Cary Ross Humber
Contact
413 Mill Neck Road
Information Williamsburg,VA USA
23185
Cell: 919.633.8494
E-mail: caryhumber@gmail.com
Web: www.math.wm.edu/∼crhumber
Security
Clearance
Department of Defense Secret (expired: 2013)
Citizenship
USA
Career
Goals
To obtain a tenure-track professorship at a liberal arts College or University.
Research
Interests
Functional analysis; geometric, algebraic, & numerical methods for partial differential equations(PDEs); inverse problems; semigroups; Riemannian geometry; quantum
groups; computational topology; dynamical systems, chaos & fractals
Education
North Carolina State University, Raleigh, NC USA
Ph.D., Applied Mathematics, May 2011
• Advisor: Professor Kazufumi Ito
• Area of Study: Applied Analysis/Control & Inverse Problems for PDEs
• Dissertation Title: Inverse Problems Governed by Evolution Equations
M.S., Applied Mathematics, December 2009
• Advisor: Professor Kazufumi Ito
• Area of Study: Interface Problems and Numerical PDEs
• Thesis Title: Numerical Methods for Interface Problems
B.S., Mathematics, May 2005
• Advisor: Professor John Franke
• Cum Laude
• Honors Thesis Title: Chaos, Fractals and their Dependence on Parameters
Experience
The College of William & Mary, Williamsburg, VA USA
Visiting Assistant Professor
August 2012 - present
• Teaching lower and upper-level undergraduate Mathematics courses.
• Advising research projects for Mathematics majors
• Advising contestants for national and regional math competitions
Naval Surface Warfare Center, Panama City, FL USA
Mathematician
September 2009 - August 2012
• Responsible for conducting independent research program as well as numerical
computations and computer simulations for various problems of interest to the
U.S. Navy.
• Examples include heat conduction, sonar imaging, signal design/optimization,
and various PDE related problems.
• Writing research proposals, internal technical reports and journal publications.
North Carolina State University, Raleigh, NC USA
Graduate Teaching Assistant
2008-May 2010
• Responsible for lecturing, lesson planning, and grading for mathematics courses.
Center for Research in Scientific Computation at NCSU, Raleigh, NC USA
Research Assistant
2007-May 2010
• Developed numerical techniques for PDE problems involving acoustic-structure
interactions.
Independent
Private Tutor
2006-2010
• Effective tutoring of high school and college students in mathematics courses.
Independent Electrical Contractor
Summer 2006
• Responsible for installation of electrical service for industrial/commercial buildings
Independent Contractor
2003-2006
• Responsible for new construction of commercial and residential property.
• Carpentry, electrical, plumbing, etc.
Computer
Languages
& Programs
Teaching
Excellent Proficiency
Basic Proficiency
MATLAB, Mathematica, LATEX, Python, MAPLE
CUDA, FORTRAN, HTML, C++, SAGE, MAGMA,
COMSOL Multiphysics
William & Mary
Math
Math
Math
Math
Math
Math
111
112
302
103
414
309
-
Calculus I
Calculus II
Ordinary Differential Equations
PreCalculus
Numerical Analysis II
Intermediate Linear Algebra
NCSU
MA 105 - Mathematics of Finance
MA 107 - PreCalculus
MA 401 - Applied Differential Equations II(Undergraduate PDE)- CoInstructor
Undergraduate
Students
William & Mary
Advised
Kayton, B. Applications of Multilinear Algebra
Pickett, C. Measure Theory for Finance
Corry, M. TBD
Ge, S. TBD
Toyos, E. TBD
Other
Advising
William & Mary
William Lowell Putnam Competition, 2014
Virginia Tech Regional Mathematics Competition, 2014
Publications
• Humber, C. “An adjoint method for initial condition reconstruction in Banach
spaces”, in preparation, 2013.
• Humber, C., Ito, K., and Huynh, Q. “One-way wave equations for synthetic aperture sonar imaging”, submitted, 2012.
• Humber, C., Ito, K. “An adjoint control method for initial condition identification
of the abstract Cauchy problem”, preprint, submitted, 2012.
• Humber, C. “The KdV equation and solitons”, In-Laboratory Independent Research (ILIR) internal report, 2012.
• Humber, C. “A control method for inverse problems governed by partial differential
equations”, In-Laboratory Independent Research (ILIR) internal report, 2012.
• Humber, C. “An adjoint control filter for nonlinear partial differential equations”,
In-Laboratory Independent Research (ILIR) internal report, 2011
• Humber, C.R., Ito, K, and Bouton, C “Nonsmooth formulation of the support
vector machine”, preprint, 2010.
• Humber, C.R. “Nonsmooth regularization and control”, In-Laboratory Independent Research (ILIR) internal report, 2010.
Invitations
• Department of Mathematics, University of California, Davis, CA
• Low-Dimensional Topology Colloquium, Georgia Institute of Technology, Atlanta,
GA
• The 6th International Conference: Inverse Problems: Modeling and Simulation;
21-26 May 2012; Turkey
Presentations
• Mathematics Colloquium, The College of William & Mary (March 2013)
• In-Laboratory Independent Research (ILIR) Mid-Year Review (April 2012)
• In-Laboratory Independent Research (ILIR) End-of-Year Review (October 2011)
• Mathematics Colloquium, NSWC (2011)
• Office of Naval Research Annual Gathering for Information Integration and Automated Image Understanding (May 2011)
• In-Laboratory Independent Research (ILIR) Mid-Year Review (April 2011)
• Naval Undersea Warfare Center, Newport, RI (September 2011)
• In-Laboratory Independent Research (ILIR) End-of-Year Review (October 2010)
• Office of Naval Research Annual Gathering for Information Integration and Automated Image Understanding (May 2010)
• In-Laboratory Independent Research (ILIR) Mid-Year Review (April 2010)
Research
Funding
In-Laboratory Independent Research (ILIR), 2011-2012, $75k
• Inverse problems for nonlinear partial differential equations
In-Laboratory Independent Research (ILIR), 2010-2011, $75k
• Nonsmooth Tikhonov regularization for state reconstruction
In-Laboratory Independent Research (ILIR), 2009-2010, $75k
• Solution of PDEs in heterogeneous materials
Research Experience for Early Graduate Students (REG), Summer 2007, $4k
• High-order finite-difference schemes for Stokes flow
Research
Experience
One way wave equation for Synthetic Aperture Sonar
High Order Finite Dierence Scheme on an Overlapped Domain for the Stokes Equations
Model Development and Parameter Estimation for a Uniform Beam Excited by
Impact and Voltage Inputs
• Estimated the parameters for a mathematical model of a steel beam excited by
piezoelectric patches.
Nonlinear Tracking and Parameter Estimation using Modified Gaussian Filters
• Missile tracking and model parameter estimation using filters based on GaussHermite quadrature.
Optimal Control of Thermal Energy
• Development of the optimal control to maintain positive heat transfer in a
physical model.
Analysis of Numerical Methods for PDEs
• Convergence and Stability analysis of computational methods for pdes/systems
of pdes.
Validation and Verification (V&V) for a Two Parameter Linear Model
• Use of Monte Carlo Simulations for the V&V of a Spring Model.
Modeling Heat Transfer in a Rod with the Heat Equation
• Estimating model parameters for the heat transfer in copper and aluminum
rods.
Research
Goals
Research in
Progress
• To expand and diversify my knowledge of mathematics.
• To make strides in theoretical and applied functional analysis as well as theoretical
and applied topology.
• To develop both theoretical and computational methods for control and inverse
problems governed by PDEs.
• To pioneer new areas of mathematics and forge links between previously unrelated
areas of mathematics.
• Ill-posed inverse problems resulting from evolution equations
• Nonsmooth regularization and parameter choice rules
• Investigating quantum groups, categorification as related to PDE in quantum
physics (e.g. quantum Coulomb problem)
• Navier-Stokes theory and methods
• Investigating computational homology (topology) with regards to sensor networks
Coursework Advanced Functional Analysis, Semigroups, Optimal Control Theory, PDEs, Stochastic PDEs, Lagrange Multiplier Theory & Optimization, Numerical Analysis, Mathematical Modeling, Model Calibration, Linear Algebra, Algebra, Chaos theory & Fractals
Workshops
& Seminars
• Non-Tenure Eligible (NTE) Teaching Excellence Workshop (April 2013)
• Characteristic Classes Reading Group, W&M (2012-2013)
• 2010 Industrial Math/Stat Modeling Workshop for Graduate Students
• Numerical Methods for Free Boundary and Moving Interface Problems at SAMSI,
RTP, NC (2007)
Professional
Affiliations •
•
•
•
Society for Industrial and Applied Mathematics (SIAM)
American Mathematical Society(AMS)
Mathematics Graduate Student Association at NCSU
NCSU SIAM Student Chapter
Service
W&M Non-Tenure Eligible (NTE) Network
Mathematics Graduate Student Association
• Third and Fourth Year Representative
Joint SIAM-SMB Conference on the Life Sciences, 2006
• Volunteer
December 22, 2014