Christopher Bishop, a distinguished professor in the Stony Brook University Department of Mathematics, has been awarded the Senior Berwick Prize from the London Mathematical Society for a pair of papers he wrote and published in the society’s journal, Proceedings of the London Mathematical Society.
Bishop was awarded the prize for his work on two papers: “Models for the Speiser Class” and “Models for the Eremenko-Lyubich Class.” According to the London Mathematical Society, the award — named after a former vice president of the society — is reserved for authors of outstanding work published in the society’s journal during “eight years ending on 31 December of year X-1.”
Winning this award has placed Bishop among the ranks of other distinguished mathematicians like John Edensor Littlewood and Thomas Hales.
“I want to know the answers to things. But it is very gratifying to have people recognize something as being especially good work,” Bishop said.
Bishop describes his work as seeking to generate more examples of two classes of non-polynomial functions, the Speiser Class and the Eremenko-Lyubich Class (named after Professor Mikhail Lyubich, the director of the Institute for Mathematical Sciences at Stony Brook).
Two commonly-known examples of the Speiser class are the familiar sine and cosine functions, which can be combined with other variables to create new sine and cosine functions. However, Bishop describes this as only being “a small corner of the whole space … It’s like living on an island and the only animals you knew were that there’s cats and dogs and a pig and a cow.”
Both papers are solely authored by Bishop and feature diagrams of “dessin d’enfant” which translates to “children’s drawing,” a term coined by French mathematician Alexander Grothendieck.
These “children’s drawings” are made up of simple sticks and arcs that are meant to represent the complex functions within these classes, which contain imaginary and 4D elements that cannot be graphed on a typical 3D XYZ plane.
By generating these deceptively simple models, Bishop was able to derive more functions of these complex classes.
“I created many new examples of these Speiser functions by showing that [for] certain that the functions corresponded to diagrams and then showing what the rules were for creating these diagrams,” he said.
Bishop is one of a small number of leading mathematicians studying these classes of functions and he believes that getting more examples of these functions that can serve as data points will allow for theorems about the commonalities within functions in the Speiser and Eremenko-Lyubich Classes.
Bishop thinks that by better understanding these classes of functions, math can be used to make sense of the natural world.
“If you look at a tree, it’s got like thousands of branches and leaves, and all the leaves are a little different,” he said. “And if you were to just try to imagine exactly what that tree is, it would probably take millions and millions of data points to describe the outline of every leaf and all the veins and everything about it. And so mathematics is one of the tools that we use to simplify things like that.”
Bishop is the first faculty member at Stony Brook to have won the Senior Berwick Prize.
“Bishop’s papers provide a ‘black box’ that is now the gold standard for constructing functions in the [Speiser class S and the Eremenko–Lyubich class B] and has been used extensively by other researchers since,” the London Mathematical Society wrote in the official prize citation for the award. “His work represents an extraordinary step-change in our understanding of these two important classes and raises fascinating questions about their subtle differences.”
