My research is incidence theory in groups acting on finite point sets and how answering questions there can help understand the geometry of these sets. Currently I am focusing on the following type of questions:
Suppose a finite point set has near-optimal geometric behaviour, can we obtain structure.
Can one bound the number of non-rigid configurations generated by a point set.
What extent does additive structure of the underlying set determine its geometric behavior.
You can read my research statement here.
(On the right is a representation of how a graph on four vertices is represented in the Euclidean group acting on it.)
Publications
A Structural Theorem for Sets With Few Triangles, joint with Sam Mansfield, arXiv:2206.09740, to appear, Combinatorica.
On Erdős Chains in the Plane. Bull. Korean Math. Soc. 58 (2021), no. 5,arXiv: 2010.14210,
Distinct Distances from Points on a Circle to a Generic Set, joint with Alex McDonald, Brian McDonald and Anurag Sahay. Integers 21 (2021), arXiv: 2005.02951
Finite Point Configurations In The Plane, Rigidity And Erdős Problems, joint with Alex Iosevich. Published in J. Proc. Steklov Inst. Math. (2018) 303: 129, arXiv: 1805.08065.
Preprints
A multi-parameter variant of the Erdős distance problem (2017), joint with Alex Iosevich and Maria Janczak, arXiv: 1712.04060.
Presentations and more
Slides from my talk at the NYC Geometry Seminar
Slides from my talk at the Point Distribution Webinar