• Assistant Professor

    NATHAN D. TOTZ

  • ACADEMIC POSITIONS & EDUCATION

    University of Miami

    2017-present, Coral Gables FL

    Assistant Professor

    University of Massachusetts Amherst

    2014-2017, Amherst MA

    Visiting Assistant Professor

     

    -Postdoctoral Mentor: Professor Andrea Nahmod

     

    Duke University

    2011-2014, Durham NC

    Assistant Research Professor

     

    -Postdoctoral Mentor: Professor J. Thomas Beale

     

    University of Michigan

    2006-2011, Ann Arbor MI

    Ph.D. in Mathematics

     

    -Thesis: A Rigorous Justification of the Modulation Approximation to the 2D Full Water Wave Problem

     

    -Thesis Advisor: Professor Sijue Wu

     

     

     

    Knox College

    2002-2006, Galesburg IL

    B.A. in Mathematics, Magna cum Laude with Honors

     

    -Senior Thesis: An In-Depth Study of Distributions
    -Senior Thesis Advisor: Professor Dennis Schneider
    -Post-Baccalaureate Fellow, Knox College, 2005-2006

     

    -Budapest Semesters in Mathematics, Fall 2004

  • PUBLICATIONS & PREPRINTS

    Research Interests

    -Partial Differential Equations arising from Fluid Mechanics

    -Dispersive PDEs

    -Asymptotic Analysis

    -PDEs in Nondeterministic Settings

    Publications & Manuscripts

    N. Totz. Existence and Uniqueness of Energy Solutions to the Stochastic Diffusive Surface Quasi-Geostrophic Equation with Additive Noise. Submitted. (Arxiv Preprint)

     

    A. Nahmod, N. Pavlovic, G. Staffilani, N. Totz. Global Flows with Invariant Measures for Inviscid Modified SQG equations. Stoch. Partial Differ. Equ. Anal. Comput. 6(2), 184-210 (2018) (Arxiv Preprint)

     

    N. Totz. Global Well-Posedness of 2D Non-Focusing Schrodinger Equations via Rigorous Modulation Approximation. J. Diff. Eq., Vol. 261, Issue 4 (2016), pp. 2251-2299. (Arxiv Preprint)

     

    N. Totz. A Justification of the Modulation Approximation to the 3D Full Water Wave Problem. Commun. Math. Phys., Vol. 335 No. 1 (2015), pp. 369-443, Springer. (Arxiv Preprint)

     

    D. Herzog, N. Totz. On a Generalization of Hormander's Theorem. Potential Anal., Vol. 42, Issue 2 (2015), pp. 403-433 (Arxiv Preprint)

     

    N. Totz, S. Wu. A Rigorous Justification of the Modulation Approximation to the 2D Full Water Wave Problem. Commun. Math. Phys., Vol. 310 No. 3 (2012), pp. 817-883, Springer. (Arxiv Preprint)

     

    N. Totz (D. Schneider, directing) An In-Depth Study of Distributions.
    Senior Thesis, Knox College (2005). (A systematic exposition of the theory of distributions in a topological vector space framework, culminating in a proof of the Malgrange-Ehrenpreis Theorem)

     

  • GRANTS & AWARDS

    2016-2021

    The interplay of evolution partial differential equations and their model equations. Award total $102,079.

    MSRI Postdoctoral Fellowship

    Fall 2015

    New Challenges in PDE: Deterministic Dynamics and Randomness in High and Infinite Dimensional Systems

     

    Supported under NSF H98230-15-1-0106

     

    -Postdoctoral Mentor: Professor Natasa Pavlovic

  • TEACHING

    Current Courses

    To be updated in Fall 2020

    Classes Instructed

     

    Spring 2019-2020, 625 (Graduate Intro. to Statistics)

    Fall 2018-2019, 624 (Graduate Intro. to Probability)

    Spring 2018, 224 (Undergrad. Intro. Prob. and Stat.)

    Fall 2017-2019, 210 (Undergraduate Linear Algebra)

    Fall 2017, 311 (Undergraduate ODE)

    Spring 2017, 524 (Intro. to Modern Analysis II)

    Spring 2017, 331 (Undergraduate ODE)

    Fall 2016, 233 (Multivariable Calculus)

    Spring 2016, 331 (Undergraduate ODE)

    Spring 2015, 235 (Linear Algebra)

    Fall 2014, 131 (Calculus 1)

    Spring 2014, 353 (Undergraduate ODE and PDE)

    Fall 2013, 212 (Multivariable Calculus)

    Fall 2012, 551 (Graduate Applied PDE and Complex Variables)

    Fall 2012, 353 (Undergraduate ODE and PDE)

    Spring 2012, 131 (Undergraduate ODE and PDE)

    Fall 2011, 103 (Multivariable Calculus)

     

    Further teaching experience available upon request.

     

    Classes Administered

    Graduate Student Instructor

    University of Michigan, Ann Arbor

     

    Co-coordinator 116 (Calculus 2), Fall 2009

     

  • CONTACT

    Email

    Email

     

    ndt27@miami.edu