time Step Domain Decomposition Method, Presentation at International Conference Latest Advances in Computational and Applied Mathematics 2016, held at MEC Hyderabad (December 15, 2016).
    • Contributed Talk : Comparative analysis of RBF-PUM and FD based collocation schemes for pricing European basket option, IGCM 2019, IISc Bangalore, December 2-4, 2019.
    • Invited Webinar : Numerical Techniques for Pricing European Basket Option. Online Lecture Series on Mathematical Modelling in Engineering and Industries. Organised by Sathyabama Institute of Science and Technology and IIITDM Kancheepuram, May 15, 2020. 

    WORKSHOPS and CONFERENCES

    • Instructional School on Computational PDEs CPDE-05, held at the Department of Mathematics, IIT Bombay during June 5 to June 24, 2005.
    • Workshop and Conference on Multi - Scale Analysis and Homogenization, held at the Department of Mathematics, IISc Bangalore during June 28 to July 14, 2010.
    • International Congress of Mathematicians (ICM) 2010 Satellite Conference - PDE and Related Topics, held at  TIFR CAM Bangalore, August 13 to August 17, 2010. 
    • International Congress of Mathematicians (ICM) 2010 held at Hyderabad during August 19 to August 27, 2010.
    • International Congress on Industrial and Applied Mathematics (ICIAM) 2011 held at Vancouver, Canada during July 18 to July 22, 2011.
    • BMS Summer School 2014 on Applied Analysis for Materials held at TU Berlin, Germany during 25 August to 5 September, 2014. 
    • Indo-German Conference on Computational Mathematics : Challenges and Opportunities towards Exascale Computing, IGCM 2019, IISc Bangalore, December 2-4, 2019.

    Referee for International Journals

    • SIAM Journal on Mathematical Analysis
    • Studies in Applied Mathematics