Teaching
My teaching is based on the idea that we should account for the various students' skills and strengths in the classroom, that failing to solve a math problem can be a formative experience, and that one should be aware of the advantages and challenges that inform a students' learning. Most of the information about the classes will be available via Canvas.
Diversifying the pipeline
We are a welcoming team that aims for excellence and diversity. One of our goals is to construct a bridge between our research group and the existing UCR programs designed to support diverse students such as women, low-income, and first-generation students. Such a bridge will provide research experience to students, expose them to contemporary mathematics, and prepare them to apply to competitive programs across the country.
Research for undergraduate students. If you are a curious student who wants to learn more about mathematics, I will be happy to talk with you about it. I work at the crossroads of geometry, combinatorics, and algebra, and I am interested in their pure or applied aspects. These mathematical constructions arise from either pure mathematical considerations or applications such as phylogenetic trees. Working together will mean reading about such theories and constructing novel examples and expositions. Specific projects include the following
Study geometric features associated with a given polynomial equation of a fixed degree.
Develop databases and computational tools to study polytopes that arise from directed graphs.
Describe families of configurations of linear maps and their classifications.
Study arrangements of points and lines in the plane.
Art
A central problem in Geometry is to construct complete databases, or colonies, of geometric objects. These databases are known as moduli spaces. In this painting, we explore the moduli space of cubic surfaces obtained with Geometric Invariant Theory and first described by Hilbert in 1893. The cubic surfaces are represented here by white balls. Red dots represent their singular points. A closer look reveals some of the 27 lines that every smooth cubic surface contains and the variation among them represents the four dimensions of the moduli space. Finally, we include, at the center, the unique point associated with more than one type of cubic surfaces.
The art work was exposed at the Mathematical Art Galleries of the 2017 Joint Mathematical Meetings. (click here for more information and a better picture!). Its title is "A colony of cubic surfaces."
