Leah Berman
2009 | Professor of Mathematics
University of Washington 2002, PhD
My broad research area is discrete geometry: I’m interested in studying objects that have pieces, such as vertices, edges, and faces, and I’m interested not only in how they connect together (combinatorial information) but also where they are in some ambient space (geometric information). For example, cubes and parallelepipeds are combinatorially the same — they both have 8 vertices, 12 edges, and 6 faces — but geometrically, they are very different. Cubes have 6 square faces, and every vertex looks the same, but some vertices in parallelepipeds are “pointy” and some are not. My primary research program concerns configurations of points and lines, which are collections of geometric points and straight lines, typically in the Euclidean plane, with q points lying on each line and k lines passing through each point. In general, it is unusual for more than two straight lines to intersect in a single point (or dually, for three or more points to be collinear), so finding examples of configurations, especially where q and k are larger than 4, is not straightforward. My research has focused on using symmetry and geometry to find new infinite families of configurations, including the smallest known 5- and 6-configurations. Other research interests include polytopes (n-dimensional geometric or combinatorial generalizations of polyhedra) and graph theory.
Highlighted works:
Berman, Leah Wrenn, Gábor Gévay and Tomaž Pisanski. Connected (nk) configurations exist for almost all n. The Art of Discrete and Applied Mathematics (2021, in press).
Berman, Leah Wrenn, Phillip DeOrsey, Jill Faudree, Tomaž Pisanski, and Arjana Žitnik. Chiral astral realizations of cyclic 3-configurations. Discrete Comput Geom 64, 542–565 (2020).
Berman, Leah Wrenn, Barry Monson, Deborah Oliveros, Gordon Williams. Fully truncated simplices and their monodromy groups. Advances in Geometry. Volume 18, Issue 2, Pages 193–206, (2018).
Berman, Leah Wrenn, Jill R. Faudree and Tomaž Pisanski. Polycyclic movable 4-configurations are plentiful. Discrete and Computational Geometry. 55, no. 3, 688–714 (2016).
Berman, Leah Wrenn, Elliott Jacksch* and Lander ver Hoef*. An infinite class of movable 5-configurations. Ars Mathematica Contemporanea. 10 (2016), no. 2, 411–425.
*denotes °®ÎŰ´«Ă˝ undergraduate students