Synergy between Several Branches of Mathematics

Gregory G. Smith is currently Professor at Queen’s University, Ontario, Canada. Thanks to a grant from the Knut and Alice Wallenberg Foundation, he will be Visiting Professor at the Department of Mathematics, KTH Royal Institute of Technology, Stockholm.

Algebraic geometry is about studying solutions to systems of polynomial equations, a branch of mathematics with roots far back in human history. A milestone came in the 17th century when René Descartes invented the coordinate system, thus managing to link algebraic equations for geometric objects with the objects’ geometry. This led to fruitful development, as the methods used in geometric reasoning could be used to solve algebraic problems. Ever since, developments in algebraic geometry have successfully progressed over four hundred years.

Today’s algebraic geometry is a broad field of study. It has branched out into many areas and developed deep interactions with other parts of mathematical endeavor, as well as with the string theory of theoretical physics. It also has many technical applications, including aircraft construction and robotics.

Professor Gregory G. Smith’s main research interests lie in a relatively new area of algebraic geometry called toric geometry. This lies at the boundary between algebra, geometry, and combinatorics. Such research, thanks to newly developed geometric and combinatorial methods, may simplify algebraic computations, which had previously been extremely challenging or entirely inaccessible. Conversely, new methods in algebraic geometry may turn out to be useful in proving theorems about geometric objects.