Vazquez has served on the Advisory Board at the National Institute of Mathematical and Biological Synthesis (NIMBioS) and the SACNAS Math Taskforce. Notable engagements include plenary lectures at the 2018 SIAM National Meeting, the 2017 AWM Research Symposium, 3rd PRIMA Congress, the 8th Australia-New Zealand Mathematics Convention (Melbourne, Australia), the 2014 Mohammed Dahleh Distinguished Lecture (UCSB), a 2014 Distinguished PIMS lecture in Mathematical Biology (University of Saskatchewan, Canada), and the 2010 BaMBA Conference (Stanford University). She has also given public lectures at multiple venues including the 2015 and 2017 National Math Festivals and the 2017 PRIMA Conference.

Vazquez obtained a B.Sc. in Mathematics from the National University of Mexico (UNAM) and a Ph.D. from Florida State University, where she worked with De Witt Sumners and was supported by fellowships from DGAPA UNAM and the Program for Mathematics and Molecular Biology/Burroughs Wellcome Fund. After receiving her doctorate, she held appointments as a Postdoctoral Fellow/Visiting Assistant Professor at UC Berkeley working with Rainer Sachs. While at Berkeley, Vazquez received an Exxon Mobil Project NExT Fellowship. She joined the faculty at San Francisco State University in 2005, and the UC Davis faculty as a CAMPOS scholar in July 2014. Vazquez has held numerous visiting positions, including appointments in the Biochemistry Department at the University of Oxford (UK), the Molecular Biology Department CID/CSIC (Barcelona), and the Institute for Mathematics and its Applications, (Minneapolis). Her research focuses on the applications of topological and discrete methods to the study of DNA, with an emphasis on the topological changes affected by enzymes such as topoisomerases and site-specific recombinases, as well as on the study of chromosomal rearrangements in radiation cytogenetics and cancer.