$e^+e^-\to\gamma\gamma^*$ at two loops in massless QED

We present an analytic computation of $e^+e^-\to\gamma\gamma^*$ at two loops in massless QED.
We reconstruct the analytic form of the amplitudes from numerical evaluations over finite fields.
We express the integrals in a basis of Goncharov polylogarithms to obtain compact expressions.
These contributions are required for N$^3$LO predictions of the process $e^+e^-\to\gamma^*$ and for NNLO corrections for ISR measurements of $e^+e^-\to\gamma\gamma^*$.