I am a PhD candidate in the Mathematics Department at the University of Oregon, working with Dev Sinha.Office: 304 Fenton Hall
Phone: (541) 346-5620
E-mail: cgiusti "at" uoregon.edu
Current Course
The syllabus for Math 246 (CRN 13690) is here. Homework is administered through WeBWorK. . The study guide for midterm 2 is here.
Research
My research interests lie in the computational aspects of algebraic topology. I enjoy exploring geometric and combinatorial properties of spaces and leveraging this data to gain an understanding of what is happening in more abstract algebraic settings. A somewhat complete summary of my current projects can be found in my research statement.
One facet of my dissertation was the construction of a family of combinatorial knot spaces called plumbers' knots. These spaces admit an algorithm for classification of components which can be exploited to algorithimcally determine if two topological knots are isotopic. Here are images of representatives of the components of the first two non-trivial spaces of plumbers' knots.
Teaching
When I internalize a piece of mathematics, it fits into a larger conceptual narrative which flows naturally from one idea to the next. When teaching I try to focus not just on communicating facts and theorems but also on imparting my "feel" for this narrative. My efforts in this direction are summarized in my teaching statement.
I am also deeply interested in the future of technology in mathematics education. I believe that the time is right for software developed and maintained by mathematicians to take its place in classrooms. The current commercial systems are expensive to both institutions and students, and all too often they fail to live up to their promise as educational tools. Some very early movements in the direction of community-based solutions come in the form of the Sage project, an open source python-based computational system in the vein of Mathematica, Matlab or Maple and the WeBWork project, an open source alternative to homework software like WebAssign.
Other Thing(s)
During the summer of 2007, I taught the math department's summer "pre-school" for incoming graduate students. The problem sets used for this session were: Set 1, Set 2 and Set 3.
