Mathematical physics

After decades of effort, mathematicians now have a complete understanding of the complicated equations that model the motion of free boundaries, like the one between ice and water.

A group of mathematicians has shown that at critical moments, a symmetry called rotational invariance is a universal property across many physical systems.

Even in an incomplete state, quantum field theory is the most successful physical theory ever discovered. Nathan Seiberg, one of its leading architects, talks about the gaps in QFT and how mathematicians could fill them.

In three towering papers, a team of mathematicians has worked out the details of Liouville quantum field theory, a two-dimensional model of quantum gravity.

The accelerating effort to understand the mathematics of quantum field theory will have profound consequences for both math and physics.

A new proof establishes the boundary at which a shape becomes so corrugated, it can be crushed.

A mathematical shortcut for analyzing black hole collisions works even in cases where it shouldn’t. As astronomers use it to search for new classes of hidden black holes, others wonder: Why?

A former graduate student reflects on how Isadore Singer, who died on February 11, brought together mathematicians, physicists and anyone else interested in the deeper connections between diverse fields.

Lauren Williams has charted an adventurous mathematical career out of the pieces of a fundamental object called the positive Grassmannian.