Cynthia Flores is an American Latina mathematician whose parents migrated from El Salvador. She grew up in Los Angeles, CA, in the Pico-Union community, working at local outdoor swap meets every weekend. Inspired by her hard-working parents and sister, she received her BS and MS in Mathematics from California State University Northridge while receiving support and mentorship from the PUMP Program (Preparing Undergraduates through Mentoring for Ph.D.s). Despite facing several challenges, in 2014 she completed a Ph.D. in mathematics from the University of California Santa Barbara in dispersive partial differential equations. She then joined the faculty at California State University Channel Islands as an Assistant Professor where she enjoys teaching ordinary and partial differential equations, supervising undergraduate research, expanding her research in well-posedness of PDEs, collaborating with community partners in data science projects, and working towards work-life balance along with her husband and children. She has been inspired by several mentors and advisors and aims to continue their shared work and legacy in creating opportunities for diversity within the mathematics community.
Cynthia Flores’s field of interest lies at the intersection of partial differential equations, harmonic analysis, and mathematical physics. Specifically, Flores is interested in the study of dispersive KdV-like and Peridynamic equations, and their corresponding well-posedness problems. The Benjamin-Ono equation is of particular interest for modeling long internal waves and presents challenges due to the presence of the nonlocal operator (and singular integral operator), the Hilbert transform, appearing in the dispersive term. Her Ph.D. Dissertation presents results on decay properties of solutions to the IVP of the Benjamin-Ono equation in weighted Sobolev spaces. Recently, Flores studied control and stability problems related to equations including the fifth order KdV equation, the Benjamin-Ono equation and its dispersion-generalized version, all posed on a periodic domain in the spatial variable. Her work focused specifically in determining if it is possible to construct a control input to apply to a system, with prescribed initial and final states, such that the solution trajectory is identical to the given conditions at the initial and final times. She also investigated the related asymptotic (in time) stability properties of the corresponding solutions if a control input is found. Recent results related to these questions can be found at https://arxiv.org/abs/1706.04798 and https://arxiv.org/abs/1709.10224.
Currently, Flores is interested in nonlocal theories of the mechanics of solids as they pertain to the propagation of crack formation in certain materials. Considering the nonlocal equation of motion with the presence of a pairwise force functions, showing existence of solutions, understanding qualitative properties of solutions, and formulating corresponding control and stability theory are of particular interest. As a faculty mentor, Flores works closely with undergraduate and master’s student researchers, supervising interdisciplinary mathematics projects in PDEs, epidemiological math models, and numerical simulations of wave phenomenon, including control models. Additionally, she works in collaboration with statisticians and the local county public health office, supervising undergraduates in data science projects in categorical machine learning modeling.