Within mathematics, there is a vast and ever expanding web of conjectures, theorems and ideas called the Langlands program. That program links seemingly disconnected subfields. It is such a force that some mathematicians say it—or some aspect of it—belongs in the esteemed ranks of the Millennium Prize Problems, a list of the top open questions in math. Edward Frenkel, a mathematician at the University of California, Berkeley, has even dubbed the Langlands program “a Grand Unified Theory of Mathematics.”
The program is named after Robert Langlands, a mathematician at the Institute for Advanced Study in Princeton, N.J. Four years ago, he was awarded the Abel Prize, one of the most prestigious awards in mathematics, for his program, which was described as “visionary.”
Langlands is retired, but in recent years the project has sprouted into “almost its own mathematical field, with many disparate parts,” which are united by “a common wellspring of inspiration,” says Steven Rayan, a mathematician and mathematical physicist at the University of Saskatchewan. It has “many avatars, some of which are still open, some of which have been resolved in beautiful ways.”
Increasingly mathematicians are finding links between the original program—and its offshoot, geometric Langlands—and other fields of science. Researchers have already discovered strong links to physics, and Rayan and other scientists continue to explore new ones. He has a hunch that, with time, links will be found between these programs and other areas as well. “I think we’re only at the tip of the iceberg there,” he says. “I think that some of the most fascinating work that will come out of the next few decades is seeing consequences and manifestations of Langlands within parts of science where the interaction with this kind of pure mathematics may have been marginal up until now.” Overall Langlands remains mysterious, Rayan adds, and to know where it is headed, he wants to “see an understanding emerge of where these programs really come from.” READ MORE...
A new set of equations can precisely describe the reflections of the Universe that appear in the warped light around a black hole.
The proximity of each reflection is dependent on the angle of observation with respect to the black hole, and the rate of the black hole's spin, according to a mathematical solution worked out by physics student Albert Sneppen of the Niels Bohr Institute in Denmark.
This is really cool, absolutely, but it's not just really cool. It also potentially gives us a new tool for probing the gravitational environment around these extreme objects.
"There is something fantastically beautiful in now understanding why the images repeat themselves in such an elegant way," Sneppen said. "On top of that, it provides new opportunities to test our understanding of gravity and black holes."
If there's one thing that black holes are famous for, it's their extreme gravity. Specifically that, beyond a certain radius, the fastest achievable velocity in the Universe, that of light in a vacuum, is insufficient to achieve escape velocity.
That point of no return is the event horizon – defined by what's called the Schwarszchild radius – and it's the reason why we say that not even light can escape from a black hole's gravity. TO READ MORE
