In this talk we will discuss the present status of theoretical studies and experimental searches performed in order to measure the di-Higgs process in various standard model (SM) final states. Furthermore, we will review the prospects of observing such channels at the 14 TeV high luminosity (HL) run of the large hadron collider (LHC). We will then discuss the prospects of observing certain non-standard final states in the di-Higgs category. Our focus will especially be on the scenario where one of the Higgs decays to a pair of $b$-jets and the other decays invisibly. We discuss the reach of the HL-LHC when (i) the production cross-section is exactly SM-like and (ii) when one includes a heavy scalar coupled to the top quarks and the SM Higgs. We will also review some other potential exotic final states.

A dark sector of particles interacting with the Higgs boson might reveal the origin of dark matter or facilitate electroweak baryogenesis. At particle colliders, the direct search for such Higgs-portal interactions is difficult if the dark particles lie above the Higgs threshold. In scenarios with electroweakly interacting mediators, two alternative signatures can facilitate the search: resonant production of mediators decaying into dark particles, and indirect effects of virtual mediators in visible Higgs decays. I will discuss the complementarity of these two approaches and present new results on virtual effects of dark fermions in Higgs decays to electroweak gauge boson pairs.

LHC searches for heavy resonances predicted by the composite Higgs paradigm has so far been performed under the simplified assumptions of a single composite state present beyond the SM particle content. However, the lack of new physics at the LHC forces us to reconsider this assumptions. After reviewing standard strategies and future prospects for composite resonant searches, I will highlight the presence of exotic decay mode can affect the reach of the LHC

The most challenging hurdle to the construction of UV complete composite Higgs models without fundamental scalars is the generation of Yukawa couplings for the Standard Model fermions. This problem may be successfully addressed if some spin-1/2 operator of the new strong dynamics has scaling dimension close to 2.5 within the conformal window. We discuss this proposal in general, and then focus on a candidate model based on a SU(3) gauge theory with light Dirac flavors.

If the Physics Beyond the Standard Model (BSM) is decoupled at higher energies, the Standard Model as an effective field theory (SM EFT) is a pertinent framework for phenomenology. The BSM effects on observables are parametrized by the Wilson coefficients of dimension-6 operators, and bounds on their values can be placed from experimental measurements. Integrating out heavy particles at one-loop to obtain expressions for the Wilson coefficients is now also simplified by the use of our universal one-loop effective action. We show how the one-loop effective action obtained from the path integral Covariant Derivative Expansion method can be written in a universal closed form. This result has general applicability beyond the SM EFT and can be used for integrating out any UV theory to obtain a low-energy EFT. We illustrate the relationship of our results to the Standard Model EFT, using as an example the supersymmetric stop and sbottom squark Lagrangian and extracting from our universal expression the Wilson coefficients of dimension-six operators composed of SM fields.
We will also cover the alternative scenario where the New Physics is also directly produced at the LHC by analyzing a selection of interesting direct searches of BSM particles.

In this talk I will discuss the hierarchy problem from a known, but less mainstream direction. I will argue that the hints we have observed for high energy physics may in fact be a smokescreen, with the new physics responsible for these hints lying much closer to accessible energies. A new mechanism, the clockwork, will be proposed as an underlying explanation and connections to extra-dimensional scenarios will be sketched, alongside LHC phenomenology.

After the 2016 13 TeV run, ATLAS and CMS have presented results targeting New Physics in a variety of final states and topologies. First, I will re-interpret the public datasets to study supersymmetric scenarios that go beyond the simplified topologies studied by the experimental collaborations, and present limits on natural SUSY. Then, I will present noteworthy (3 sigma) excesses buried in the CMS jets+MET searches, and present some simplified models that can provide a good fit. I will conclude by discussing their plausibility and which additional search channels could verify or reject these hypotheses.

The clockwork mechanism has recently been proposed as a natural way to generate hierarchies among parameters in certain models. The mechanism is characterised by a very specific pattern of spontaneous and explicit symmetry breaking, and the presence of new light states. In this talk, I will discuss the clockwork mechanism and its manifestation in the scalar, fermion and gauge boson cases. I will also present a possible generalization of the Abelian clockwork models to non-Abelian clockwork models. Moreover, I will show how the clockwork mechanism can be used to generate flavor symmetries in the Standard Model. I will briefly discuss the continuum clockwork model, which are realised in five-dimensional linear-dilaton geometries.

In this talk I will discuss low-scale leptogenesis with a particular focus on its testable regimes. In the first part I will discuss leptogenesis with right-handed neutrinos around the electroweak scale, briefly presenting the theoretical description of this mechanism in relation to flavour effects, together with its relevance for testable models at the electroweak scale. In the second part I will focus on leptogenesis below the electroweak scale, and discuss how leptogenesis can proceed, in this case, via the lepton-number violating decays of the Higgs scalar doublet. I will also briefly comment on the testability of this scenario in the near future, for instance at the proposed SHiP experiment at CERN, and the relation with the other mechanism active in the same mass range, i.e. leptogenesis via right-handed neutrino oscillations.