Krishnan graduated from Sheffield University with a BSc Hons in Mathematics in 1999 and took an MSc in Medical Statistics at Leicester University in 2000-2001. He worked for 6 years at the MRC Clinical Trials Unit, on a variety of HIV trials and observational studies, with an emphasis on HIV seroconverters (individuals with well estimated dates of HIV infection). In October 2010, on gaining his PhD at LSHTM for a project looking at environmental risk factors for heart disease, he joined the department as a lecturer, and later senior lecturer. He completed an National Institute for Health Research postdoctoral fellowship to study the effects of widely prescribed drugs on cancer risk (2012-2014). He has since been awarded a Wellcome Trust/Royal Society Sir Henry Dale Fellowship to study cardiovascular disease risks among people with a history of cancer (2015 to present).