### Speaker

Søren Fournais
(University of Copenhagen)

### Description

The ground state energy density $e(\rho)$ of a large system of interacting bosons in $3$ dimensions at density $\rho$ satisfies the formula

$$
e(\rho) = 4 \pi \rho^2 a \Big( 1 + \frac{15}{128 \sqrt{\pi}} \sqrt{\rho a^3} \Big) + \text{higher order terms},
$$
in the dilute limit $\rho a^3 \ll 1$. Here $a$ is the scattering length of the interaction potential. This is the celebrated Lee-Huang-Yang formula for the energy density.
In this talk, I will review the proof of the lower bound in this formula. I will also comment on the harder $2$-dimensional case and how the proof can be modified to accommodate this case.