Research Projects

Several fundamental questions in the field of computational algebra have in its core certain linear algebraic primitives such as fast fourier transforms, multipoint evaluation, linear system solving, polynomial interpolation, and matrix multiplication. These primitives are intimately connected to one another and are often the main bottlenecks in implementing fast algorithms for these tasks. The primary objective of this project is to obtain fast algorithms for many of these linear-algebraic primitives. As a consequence, these could lead to improvements in fundamental questions such as matrix multiplication, which is also essential in fields outside of computational algebra such as machine learning and optimisation. A key methodology in this project is to design "non-algebraic" algorithm for these algebraic questions as they have been relatively unexplored.