# Recently Added

## History of Science Lecture Series: Race by Numbers

## Chow motives, L-functions, and powers of algebraic Hecke characters

The Langlands and Fontaine–Mazur conjectures in number theory describe when an automorphic representation f arises geometrically, meaning that there is a smooth projective variety X, or more generally a Chow motive M in the cohomology of X, such that there is an equality of L-functions L(M,s) = L(f,s). We explicitly describe how to produce such a variety X and Chow motive M in the case of powers of certain automorphic representations, called algebraic Hecke characters. This is joint work with J. Lang.

## Anyonic-String/Brane Träumerei: Quantum 4d Yang-Mills Gauge Theories and Time-Reversal Symmetric 5d TQFT

My talk will aim to be a friendly introduction for condensed matter friends, mathematicians, and QFT theorists alike --- I shall quickly review and warm up the use of higher symmetries and anomalies of gauge theories and condensed matter systems. Then I will present the results of recent work [arXiv:1904.00994].

## How does the rank of an elliptic curve grow in towers of number fields?

## Dimension of the stationary measure for random matrix products in $SL_2(\mathbb{R})$

## Loops in hydrodynamic turbulence

## Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK

## Reinterpreting Political Violence in 20th-Century Europe: A Comparative Perspective

## Etale and crystalline companions

Deligne's "Weil II" paper includes a far-reaching conjecture to the

effect that for a smooth variety on a finite field of characteristic p,

for any prime l distinct from p, l-adic representations of the etale

fundamental group do not occur in isolation: they always exist in

compatible families that vary across l, including a somewhat more

mysterious counterpart for l=p (the "petit camarade cristallin"). We

explain in more detail what this all means, indicate some key