## A probabilistic Takens theorem

## Two Important Milestones in the History of the Universe: The Last Scattering Surface, the Black Body Photosphere of the Universe and Distortions of the CMB Spectrum

Our Universe is filled with Cosmic Microwave Background (CMB) radiation having an almost perfect black body spectrum with a temperature of To=2.7K. The number density of photons in our Universe exceeds the number density of electrons by a factor of more than a billion. In the expanding Universe the temperature at early times was higher than today: Tr = To (1+z), where z is the redshift.

## Nuclear Policy in the age of Putin and Xi

## Singularity formation for some incompressible Euler flows

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 finite time for some range of $a>0$. The approach we follow is to isolate a simple non-linear equation which encodes the leading order dynamics of solutions to the Euler equation in some regimes and then prove that the simple equation has stable self-similar blow-up solutions.

## Inward Bound: Discovering and Exploring the Milky Way's Black Hole

## Singularities in reductions of Shimura varieties

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 arise in the reductions

modulo $p$ of integral models of Shimura varieties. For PEL type

Shimura varieties with parahoric level structure at $p$, this question

has been studied since the 1990's. Due to the recent construction of

## Islamic Manuscript Traditions

## Globally Consistent Three-family Standard Models in F-theory

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 exploration of the landscape of

F-theory three-family Standard Models with a gauge coupling unification.

Employing algebraic geometry techniques, all global consistency

conditions of these models can be reduced to a single criterion on the

## Remembering Irving Lavin, 1927-2019: Remembrances