Multi-loop amplitudes with multiple legs are hardcore problems in the field of amplitude. These amplitudes are crucial for the precision frontier of Quantum Chromodynamics (QCD). In this talk, the speaker will present the latest progress in this direction: the two-loop five-point nonplanar amplitudes. Without dual conformal symmetry, this amplitude seems untouchable. However, with new techniques from symbol construction, uniformly transcendental basis and integration-by-parts (IBP) from computational algebraic geometry, the speaker and his collaborators manage to get the analytical master integrals and the N=4 super-Yang-Mills/N=8 supergravity amplitudes. The speaker will also provide an outlook for two-loop five-point QCD amplitudes.
