Resume

• 2011

  Doctor of Philosophy - PhD

  Doctoral dissertation in algebraic topology and homotopy theory advised by Dr. Jeffrey Strom.

  Mathematics

  Math Club

  Pi Mu Epsilon (Mathematics Honor Society)

  Phi Kappa Phi (Honor Society)

  Golden Key Honor Society

  Western Michigan University

  Discrete Mathematics I

  Algebraic Topology I

  Foundations of Higher Mathematics

  Formal Reasoning

  Higher Geometry

  Abstract Algebra and Number Theory (Undergraduate)

  Capstone in Mathematics

  Axiomatic Geometry

  Abstract Algebra I (Graduate)

  Calculus I

  Abstract Algebra II (Undergraduate)

  Differential Topology

  Algebraic Topology II

  Complex Analysis

  Abstract Algebra II (Graduate)

  Analysis I (Undergraduate)

  Honors Calculus II

  Analysis II (Undergraduate)

  Discrete Mathematics II

  Doctoral Dissertation

• 3.57

  Bachelor of Science - BS

  Major in mathematics

  minor in philosophy

  and additional coursework in physics and teacher education.

  Mathematics

  Honors College

  Michigan State University

• Problem solving

  Homotopy theory

  Numerical analysis

  Python

  Academic advising

  Algebraic topology

  Teaching

  Category theory

  MATLAB

  Research

  Data analysis

  Google suite

  Linux

  Topological data analysis

  LaTeX

  Microsoft Excel

  Mathematics research

  Mathematics education

  Github

  Mathematical modeling

  Resolving classes and resolvable spaces in rational homotopy theory

  In homotopy theory

  there are essentially two ways of constructing new spaces: (1) \"gluing\" known spaces together (via homotopy colimits); or (2) \"carving\" from blocks of known spaces (via homotopy limits). \n\nIn this work

  we examine the use of homotopy limits in the construction and understanding of topological spaces. Focusing on a class of computationally well-behaved spaces (known as rational spaces)

  we associate algebraic data (namely: commutative differential graded algebras) to spaces and use these algebraic models to characterize when we can think of one space as carved from another.\n\nWe then use this characterization to investigate spaces carved from well-known spaces such as spheres

  Eilenberg-MacLane spaces

  and projective spaces. Furthermore

  we study applications to the theory of rational quadratic forms

  including an explicit cone decomposition for the spatial model assigned to a quadratic form.

  Resolving classes and resolvable spaces in rational homotopy theory

  I have offered my service as a writer of mathematical reviews for zbMATH since 2016.

  Reviews in Mathematics

  Rational spaces in resolving classes

  Using algebraic data to model rational topological spaces

  we uncover a quotient of the Witt group (of quadratic forms) embedded in a complicated topological structure (called the resolvability relation).

  Rational spaces in resolving classes

  We exhibit well-known correspondences between non-associative algebraic structures and sharply transitive actions as a related assortment of categorical equivalences.

  On the topological characterization of gestures in a convenient category of spaces (to appear)

  In mathematical music theory

  a gesture is a formal way of mapping a directed graph into a topological space. The resulting network of paths in the space can then be used to model the physical motion of performers or listeners as well as the conceptual motion of musical relationships in a piece. This work revisits a topological (as opposed to combinatorial) characterization of gestures in a novel way.

  Clark

  Timothy

  Clark

  Western Michigan University

  Adrian College

  Kalamazoo

  MI

  In addition to the usual teaching

  tutoring

  and research duties

  I held the following positions: Graduate Mentor

  Mathematics Tutor Lab Coordinator

  and Assistant to the Director of the Developmental Mathematics Program.

  Graduate Teaching Associate

  Western Michigan University

  Adrian

  MI

  I currently hold a tenure-track assistant professor position in the Department of Mathematics at Adrian College. Duties include teaching a wide spectrum of undergraduate mathematics courses

  scholarly research and professional development

  college service

  and academic advising.

  Assistant Professor

  Adrian College

  https://www.maa.org/

  Member

  Mathematics Association of America

  http://www.smcm-net.info/

  Member

  Society for Mathematics and Computation in Music

  https://www.ams.org/home/page

  Member

  American Mathematical Society

  German

  Graduate Research and Creativity Scholar

  Presented annually to a doctoral student in recognition of scholarly productivity.

  Western Michigan University Mathematics Department

  Charles H. Butler Excellence in Teaching Award

  Presented annually to graduate teaching assistants in recognition of excellence in teaching over an extended period.

  Western Michigan University Mathematics Department

  Graduate Service Award

  Presented annually to a graduate student in recognition of extraordinary dedication and outstanding service to the Department of Mathematics.

  Western Michigan University Mathematics Department

  Grad Talks: 3 Minute Thesis Competition Prize Winner

  The 3 Minute Thesis Competition challenges graduate students to explain their research to a non-specialist audience in under three minutes.

  Western Michigan University Graduate Student Association