Physicists have chased a unified description of nature for more than a century, yet quantum theory and gravity have stubbornly resisted every attempt to bring them under one roof. A new geodesic-based ...

Riemannian manifolds or geodesic metric spaces of finite or infinite dimension occur in many areas of mathematics. We are interested in the interplay between their local geometry and global ...

Quantum deviations Large masses such as a galaxy curve space–time and objects move along geodesics within this curvature. If space–time itself has quantum properties, then deviations arise between a ...

Physicists have long struggled to unite quantum mechanics—the theory governing tiny particles—with Einstein’s theory of gravity, which explains the behavior of stars, planets, and the structure of the ...

As John Wheeler distilled Einstein’s general relativity: spacetime tells matter how to move, and matter tells spacetime how to curve. A century on, the metaphor has migrated from cosmology to grand ...

Metric measure spaces extend the classical notion of smooth manifolds by equipping a set with both a distance function and a reference measure. This abstraction permits the study of spaces that may ...

It is something like the "Holy Grail" of physics: unifying particle physics and gravitation. The world of tiny particles is described extremely well by quantum theory, while the world of gravitation ...