Caroline Hills

On October 30 I successfully defended my dissertation, titled “A Study of Singularities in Homotopy Continuation for Kinematic Applications”. I will graduate in January 2025 from Notre Dame and begin a full time job as a Mathematician at the Johns Hopkins University Applied Physics Laboratory.

The paper “Computing complete solution sets for approximate four-bar path synthesis” with Aravind Baskar, Mark Plecnik, and Jonathan Hauenstein was recently accepted for publication in Mechanism and Machine Theory.

I presented my work Robotic Kinematic Optimization Applications at the Joint Mathematic Meetings AMS Special Session on Topological and Algebraic Approaches for Optimization in San Francisco, CA.

This semester I am the course instructor for Intro to Applied Math Methods II, ACMS 20750-01.

In the summer I will be interning with the Johns Hopkins Applied Physics Laboratory.

The paper “Max-convolution through numerics and tropical geometry”, with Taylor Brysiewicz and Jonathan Hauenstein, has been accepted into Numerical Algorithms.

Our paper, Assessing reliability of movement screenings using a markerless motion
capture system, joint work with the ACMS and ND Athletics Departments, was recently accepted into The Orthopaedic Journal of Sports Medicine.

I am currently completing a summer internship and have updated “Publications and Preprints” to reflect recent work. I co-organized the “Numerical Methods in Algebraic Geometry” mini-symposium with Paul Brieding, Emma Cobian, and Jose Rodriguez held next month at SIAM Conference on Applied Algebraic Geometry in Eindhoven, The Netherlands.

This past week, I attended the Society for Industrial and Applied Mathematics Conference on Computational Science and Engineering held in Amsterdam, The Netherlands. I was the student representative for Notre Dame’s SIAM chapter.