Conference

Umbral moonshine attaches mock modular forms and meromorphic Jacobi forms to automorphisms of the Niemeier lattices. It is now known that this association can be recovered from specific, graded modules for the Niemeier lattice automorphism groups. We will describe recent progress in a program to realize these modules explicitly.

We observe a relationship between the representation theory of the Thompson sporadic group and a weakly holomorphic modular form of weight one-half that appears in Zagier's work on traces of singular moduli and Borcherds products. We conjecture the existence of an infinite dimensional graded module for the Thompson group and use the observed relationship to propose a McKay-Thompson series for each conjugacy class of the Thompson group and then construct weakly holomorphic weight one-half forms at higher level that coincide with the proposed McKay-Thompson series. We also observe a discriminant property in this conjectured moonshine for the Thompson group that is closely related to the discriminant property conjectured to exist in Umbral Moonshine.

This talk will summarize some recent results in bimetric theory, including the existence of the square-root matrix, possible connection to partial masslessness and conformal gravity, the structure of constraints and finally, the cosmological implications of the theory.

Theories with large kinetic interactions have very relevant phenomenological applications in cosmology, in particular in the context of cosmic acceleration. Their Effective Field Theory (EFT) description relies on the so-called Vainshtein effect being operative. When incorporated at the quantum level, this mechanism ensures the validity of the theory in a non-trivial way. I will discuss how to estimate the regime of validity of such EFTs on the basis of computing the quantum corrections to the classical theory. I will point out how some lessons learned from the study of quantum effects in these theories might help us to tackle the significance of superluminalities and revisit what properties a healthy EFT should have.

I will review the notorious cosmological constant problem, sometimes described as the worst fine tuning problem in Physics. I will explain the true nature of the problem, which is one of radiative instability against any change in the effective description. I will recall Weinberg’s venerable no-go theorem that prohibits certain attempts to “solve” this problem before going on to explain a new mechanism that circumvents Weinberg. This is the vacuum energy sequester, a global modification of GR that results in the cancellation of large vacuum energy contributions from a protected matter sector (taken to include the Standard Model) at each and every order in the perturbative loop expansion. Cosmological consequences are a Universe which has finite space-time volume, will ultimately crunch, and for which dark energy can only be a transient. Furthermore, using a linear scalar potential within the sequestering set-up, I will show that dark energy today can be intimately related to the trigger that brings about cosmological collapse in the not too distant future, at the same time providing a possible solution to the “Why Now?” problem.