Mats Boijs
Professor in mathematics
About Mats Boij's research
Algebraic geometry has always been about solutions to systems of polynomial equations, and its roots stretch far back into the history of mankind. A number of advances were made during the 19th century, but we lacked the tools for making further progress. During the 20th century, commutative algebra became a mechanism that could be used to solve many of these problems. Since the 1960s, computers have made extensive calculations possible within this field. Nevertheless, computers still have significant limitations; even seemingly minor problems can prevent calculations from being completed within a lifetime using today’s technology.
In his work with Jonas Söderberg, Mats Boij embarked on a new direction within the study of syzygies, a type of algebraic relationship. Although David Hilbert paved the way for this over 100 years ago, there was only limited knowledge at the time of the numerical properties of these syzygies. Their work led to what is now known as Boij-Söderberg theory, which has also resulted in unexpected breakthroughs in other areas, such as cohomology of vector bundles.
As with all basic research within mathematics, it is hard to predict in advance where the applications will arise, but commutative algebra and algebraic geometry are used within such diverse branches of science as theoretical physics, biostatistics and computer science.