Professor Toro was born in Bogotá, Colombia. She received her B.S. from the Universidad Nacional de Colombia in Bogotá and her Ph.D. from Stanford University. She has been a member of the Institute for Advanced Study in Princeton, of the Mathematical Sciences Research Institute (MSRI) in Berkeley and a fellow at the Radcliffe Institute for Advanced Study. Her awards include a Guggenheim Foundation Fellowship, two Simons Foundation Fellowships, and the Landolt Distinguished Graduate Mentor Award, from the University of Washington. She is a Fellow of the AMS, and a ``Miembro Correspondiente de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales”. In 2020 she was elected as a Member of the American Academy of Arts and Sciences, and received the Blackwell-Tapia prize.
She was an invited speaker to ICM 2010 in Hyderabad, India. She delivered an invited address at the Joint Mathematics Meeting in New Orleans, Louisiana in 2011, and the NAM Clayton-Woodard Lecture at the Joint Mathematics Meeting in Seattle, Washington in 2016. In 2020 she was the inaugural AMS Mirzakhani Lecture speaker at the Joint Mathematics Meeting in Denver, Colorado.
She serves as a member of the Board of Trustees of the Institute for Pure and Applied Mathematics (IPAM) at UCLA, a member of the Board of Directors of the Banff International Research Station (BIRS) and as co-chair of the Scientific Advisory Committee of MSRI in Berkeley. She is a member of the US National Committees for the International Mathematical Union.