Vardayani Ratti

  • My research interest is in Mathematical Biology, in particular applications in ecology, infectious diseases, pollination biology and agriculture.

  • Recent invited talks

    • Rochester Institute of Technology, Rochester, USA, 2018

    • Arizona State University, Arizona, USA, 2018

    • AMS Special Session at Spring Eastern Sectional Meetin, Northeastern University, Boston, 2018

    • Sonia Kovalevsky Day, Dartmouth College, USA, 2018

    • Bowdoin College, Maine, USA, 2018

    • Fields Institute's Workshop on Pollinators and Pollination Modeling, Toronto, 2018

    • Joint Mathematics Meeting, San Diego, USA, 2018

    • Minisymposium on Mathematical Biology, Dartmouth College, 2017

    • Joint Mathematics Meetings, Atlanta, USA, 2017

    • Society of Mathematical Biology (SMB) Annual Meeting and Conference, Nottingham, UK, 2016

    Contact

    John Wesley Young Research Instructor
    Dartmouth College
    Department of Mathematics
    27 N. Main Street
    Hanover, NH 03755
    Email: vardayani.ratti@dartmouth.edu
    Phone: (+1) 603-646-3507
    Office: 314 Kemeny Hall

    Research


    Manuscripts


    Book Chapter


    Theses

    • Ratti, V. Predictive Modeling of the Disease Dynamics of Honeybee-Varroa destructor-Virus Systems. Ph.D. Thesis

    • Ratti, V. Local Stability Analysis of the Honeybee-Varroa destructor-Acute Bee Paralysis Virus. M.Sc. Thesis

    Last modified on .


    Teaching


    Spring 2019


    • MATH 22: Linear Algebra with Applications
      This course presents the fundamental concepts and applications of linear algebra with emphasis on Euclidean space. Significant goals of the course are that the student develop the ability to perform meaningful computations and to write accurate proofs. Topics include bases, subspaces, dimension, determinants, characteristic polynomials, eigenvalues, eigenvectors, and especially matrix representations of linear transformations and change of basis. Applications may be drawn from areas such as optimization, statistics, biology, physics, and signal processing.
    • Textbook: Linear Algebra and Its Applications by Otto Breschler, Pearson 2013

    Past Courses


    • MATH 3: Calculus , Winter and Fall 2018
      This course involves collaborative learning. It is an introduction to single variable calculus aimed at students who have seen some calculus before, either before matriculation or in introductory calculus course (Math 1). Math 3 begins by revisiting the core topics in Math 1 - convergence, limits, and derivatives - in greater depth before moving to applications of differentiation such as related rates, finding extreme values, and optimization. The course then turns to integration theory, introducing the integral via Riemann sums, the fundamental theorem of calculus, and basic techniques of integration.
    • Textbook: ``Calculus'' by Herman and Strang's, Volume 1. (open access PDF)
    • Math 8: Calculus of Functions of one and Several Variables, Spring 2018
      This course is a sequel to Math 3 and provides an introduction to Taylor series and functions of several variables. The first third of the course is devoted to approximation of functions by Taylor polynomials and representing functions by Taylor series. The second third of the course introduces vector-valued functions. It begins with the study of vector geometry, equations of lines and planes, and space curves. The last third of the course is devoted to studying differential calculus of functions of several variables.
    • Textbook: ``Calculus", by James Stewart, 8th Edition, ISBN: 978-1-285-74062-1
    • MATH 76: Topics in Applied Mathematics, Winter 2018
      This course is designed to provide students with the basic tools for building and analyzing mathematical models in Biology primarily using ordinary differential equations. In addition, you will learn how to analyze and simulate the models. You will also learn to interpret and communicate the results in the context of biology.
    • Textbooks:
    • MATH 22: Linear Algebra with Applications, Fall 2017
      This course presents the fundamental concepts and applications of linear algebra with emphasis on Euclidean space. Significant goals of the course are that the student develop the ability to perform meaningful computations and to write accurate proofs. Topics include bases, subspaces, dimension, determinants, characteristic polynomials, eigenvalues, eigenvectors, and especially matrix representations of linear transformations and change of basis. Applications may be drawn from areas such as optimization, statistics, biology, physics, and signal processing.
    • Textbook: Linear Algebra and Its Applications (5th Edition) by David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson 2015
    • MATH 13: Multivariable Calculus, Winter 2017
      This course is a sequel to Math 8 and provides an introduction to calculus of vector-valued functions. The course starts with iterated, double, triple, and surface integrals including change of coordinates. The remainder of the course is devoted to vector fields, line integrals, Green’s theorem, curl and divergence, and Stokes’ theorem.
    • Textbook: ``Calculus Early Transcendentals Multivariable", by Rogawski & Adams, 3rd Edition, ISBN: 978-1464171758
    • MATH 23: Differential Equations, Fall 2016
      This course is a survey of important types of differential equations, both linear and nonlinear. Topics include the study of systems of ordinary differential equations using eigenvectors and eigenvalues, numerical solutions of first and second order equations and of systems, and the solution of elementary partial differential equations using Fourier series.
    • Textbook: Elementary Differential Equations and Boundary Value Problems (10th Edition) by Boyce & DiPrima, Wiley 2012

    Graduate Teaching Assistant (2009 - 2015)


    • Partial Differential Equations, Winter 2015
    • Biomathematics I, Winter 2014
    • Matrix Algebra, Winter 2014
    • Linear Algebra, Winter 2013
    • Integrated Math Physics I, Fall 2012
    • Elements of Calculus II, Winter 2010, Fall 2010, Fall 2011
    • Differential Equations I, Winter 2010, Fall 2010
    • Applied Differential Equations II, Winter 2011, Winter 2010
    • Biomathematics, Winter 2011

    Last modified on .


    Brief Curriculum Vitae

    Detail CV


    Employment

       Dartmouth College,   NH USA;   JWY Research Instructor,   July 2016 - Current

       University of Guelph,   ON Canada;   NSERC-ENGAGE Postdoctoral Fellow,   January 2016 - July 2016

       University of Guelph,   ON Canada;   Graduate Teaching Assistant,   September 2009 - April 2015

       University of Guelph,   ON Canada;   Graduate Research Assistant


    Education

       University of Guelph,   ON, Canada

       Panjab University,   Chandigarh, India

    • M.Sc. (Honours), Mathematics (Course based)

    Selected Talks

    • Arizona State University. 2018

    • Rochester Institute of Technology, Rochester. 2018

    • JMM. 2018

    • Ratti,V.; Kevan, P.G.; Eberl, H.J.(2017) Studying the effect of homing failure on a colony infested with varroa destructor and virus. Joint Mathematics Meetings (JMM), Atlanta, USA.

    • Ratti,V.; Kevan, P.G.; Eberl, H.J.(2016) An interplay between division of labour and disease in a honeybee colony. Society of Mathematical Biology (SMB) Annual Meeting and Conference, Nottingham, UK.

    • Ratti,V.; Kevan, P.G.; Eberl, H.J.(2015) An interplay between division of labour and disease in a honeybee colony. The 2015 AMMCS-CAIMS Congress, Waterloo, Canada.

    • Ratti,V.; Kevan, P.G.; Eberl, H.J.(2015) Mathematical model of the honeybee-varroa destructor-acute bee paralysis virus complex. The 2015 BIOMAT. International Symposium on Mathematical and Computational Biology, Indian Institute of Technology Roorkee, India.

    • Ratti,V.; Kevan, P.G.; Eberl, H.J.(2013) Save honeybees with mathematics. Canadian Association of Professional Apiculturists, Edmonton, Alberta, Canada.

    • Ratti,V.; Kevan, P.G.; Eberl, H.J.(2013) Mathematical model of the honeybee-varroa destructor-acute bee paralysis virus complex with seasonal coefficients. Society of Mathematical Biology (SMB) Annual Meeting and Conference, Tempe, Arizona.

    • Ratti,V.; Kevan, P.G.; Eberl, H.J.(2013) Mathematical model of the honeybee-varroa destructor-acute bee paralysis virus complex with seasonal coefficients. 2013 Southwestern Ontario Graduate Mathematics and Statistics Conference, University of Guelph, Canada.

    • Ratti,V.; Gunderson, S. (2012) Associative learning in honeybees. Missouri Botanical Garden (MBG), St.Louis, Missouri, United States.

    • Ratti, V.; Kevan, P.G.; Eberl, H.J.(2011) Mathematical model of the honeybee-varroa destructor-acute bee paralysis virus complex. The 5th Geoffrey J. Butler Memorial Conference on Differential Equations and Population Biology, University of Alberta, Canada.

    • Ratti, V.; Kevan, P.G.; Eberl, H.J.(2011) Mathematical model of the honeybee-varroa destructor-acute bee paralysis virus complex. CMS Winter meeting 2011, Toronto, Canada.


    Refereeing

    • Journal of Mathematical Bioscience and Engineering

    Department Service

    • Applied Mathematics Seminar (2017-2018)
      Dartmouth College

    Teaching Experience

         Please see here for my teaching experience.