This award is made as part of the FY 2026 Mathematical Sciences Postdoctoral Research Fellowships Program. Each of the fellowships supports a research and training project at a host institution in the mathematical sciences, including applications to other disciplines, under the mentorship of a sponsoring scientist. The title of the project for this fellowship to Vinayak Kumar is “Using Randomness To Demonstrate the Power and Limitations of Computing”. The host institution for the fellowship is the University of California - Berkeley and the sponsoring scientist is Venkatesan Guruswami. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.