Atlanta, GA | Posted: June 6, 2019
The journal Research in the Mathematical Sciences has selected a paper coauthored by Georgia Tech mathematicians Matthew Baker and Joseph Rabinoff as one of the inaugural recipients of its Best Article Award.
The journal recognized the paper – titled “Lifting harmonic morphisms I. metrized complexes and Berkovich skeleta” – as outstanding and highly influential. Other authors are Omid Amini, of CNRS, Paris, and Erwan Brugallé, of Université Pierre et Marie Curie, Paris.
“The paper provides a piece of foundational work that is useful in many areas of mathematics.”
The article is about finding algebraic functions between algebraic curves. Algebraic curves are one-dimensional shapes defined by polynomial equations. For example, X^{2} + Y^{2} = 1 defines a circle.
“In some sense, algebraic curves are well understood,” Baker says. He is a professor in the School of Mathematics and associate dean for faculty development in the College of Sciences. “But the theory is very rich, and there’s still a lot we don’t know about them.”
The essential idea of the paper is to chop algebraic curves into simpler pieces and then keep track of two things: which pieces are connected to what others and which pieces of one curve are sent by the function to what pieces of another curve.
“It turns out that this method is enough to recover a lot of information about the original pairs of curves and the function between them,” says Rabinoff, an associate professor in the School of Mathematics. “One subtlety is that the whole construction is carried out in an exotic context called “Berkovich spaces” and their skeleta, which arise naturally in number theory.”
“The paper provides a piece of foundational work that is useful in many areas of mathematics,” Baker says. “For example, it has become an important tool in a relatively new area called tropical geometry. It is also the starting point for studying wildly ramified functions between algebraic curves. This topic is of interest to several groups of mathematicians around the world.”
Research in the Mathematical Sciences, launched in 2013, is an international, peer-reviewed hybrid journal covering the full scope of theoretical mathematics, applied mathematics, and theoretical computer science. The journal launched the Best Article Awards to celebrate its fifth anniversary.