KMap
I am a professor of mathematics and public health at the University of Arizona. This site describes my work as a member of an international community of researchers and educators. The menus at the top contain information about me and my professional activities. Some of the blog items below tell professional stories; others summarize information I have collected on important academic issues, or point to interesting work that I have seen in the recent literature. Collectively, the pages in this site illustrate my passion for curiosity-driven research, for elegant applications, and for discovering and sharing knowledge.

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Courses
  • EIS
    Explorations in Integrated Science

  • RAOV
    Real Analysis of One Variable

  • FMRW
    Formal Mathematical Reasoning and Writing

  • MM
    Mathematical Modeling

Grants
  • Funding agency logo
    RAPID: Networked Data-Driven Modelling of the COVID-19 Outbreak with a Performativity-Aware Calibration Learning Algorithm

    Co-Investigator (COI)

    2020

    $156.4K
    Active
  • Funding agency logo
    DARPA Chikungunya Challenge Prize

    Principal Investigator (PI)

    2015

    $150.0K
    Active
  • Funding agency logo
    The Sixth International Conference on Mathematical Modeling and Analysis of Populations in Biological Systems

    Co-Investigator (COI)

    2017

    $18.0K
  • Funding agency logo
    Simulation Modeling of Public Health Interventions on Dengue Vector Abundance: Current and Future Estimations

    Key Personnel (KP)

    2014

    $573.6K
  • Funding agency logo
    Intel Math National Training Agency: Revision of the Intel Math Curriculum

    Principal Investigator (PI)

    2012

    $50.0K
  • Funding agency logo
    Intel Math National Training Agency

    Principal Investigator (PI)

    2011

    $65.0K
  • Funding agency logo
    "New: GK-12" Graduate Students and Teacher Engaging in Mathematical Sciences (G-Teams)

    Principal Investigator (PI)

    2009

    $3.0M
  • Funding agency logo
    Proposal to Implement the Intel Math Program in the United States

    Principal Investigator (PI)

    2009

    $182.4K
Technologies / Patents
      News
      • 6 From UA Recognized in New Class of Fellows by AAAS

        2017

      • Students Use CyVerse to Help Predict Mosquito-Borne Diseases

        2017

      • 2 From UA Solve Public Health Issue, Win Competition

        2015

      • UA Program Working to Improve Math Instruction, Learning

        2009

      Publications (61)
      Recent
      • Multiple Scale Asymptotics of Map Enumeration

        2023

      • Epidemics from the Eye of the Pathogen

        2022

      • Dynamics of Non-polar Solutions to the Discrete Painlevé I Equation

        2022

      • Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the United States

        2022

      • The United States COVID-19 Forecast Hub dataset

        2022

      • Non-recursive Counts of Graphs on Surfaces

        2022

      • Aedes-AI: Neural network models of mosquito abundance

        2021

      • Parameter Estimation from ICC curves

        2021

      • A 70% Reduction in Mosquito Populations Does Not Require Removal of 70% of Mosquitoes

        2020

      • Collaborative efforts to forecast seasonal influenza in the United States, 2015–2016

        2019

      • A new gravity model for spatial interaction

        2019

      • On collisions times of `self-sorting' interacting particles in one-dimension with random initial positions and velocities

        2018

      • The Phase Structure of Grain Boundaries

        2018

      • Summary Results of the 2014-2015 DARPA Chikungunya Challenge

        2018

      • Effect of temperature thresholds on modeled Aedes aegypti population dynamics

        2017

      • Aedes aegypti (Diptera: Culicidae) abundance model improved with relative humidity and precipitation-driven egg hatching

        2017

      • Data-driven outbreak forecasting with a simple nonlinear growth model

        2016

      • Capillary induced deformations of a thin elastic sheet

        2016

      • Two-dimensional capillary origami

        2016

      • Two-dimensional capillary origami with pinned contact line

        2015

      • Projection of Climate Change Influences on U.S. West Nile Virus Vectors

        2015

      • Regularized Model of Post-Touchdown Configurations in Electrostatic MEMS: Interface Dynamics

        2015

      • Explorations in integrated science

        2014

      • Regularized model of post-touchdown configurations in electrostatic MEMS: Equilibrium analysis

        2014

      • Erratum: Collective behaviors in two-dimensional systems of interacting particles (SIAM Journal on Applied Dynamical Systems (2011) 10 (1213-1231))

        2013

      • Effect of disjoining pressure in a thin film equation with non-uniform forcing

        2013

      • The quenching set of a MEMS capacitor in two-dimensional geometries

        2013

      • Multiple quenching solutions of a fourth order parabolic PDE with a singular nonlinearity modeling a mems capacitor

        2012

      • Collective behaviors in two-dimensional systems of interacting particles

        2011

      • Reduced models for the pacemaker dynamics of cardiac cells

        2011

      • Instability of local deformations of an elastic rod: Numerical evaluation of the evans function

        2011

      • Reverse draining of a magnetic soap film - Analysis and simulation of a thin film equation with non-uniform forcing

        2009

      • Hydrodynamics of bacterial colonies

        2007

      • Spectral stability of local deformations of an elastic rod: Hamiltonian formalism

        2005

      • Hydrodynamics of bacterial colonies: Phase diagrams

        2004

      • Inverse cascade and energy transfer in forced low-Reynolds number two-dimensional turbulence

        2004

      • Hydrodynamics of bacterial colonies: A model

        2003

      • Instability of local deformations of an elastic rod

        2003

      • Traveling hole solutions of the complex Ginzburg-Landau equation: A review

        2001

      • Pulses, fronts and oscillations of an elastic rod

        1999

      • Control-parameter-dependent Swift-Hohenberg equation as a model for bioconvection patterns

        1999

      • A complex pattern of traveling stripes is produced by swimming cells of Bacillus subtilis

        1998

      • Pulses of tunable size near a subcritical bifurcation

        1998

      • Traveling hole solutions to the complex Ginzburg-Landau equation as perturbations of nonlinear Schrödinger dark solitons

        1997

      • Loss-induced transverse effects in lasers

        1997

      • Controlling optical turbulence

        1997

      • Measuring disorder with correlation functions of averaged patterns

        1996

      • Temporal forcing of traveling wave patterns

        1996

      • Travelling wave patterns in lasers with curved mirrors

        1996

      • Correlation functions in the presence of optical vortices

        1994

      • Spatio-temporal intermittency in a 1D convective pattern: Theoretical model and experiments

        1992

      • Localized phase jumps in wave trains

        1992

      • Dynamics of Bloch Walls in a Rotating Magnetic Field: A Model

        1991

      • Statistical properties of defect-mediated turbulence

        1990

      • Breaking chirality in nonequilibrium systems

        1990

      • Defects in Roll-Hexagon competition

        1990

      • Defect-mediated turbulence

        1989

      • Une forme de turbulence associ eacute;e aux d eacute;fauts topologiques

        1989

      • A form of turbulence associated with defects

        1989

      • Defect-mediated turbulence in wave patterns

        1988

      • Topological defects of wave patterns

        1987

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