[ Mathematics | University of North Carolina, Chapel Hill

Site is in the process of moving to a New Location and will shut down completely by November 2018.

Office: Phillips Hall 324 D
Office Hours for Spring 2018: W: 11:00am-12:30pm, F: 12pm-1:30pm.
Department Phone: +001 (919) 962-1294
Department Fax: +001 (919) 962-2568
E-Mail: marzuola "at" math "dot" unc "dot" edu

Department of Mathematics
University of North Carolina, Chapel Hill
CB #3250, Phillips Hall
Chapel Hill, NC 27599

Analysis Seminar and Departmental Colloquia:

  • Analysis Seminar Schedule: co-organized with Yaiza Canzani and Hans Christianson held typically Wednesday afternoons from 4-5pm in Phillips Hall 381.

  • Colloquium Schedule: held Thursday afternoons from 4-5pm in Phillips Hall 332.

    Conferences Organized (most recent first):

  • SIAM Minisymposium on Challenges in Mathematical Modeling, Analysis and Computation of Quantum Systems: organized with Dio Margetis at SIAM Nonlinear Waves in Anaheim, CA, Monday, June 11th, 2018.

  • SIAM Minisymposium on Problems in Quasilinear Dispersive PDE: organized with David Ambrose at Joint Math Meeting in San Diego, CA, Saturday, January 13th, 2018.

  • Waves, Spectral Theory and Applications - Part 2: October 20-22, 2017. An NSF funded conference as a follow up to the workshop in 2015 held at the University of North Carolina, Chapel Hill.

  • Nonlinear Partial Differential Equations on Graphs (with Reika Fukuizumi, Dmitry Pelinovsky and Guido Schneider)}: June 18-24, 2017 in Oberwolfach, Germany.

  • SIAM PDE 2015 meeting: On Organizing Committee for Co-Chairs David Lannes and Lia Bronsard. Meeting to be held December 7-10, 2015 in Scottsdale, Arizona.

  • Waves, Spectral Theory and Applications: September 10-11, 2015. An NSF funded conference in honor of the work of Michael Weinstein on his 60th birthday to be held at the Princeton Center for Theoretical Sciences co-organized with Peter Constantin, Roy Goodman, Panos Kevrekidis, Eduard Kirr, Judith Miller, Gideon Simpson and Vadim Zharnitsky.

  • Dynamics in Geometric Dispersive Equations and the Effects of Trapping, Scattering and Weak Turbulence: co-organized with Stephen Gustafson and Daniel Tataru held at the Banff International Research Station May 4-9, 2014.

  • UNC PDE Mini-Schools: series of 3 mini-courses for graduate students given in 2013-2014 at UNC co-organized with Hans Christianson and Jason Metcalfe.

  • A Conference on Partial Differential Equations - Analytic and Geometric Aspects: co-organized with Hans Christianson and Anna Mazzucato in honor of Michael Taylor's 65th Birthday, held July 16-20, 2012 at UNC.

  • AMS Special Session on Nonlinear Dispersive Equations: co-organized with Sarah Raynor and Gideon Simpson held September 24-25, 2011 in Winston-Salem, NC, USA.

  • ICIAM minisymposium on Dispersive Partial Differential Equations in Mathematical Physics: co-organized with Stephen Gustafson, Jason Metcalfe, Tai-Peng Tsai and Ian Zwiers held July 18-22, 2011 in Vancouver, Canada.

  • SIAM minisymposium on Modulation of Nonlinear Solutions in Dispersive Partial Differential Equations: co-organized with Justin Holmer and Gideon Simpson held August 16-19, 2010 in Philadelphia, PA, USA.

  • AMS Special Session on Nonlinear Dispersive Equations: co-organized with Sebastian Herr held April 25-26, 2009 in San Francisco, CA, USA.

  • Nonlinear Structures Arising in Dispersive Partial Differential Equations: co-organized with Herbert Koch held March 2-6, 2009 in Bonn, Germany.

    Professional Materials:

  • CV (PDF)
  • Research Statement (PDF)
  • Teaching Statement (PDF)

    Current Teaching:

  • Math 233 - Spring 2018 (Course Web-page)

  • Past Teaching:

  • Math 547 - Fall 2017 (Course Web-page)
  • Math 653 - Fall 2016 (Course Web-page)
  • Math 547 - Spring 2016 (Course Web-page)
  • Math 754 - Spring 2016 (Course Web-page)
  • Math 555 - Spring 2015 (Course Web-page)
  • Math 383 and Lab - Fall 2014 (Course Web-page)
  • Math 547 - Spring 2014 (Course Web-page)
  • Math 754 - Spring 2014 (Course Web-page)
  • Math 547 - Fall 2013 (Course Web-page)
  • Lectures on Nonlinear Waves - Karlsruhe Institute of Technology - Summer 2013 (Course Web-page)
  • Math 547 - Spring 2013 (Course Web-page)
  • Nonlinear Waves: Analysis & Numerics - Universität Bielefeld - Summer 2012 (Course Web-page)
  • Math 89 - Spring 2012 (Course Web-page)
  • Math 751 - Fall 2011 (Course Web-page)
  • Math 383 - Fall 2011 (Course Web-page)
  • Math 564 - Spring 2011 (Course Web-page)
  • Math 383 - Fall 2010 (Course Web-page)
  • APMA 4001 - Spring 2010 (Course Web-page)
  • APMA 6302 - Fall 2009 (Course Web-page)

  • Former and Current Graduate Student Researchers:

  • Matt Harris (Master's Degree Awarded May 2013, currently a consultant at Deloitte) - Master's Thesis on "Numerically Computing Bound States" - Note, techniques are all correct and applicable, but the geometric potential in H^2 takes an attractive character in the simulations and it should take a repulsive character. This should suggest interesting calculations in higher dimensional H^{n+1} spaces.
  • David Webb (Ph.D. student, Graduated August 2017, now an instructor at Shorter University) - "Nonlinear Dirac Equations"
  • Quentin Robinson (Ph.D. student, Graduated May 2018) - "Surface disturbances generated by fluid flow past an obstacle or over topography as predicted by the Korteweg-de Vries and the Euler equations"
  • Yuan Gao (Ph.D. student, expected graduation May 2019, co-advised with Katie Newhall) - Metropolis dynamics of random spin systems.
  • Sterling Swygert (Ph.D. student, expected graduation May 2019) - Working on analysis thin film models in geometric settings and stability of periodic waves in degenerate dissipative models.
  • Dmitro Golovanich (Ph.D. student, expected graduation May 2020) - Potential perturbations of non-self-adjoint problems related to stability theory and NLS dynamics with potentials.
  • Grace Conte (Ph.D. student, expected graduation May 2021) - Adjoint continuation on quantum graphs.
  • Wesley Hamilton (Ph.D. student, expected graduation May 2021) - Data analysis and spectral properties of graph Laplacians.

  • Formber and Current Undergraduate Student Researchers:

  • Nathan Vaughn (Undergrad Researcher, graduated May 2015, currently a graduate student at University of Michigan) - Bifurcations in Thin-Film Traveling Waves - Resulting in Publication "A numerical study of traveling waves for a model of thin films in cylindrical domains".
  • Anya Katsevich (Undergrad Researcher, graduated May 2017, currently a graduate student at the Courant Institute) - Honors Thesis on "The hydrodynamic limit of a crystal surface jump diffusion with Metropolis-type rates" Metropolis rates in crystal evolution problems and spin systems, coarse graining, numerics and convergence. Working to turn thesis results into a publication.
  • Alan Luner (Undergrad Researcher, expected graduation May 2018) - Working on using Finite Element solvers to understand properties of fluid flow in different geometries and to construct nonlinear solutions to problems related to Density Functional Theory.

  • About Me:

    I received my undergraduate degree from the University of Oklahoma in 2002, where I wrote an undergraduate thesis on Numerical Semigroups with Professor Andy Miller. Then, I went to UC-Berkeley where I finished my Ph.D. working with Professor Daniel Tataru in 2007. My thesis topic was the asymptotic behavior of solutions to the Nonlinear Schrödinger Equation (NLSE).

    From 2007-2008 and 2009-2010, I was at Columbia University as a National Science Foundation Postdoctoral Research Fellow working with Professor Michael Weinstein. However, I spent the academic year 2008-2009 as a Hausdorff Center Postdoc with Professor Herbert Koch at the University of Bonn.

    Presently, I am an Associate Professor in the Analysis Group and the Director of Undergraduate Studies at the University of North Carolina, Chapel Hill, where I am lucky enough to study/discuss PDE using tools from microlocal analysis almost every day with my PDE colleagues Yaiza Canzani, Hans Christianson, Jason Metcalfe, Michael Taylor, and Mark Williams. In addition, I get to talk about models, applications and numerics with Chris Jones, Laura Miller, Katie Newhall, Boyce Griffith, Nancy Rodriguez as well as members of our Applied Fluids Group such as Roberto Camassa and Rich McLaughlin.

    My research interests lie mainly in phenomenological descriptions of solutions to linear/nonlinear PDE's related to quantum mechanics and other physical models that give rise to Hamiltonian structure.

    Research supported in part by NSF Applied Math Grant DMS-1312874 (2013-2017) and NSF CAREER Grant DMS-1352353 (2014-Present).

    Research Topics:

    Soliton and vortex existence/stability, well-posedness theory quasilinear and degenerate models, linear scattering theory, spectral theory, Strichartz/dispersive estimates, microlocal analysis, properties of eigenfunctions on billiards, classical dynamics descriptions of PDE solutions, graph Laplacian spectral problems, quantum graphs, numerical simulations, asymptotic analysis, degenerate dispersive/diffusive equations with applications in nonlinear optics, fluid dynamics, topological physics, quantum mechanics, general relativity, quantum chemistry, statistical physics, weak turbulence.

    Papers, Preprints and Presentations:

    Lecture Notes (Works in Progress!):

  • An evolving set of lecture notes on nonlinear bound states, spectral theory, stability and scattering - PDF. The goal is to add more on spectral theory, applications in Chemistry and Physics, as well as a fair number of problems over time. Comments are welcome.
  • An first attempt at a lab manual for a Matlab based computational companion to the first course in ODEs at UNC - PDF. The goal is to add more discussion of topics, fine tune the length of weekly assignments and add more sample codes over time.

  • Links

    My Collaborators:
    Mathematical Papers and Tables:
    Online Manuals:

    Open Access in Science: News: More Information: Miscellanea:

    This page was stolen from Ronald van Luijk (thanks!) and last modified at August 16th, 2007.