His work addresses a major problem in the field of mathematics related to the upper bound for the number of solutions for a particular theorem.

Ge studies solutions to systems of polynomial equations, where the solutions are required to be integer numbers or fractions, such as those of Fermat’s last theorem, Xn + Yn = Zn. 

His research expands on the work of many other mathematicians, including Gerd Faltings, who in 1986 won the Fields medal (one of mathematics highest honors) for proving the Mordell conjecture, which says that certain types of equations should have only finitely many solutions.

In 2019 another group of researchers set about finding ways to uniformly bound the number of possible solutions as well. They considered a collection of one-dimensional equations to prove that there was an upper bound for the number of solutions that applied to every equation in the collection. Ge studied their work and went on to prove a uniform bound for an important family of two-dimensional equations, thereby giving a uniform version of a theorem. 

Ge’s result, “by itself, would have represented one of the best math PhDs at Brown in recent years,” says Joseph H. Silverman, a nominator and professor of Mathematics.

He went on to work closely with researchers from outside of Brown to definitively solve the uniformity problem for all collections of equations of all dimensions. “This is a paper that will be cited by researchers for years to come,” says Silverman

Ge’s “work is exceptional, as it addresses and solves a major problem in the field,” says nominator Dan Abramovich, L. Herbert Ballou University professor of Mathematics.

Ge expressed what an honor the award was to receive and that it gives him encouragement to continue his research. Next fall he will begin a postdoctoral appointment at Princeton University.