Symmetry

A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties.

Physicists have been busy exploring how our universe might emerge like a hologram out of a two-dimensional sheet. New clues have come from the symmetries found on an infinitely distant “celestial sphere.”

The “gravitational memory effect” predicts that a passing gravitational wave should forever alter the structure of space-time. Physicists have linked the phenomenon to fundamental cosmic symmetries and a potential solution to the black hole information paradox.

In nonreciprocal systems, where Newton’s third law falls apart, “exceptional points” are helping researchers understand phase transitions and possibly other phenomena.

Watanabe invented a new way of distinguishing shapes on his way to solving the last open case of the Smale conjecture, a central question in topology about symmetries of the sphere.

The n-queens problem is about finding how many different ways queens can be placed on a chessboard so that none attack each other. A mathematician has now all but solved it.

By focusing on relationships between solutions to polynomial equations, rather than the exact solutions themselves, Évariste Galois changed the course of modern mathematics.

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.