Dr Efthymios Sofos awarded funding from the New Horizons Fund (EPSRC)

Researchers from the University of Glasgow’s College of Science & Engineering are sharing in new funding for adventurous, high-risk research.

Four projects from three Schools have received support from the £25.5m New Horizons fund, administered by the Engineering and Physical Science Research Council (EPSRC).

A total of 126 adventurous projects in the mathematical and physical sciences will benefit from the pilot funding from EPSRC, part of UK Research and Innovation (UKRI).

Grants of up to £200,000 to cover a maximum of two years’ work were available to New Horizons applicants, with a streamlined application process and a review process focused on the transformational potential of the research.

Dr Efthymios Sofos (School of Mathematics and Statistics) will build on previous research undertaken with Professor Alexei Skorobogatov in Imperial College London on Schinzel’s Hypothesis H, which states that any polynomial produces primes, unless there is an obvious obstruction. Dr Sofos and Professor Skorobogatov settled Schinzel's Hypothesis H for all randomly chosen polynomials.

Their new project will develop the consequences in Diophantine geometry. Hilbert's famous tenth problem states that there exists a finite algorithm for deciding whether a Diophantine equation can be solved in the integers. Hilbert's claim was famously disproved by Matiyasevich. The team’s work reveals strong evidence to the surprising statement that the contrary holds when it comes to solving equations in the rationals: the finite time Hasse-principle algorithm holds for all randomly chosen equations.