Resume

• 2003

  Doctor of Philosophy (PhD)

  Thesis: \"Integrability of Second-Order Partial Differential Equations and the Geometry of GL(2)-Structures\"

  Mathematics

  Duke University

• 1999

  Society for Industrial and Applied Mathematics

  Mathematical Association of America

  American Mathematical Society

  American Association for the Advancement of Science

  German

  English

  French

  Bachelor of Science (B.S.)

  Physics and Mathematics

  University of Wisconsin-Madison

• Differential Geometry

  SciPy

  SQL

  Linux System Administration

  Mercurial

  JavaScript

  Mathematical Programming

  CSS

  Analysis

  Computer Network Operations

  Mathematical Analysis

  NumPy

  HTML5

  LaTeX

  IPv6

  Maple

  Differential Equations

  Python

  R

  Git

  Constructing Involutive Tableaux with Guillemin Normal Form

  Constructing Involutive Tableaux with Guillemin Normal Form

  ... classifying integrable systems in three dimensions using invariant curvature representations. This clarifies the meaning of “wave-like equation” through the geometry of superposition phenomena.

  Integrable GL(2) Geometry and Hydrodynamic Partial Differential Equations

  Degeneracy of the Characteristic Variety

  Goals: Push scientific and technological progress through clear thinking and mathematical insight. Develop geometric methods for machine learning multivariable dynamics

  multiscale data analysis

  computer vision

  control theory

  and other problems requiring automated coordinate-independent characterization.\nMathematical specialties: Analysis and Geometry. Specifically: initial-value problems and integrability phenomena; analysis on manifolds; differential geometry; data and object classification through geometric

  topological

  and homological invariants.\nComputational specialties: Object-oriented programming

  algorithm design

  open-source development

  \nand advanced Linux/UNIX system administration.

  Abraham

  GEOMETRIC DATA ANALYTICS

  University of Wisconsin-Stout

  McGill University

  Fordham University

  Researched the geometry of integrable systems and conservation laws

  particularly using techniques from homological algebra and differential geometry. Mentored by Niky Kamran. Supported by an All-Institutes Postdoctoral Fellowship through MSRI’s core NSF grant DMS-0441170. Notable Projects: \n-- International Workshop --- Organized a week-long intensive workshop at Centre de Recherches\nMathématiques and Université de Montréal

  drawing worldwide experts in moving frames. Joint with Francis Valiquette.\n-- Research Conference --- Organized a special session at the Summer Meeting of the Canadian\nMathematical Society at Dalhousie University. Joint with Francis Valiquette.

  McGill University

  Fordham University

  Greater New York City Area

  Performing full-time faculty duties: 15-credit teaching load

  student mentoring

  active participation in department committees

  curriculum improvement

  and technical infrastructure development. Notable Roles:\n\n• Administrator — Proposed

  negotiated

  designed

  implemented

  and maintained Research Computing Cluster

  a virtualized Linux environment for interdepartmental high-performance research computing.\n\n• Developer — Wrote symbol.sage Python module for micro-local analysis and characterization of partial differential equations in the open-source Sage computer-algebra system.\n\n• Manager — Collaborated with deans

  advisors

  and instructors to adapt courses for evolving student enrollment. Tracked student progress and improved outcomes.\n\n• Mentor — Directed undergraduate research in computational methods for vector graphics and computer vision. Trained students in data preparation and scientific publishing.\n\n• Referee — Provided detailed peer-review for top-tier research journals Selecta Mathematica

  Journal of Differential Geometry

  Communications in Analysis and Geometry

  and AMS Mathematical Reviews.\n\n• Researcher — Continued study of geometric and computational methods for differential equations

  presenting results at international institutions including Brno Czech

  Berkeley

  CRM

  Texas A&M

  Fields Institute

  and CUNY.

  Peter M. Curran Visiting Assistant Professor

  Menomonie

  WI

  USA

  Assistant Professor

  University of Wisconsin-Stout

  Raleigh-Durham

  North Carolina Area

  Senior Mathematician

  GEOMETRIC DATA ANALYTICS