This colloquium will be given by Valentin Khoze of Durham University.
I will introduce and review the recently proposed idea of Higgsplosion. Higgsplosion occurs at a critical energy in the 10^2-10^3 TeV range and leads to an exponentially growing decay rate of highly energetic particles into multiple Higgs bosons. We argue that this a new dynamical phenomenon in the Higgs-sector which involves the final state Higgs multiplicities n in the regime nλ ≫ 1 where λ is the Higgs self-coupling. In a Higgsploding theory, the cross-sections for producing ultra-high multiplicities of Higgs bosons are likely to become observable and even dominant in this energy range. At the same time, the apparent exponential growth of these cross-sections at even higher energies is tamed and automatically cut-off by a related Higgspersion mechanism. As a result, multi-Higgs production does not violate perturbative unitarity. The effects of Higgsplosion alter quantum corrections from very heavy states to the Higgs boson mass. Above a certain energy, which is much smaller than their masses, these states would rapidly decay into multiple Higgs bosons. The loop integrals contributing to the Higgs mass will be cut off not by the masses of the heavy states, but by the characteristic loop momenta where their decay widths become comparable to their masses. This suppresses the radiative corrections from the heavy states to the Higgs boson mass, solving the Hierarchy problem. We argue that Higgsplosion regulates all n-point functions, thereby embedding the Standard Model of particle physics and its extensions into an asymptotically safe theory. There are no Landau poles and the Higgs self-coupling stays positive.