Carol Ann Downes

I am a fifth year Ph.D. student in Rice University's Mathematics Department with Robert Hardt as my thesis advisor. My research interests include geometric measure theory, optimal transport theory, their applications to economics and political science, and the scholarship of teaching and learning in mathematics.


Papers (in progress)

  • A mass reducing flow for real flat chains and applications to transport networks, 2016.
  • Explaining the impact of cosponsorship in legislative processes: A political science application of optimal transport theory, 2016 (joint work with Philip D. Waggoner)
  • Reading assignments in mathematics higher education: A literature review, 2016 (POSTER)


  • Flow on a transport path

    Here, the flow is minimizing the cost of transporting two sources to two sinks.

  • Flow on a transport path

    Above, the flow is minimizing the cost of transporting one central source to twenty four sinks.

  • Flow on a square (cycle)

    The flow first rounds off the corners of the square before minimizing to some point inside the square.

Teaching Experience

Instructor of Record

Seminars and Teaching Service

  • VIGRE Seminar on Optimal Transport Networks (Spring 2016)
  • VIGRE Seminar on Steiner Trees (Summer and Fall 2015)
  • Rice's Center for Teaching Excellence Liason

REU Advisor

  • Rice University RTG's Mathematics REU (Summer 2016)

Teaching Assistant

  • Calculus Coordinator
    • Trained and managed TAs in active learning techniques
  • Math101 Calculus I
  • Math102 Calculus II
  • Math212 Multivariable Calculus

Teaching Professional Development