His research encompasses many areas of mathematics and their applications, with diverse publications in journals such as SIAM Review, Physical Review Letters, Journal of Theoretical Biology, Geophysical and Astrophysical Fluid Dynamics, Nonlinearity, Journal of Computational Dynamics, Combustion Theory and Modelling, Physica D, SIAM Journal on Applied Dynamical Systems, Scientific Reports and Journal of Fluid Mechanics, as well as a sole-author monograph in the area of applied analysis published by the Society of Industrial and Applied Mathematics. His awards include a Future Fellowship from the Australian Research Council, the Endeavour Research Leadership Award from the Australian Commonwealth Department of Education and Training, the J.H. Michell Medal from the Australian/New Zealand Industrial and Applied Mathematics Society, and the Stella Dafermos Award from Brown University.
Sanjeeva's extensive teaching experiences include 85+ course offerings in mathematics, statistics and data; undergraduate and postgraduate; large service and small project-based; application-dominant to theoretical; and mathematics enrichment for humanities students to specialized research courses. He has been at the forefront in mathematical pedagogy in areas such as mathematical motivation, student-centred learning, project-based courses, peer-assessed teaching tools, accessing higher cognitive levels in the Bloom taxonomy, leveraging learning management systems for innovative engagement, and writing in mathematics; and had an article in the Mathematical Association of America Focus Magazine (2008) on a method for flipping a Real Analysis course before the term ''flipping'' was even known. He has also led curriculum development efforts at the program level, including at a joint Australian-Chinese undergraduate college. As the Director (a.k.a. Associate Dean) of Learning and Teaching at the Faculty of Engineering, Computer and Mathematical Sciences (University of Adelaide; 2020--2022), he led significant efforts in modifications to course delivery and examinations during a time of turmoil.
Sanjeeva's service to the profession occurs at many levels. As an elected board member of the professional peak body, the Australian Mathematical Sciences Institute , Sanjeeva contributes to discussions on national and state issues (such as the national curriculum, the weakening mathematics performance among Australian students in the PISA tests, and mathematics towards the job force) in mathematics education. His volunteer work includes being a Governing Council member of Glenunga International High School, being a judge assessing the Global Undergraduate Awards , working with teachers at Norwood Primary School in mathematics enrichment, mentoring the Student Robotics Club of South Australia (which has won two First Place awards at the World FIRST Lego League competitions), and participating in the Aboriginal Summer School for Excellence in Technology and Science over many years. A team he advised was an overall winner of the Mathematical Contest in Modeling in 2015, the only Australian team to have ever won this contest.
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