Feynman famously said "I think I can safely say that nobody understands quantum mechanics." That was in 1965 but it's still true.
The scattering amplitudes in a certain case of N=4 Super Yang-Mills theory are more symmetric than people first expected. This has applications to "total positivity" and "integrable systems".
This will not help you build an app, but it's beautiful and represents an important shift in mathematics.
I went to his lecture from 1-3 and we got an encore from 3-5 and another from 5-6. It is no surprise his paper is verbose clocking at 154 pages.
Scattering Amplitudes and the Positive Grassmannian http://arxiv.org/abs/1212.5605
Alejandro Morales has some lecture notes on a course on the Positive Grassmanian The professor was Alexander Postnikov at MIT.
http://www.thales.math.uqam.ca/~ahmorales/18.318lecs/lecture...
Feynman famously said "I think I can safely say that nobody understands quantum mechanics." That was in 1965 but it's still true.
The scattering amplitudes in a certain case of N=4 Super Yang-Mills theory are more symmetric than people first expected. This has applications to "total positivity" and "integrable systems".
This will not help you build an app, but it's beautiful and represents an important shift in mathematics.