There has been a breakthrough in the mathematics of quantum fields. One of the interesting aspects of electromagnetic fields is you can reverse the E and the M and the equations stay the same.
Simple as it seems, physicists couldn't explain it till just this week, when a team of mathematicians solved the first part of the geometric Langlands conjecture.
This longstanding math problem relates number theory to the shape of Riemann surfaces, which are topological shapes derived from harmonic analysis (as in waves). These shapes could be spheres, donuts, or donuts with many holes. It turns out that the fundamental group of these shapes is related to the algebra of sheaves on the surface, which is what explains the symmetry.
This is a good read if you like math:
www.nature.com
Simple as it seems, physicists couldn't explain it till just this week, when a team of mathematicians solved the first part of the geometric Langlands conjecture.
This longstanding math problem relates number theory to the shape of Riemann surfaces, which are topological shapes derived from harmonic analysis (as in waves). These shapes could be spheres, donuts, or donuts with many holes. It turns out that the fundamental group of these shapes is related to the algebra of sheaves on the surface, which is what explains the symmetry.
This is a good read if you like math:
The breakthrough proof bringing mathematics closer to a grand unified theory
The Langlands programme has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore.
www.nature.com
