Born in Guadalajara, Mexico, Andrea Arauza Rivera is the daughter of a proud Mexican family. Andrea spent the first 10 years of her life moving between Mexico, Nevada, and Texas. In Texas, her father acquired legal residency and then citizenship to the United States; through the Immigration and Naturalization Act of 1996, Andrea inherited citizenship when she was 11. As many Mexican-American children do, Andrea struggled to hold on to her heritage while trying to fit into this new world. With every complement from teachers for speaking English without an accent, she learned that to be an academic she needed to check her culture at the door.
The Arauza family eventually settled in the California Central Valley where Andrea first fell in love with solving puzzles. After graduating high school, she attended Modesto Junior College before transferring to Cal State Stanislaus. Working the 6:00PM-2:00AM shift at Del Taco allowed Andrea to finance her education without putting an additional burden on her parents. At Stanislaus, Andrea came to understand that her love for mathematics would lead to financial stability and independence.
In 2012, Andrea began the Mathematics PhD program at the University of California, Riverside. Graduate school was a trying time. Isolation is often a part of the package for people of color studying mathematics. More than ever, Andrea embraced her identity as a Chicana and made a lifelong commitment to fighting for justice and equity. It is unjust that the privileged can have a nearly exclusive claim on the identity of “mathematician”
Andrea’s research is in functional analysis and fractal geometry. Consider the connection between geometry and algebra. We study the graph of a parabola by studying the algebraic relationship y = x^2. This connection extends far beyond basic high school math. There is a well known duality (in the sense of category theory) between compact Hausdorff topological spaces and commutative unital C* algebras. Studying the geometric and topological properties of a space X turns out to be the same as studying properties of the algebra of continuous functions on X, namely C(X). If you have a problem about topological spaces, you can translate the problem into one about algebras, use the powerful machinery of linear/operator algebra(s) to solve the problem, and then translate the solution back to the land of topological spaces. One can lift the requirement of commutativity and study the “geometry” of noncommutative C* algebras. This is the field of noncommutative geometry.
Fractal spaces are known to have complex geometric properties and one can use the tools from noncommutative geometry to study them. Andrea’s work is in constructing spectral triples (a tool from noncommutative geometry) that can be used to reformulate notions of dimension, metric, and measure for fractal spaces. One goal of this work is to create new tools which can be used in the study of analysis and differential equations on fractals. Together with a research group of undergraduate and graduate students, Andrea continues her work on analysis and fractal geometry at Cal State East Bay.
Andrea’s passion for teaching and mentoring stems from the desire to use mathematics as a tool for social justice. Teaching mathematics well is an act of empowerment and the tenants of culturally responsive teaching form the core of Andrea’s teaching philosophy--communicating high expectations, student-centered instruction and culturally mediated instruction, among others.
Students from underrepresented groups are particularly well served by more engaging, active, and collaborative teaching techniques. As a project NExT Fellow, Andrea’s knowledge of research based teaching practices has grown and her teaching continues to evolve. She is committed to creating an environment in which students feel empowered and challenged to develop their mathematical creativity. Her classroom is often loud with the voices of students discussing ideas. Andrea continues to explore new teaching strategies and thinks carefully about developing more equitable methods of assessment.
At UC Riverside, Andrea was an active participant of the events put on by the Chicanx Student Programs group. She served as a Chicanx Peer mentor to a group of undergraduates, was featured on panels to demystify graduate school, gave talks on fractal geometry and volunteered during the Chicanx Youth Conference. For a year, she was also the mathematics instructor for the UC Riverside Upward Bound program.
In the summer of 2017, Andrea was a teaching assistant for the PUMP (preparing undergraduates through mentorship towards PhDs) program. PUMP aims to identify and prepare students from underrepresented groups to earn graduate degrees in mathematics. Through PUMP, Andrea formed connections with the Pacific Math Alliance, a regional branch of the National Math Alliance which seeks to better representation in mathematics. In 2019, Andrea chaired the organizing committee for the Pacific Math Alliance conference. The conference took place at Cal State East Bay and featured graduate school workshops, mathematics talks, talks on teaching and mentoring, and career panels, for its 200 participants.
This month is an opportunity to cherish the many contributions of our gente to mathematics and society. We have always been mathematicians, and now we come together to share and rejoice in our stories. Stories of perseverance, of joy, of triumph in mathematics. Stories that extend beyond our own lives to the lives of our ancestors and our children. We have always been mathematicians and will always be mathematicians.