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Ancient Gauls only feared one thing: That the sky might fall on their heads. They did not worry about Quantum Gravity, presumably because it was considered irrelevant at energies accessible at the time. This viewpoint, which has survived to our day, is challenged by the ideas of the Swampland Program, which posits that gravity has a subtle but universal imprint even at low energies. I will introduce the Swampland idea, the most widely studied Swampland constraints, and explain how these have been used to make predictions both for String Theory and phenomenology, including a micrometer-sized extra dimension.

We present a fully calculable UV complete toy model of a Peccei-Quinn (PQ) axion coupled to magnetic monopoles as well as electric charges. The theory has manifest electric-magnetic duality built in. We find that the axion-photon coupling contains the usual anomaly term, plus periodic corrections which can also become large if the monopole is light, without violating the discrete axion shift symmetry. These additional periodic terms can be identified as the non-perturbative corrections due to the monopoles (and other BPS states), but can also be interpreted as a sum over instanton corrections. The key aspect helping reconcile axion coupling quantization with electric-magnetic duality is the fact that the axion itself undergoes a non-linear transformation under electric-magnetic duality. The theory analyzed here is just the original N=2 supersymmetric SU(2) Seiberg-Witten theory, which contains a PQ axion due to an anomalous spontaneously broken global R-symmetry, as well as massless fermionic monopoles and dyons at special points in the moduli space. Hence the entire machinery of the Seiberg-Witten solution can be applied to reliably calculate the photon-axion coupling in different duality frames. We show explicitly that the physically observable axion-photon amplitude is duality invariant, as it had to be. Based on arXiv: 2411.15312.

Recent developments in non-invertible symmetry-preserving quantum lattice models allow access to many 2D CFTs, and RG flows among them. Density matrix renormalization group (DMRG), on the other hand, allows us to study these lattice models super efficiently. I will explain our recent work on combining these methods to study the coupled tricritical Ising model, in search of irrational CFTs. If time permits, I will also discuss the RG flow connecting different conformal interfaces between the Ising CFT and the tricritical Ising CFT.

Unlike the usual Nielsen complexity of a quantum mechanical system, the Krylov complexity (defined in 2019) is purely algorithmic for a countable quantum mechanical system, yet, despite being relatable to Nielsen complexity, a general holographic description for it was still lacking. Based on a proposal for AdS_3/CFT_2, we give a general formula, and consider 3 relevant cases: N=4 SYM, where we find a relation to an SL(2)-based spin chain (possibly related to the Krylov chain), confining systems exemplified by an asymptotically AdS_3 one, and a warped AdS_3/2 one, dual to a CFT quiver. The analysis of all other cases should follow along the lines of these ones.

After describing elastic interactions and the discovery of the odderon by the TOTEM and D0 Collaborations, we will discuss new kinematical regimes where the gluon density in the proton or Pb can be very large which leads to new equations in Quantum Chromodynamics.  We will also present the latest expectations on beyond standard model physics and especially the production of axion-like particles using intact protons after the collision.  We will finish by describing briefly the Low Gain Avalanche Detectors and their applications in medicine for cancer treatment and with NASA to measure cosmic rays.