Undergraduate Research & Scholarships

Nikhil Sharma L&S Sciences

Analysis of Matrix Multiplication Complexity Using Properties of Tensors

Matrix multiplication is one of the most fundamental operations in mathematics, and its usage is extensively pervasive in modern-day computer systems; innumerable algorithms employ techniques from linear algebra in their implementation. As a result, it’s critical to perform matrix multiplication as quickly as possible to ensure the smooth and efficient performance of everyday computer applications. It’s been shown in existing literature that there is an intrinsic relationship between properties of matrix multiplication and a special geometric object known as a tensor. To date, an extensive exploration observing this relationship in specific cases has not been performed. In my research project, I plan to conduct a detailed mapping of how these properties of tensors correspond to matrix multiplication and their effect on the time complexity of performing the multiplication. As a dual major in computer science, this problem is especially interesting and relevant to me, and I look forward to contributing towards a breakthrough in the field.

Message To Sponsor

The SURF program was an incredible opportunity that opened my eyes to the rigor and depth of understanding required in mathematical research. It was very exciting to conduct research in matrix complexity theory which has the potential to someday have widespread ramifications on the field of computing, and has piqued my interest in more advanced mathematical study. I certainly plan to strive to keep up-to-date with research advances in the fields of mathematics which interest me, and hope to continue conducting research. A big thank you to David Sherrill, without whom this experience would not have been possible!