We describe a recent construction of self-similar blow-up
solutions of the incompressible Euler equation. A consequence of
the construction is that there exist finite-energy $C^{1,a}$
solutions to the Euler equation which develop a singularity
in...
The singularities in the reduction modulo $p$ of the modular
curve $Y_0(p)$ are visualized by the famous picture of two curves
meeting transversally at the supersingular points. It is a
fundamental question to understand the singularities which...
We present recent advances in constructions of globally
consistent
F-theory compactifications with the exact chiral spectrum of the
minimal
supersymmetric Standard Model. We highlight the first such example
and
then turn to a subsequent systematic...
