Degrees

Ph.D. University of Michigan (2002)
M.S.  University of Michigan (1999) 
B.A. Scripps College (1997)

Research Interests

My research lies at the intersection of computational commutative algebra, algebraic geometry, combinatorics, and applications.  One of the major threads of inquiry in commutative algebra is to try to understand algebraic properties of sets of polynomials. Algebraic geometers study varieties, which are the solution sets of systems of polynomial equations.  I am interested in studying systems of nonlinear polynomial equations that arise in geometric problems with a combinatorial flavor and in applications, especially rigidity theory.

The fundamental object of study in rigidity theory is a bar-and-joint framework, and mechanisms based on bar-and-joint frameworks have a long and rich history.  I have enjoyed exploring connections between rigidity theory and algebraic geometry as well as applications of rigidity theory to areas including computer-aided design, architecture, and the control of formations of robots.

Teaching Interests

I enjoy teaching students with a wide range of interests and backgrounds. I believe that everyone is capable of deepening their understanding of mathematics, and my goal is to help each student discover how to unlock the next level of understanding in their mathematical journey.  I have taught core courses at all levels including calculus, linear algebra, discrete mathematics, real analysis, and abstract algebra, as well as electives ranging from the mathematics of perspective drawing to computational algebraic geometry, topology, and rigidity theory.

Awards and Honors

AWM Distinguished Speaker, University of Oregon, 2022.

Merten M. Hasse Prize (joint with Zvi Rosen and Louis Theran), MAA, 2021.

Best Paper Award (joint with Audrey St.John), Symposium on Solid and Physical Modeling, SPM 2012.

Meribeth E. Cameron Faculty Award for Scholarship, Mount Holyoke College, 2012.

National Science Foundation grant DMS-0600471, 2006-2009.

National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship, DMS-0201607, 2002-2003, 2004-2005.

Links

My personal website is available here.