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We study chiral algebras associated with Argyres-Douglas theories engineered from M5 brane. For the theory engineered using 6d (2,0) type J theory on a sphere with a single irregular singularity (without mass parameter), its chiral algebra is the minimal model of W algebra of JJ type. For the theory engineered using an irregular singularity and a regular full singularity, its chiral algebra is the affine Kac-Moody algebra of JJ type. We can obtain the Schur and Hall-Littlewood index of these theories by computing the vacua character of the corresponding chiral algebra.

Lack of fine tuning in effective field theory does not ensure that a particular scenario is natural or even realizable in a UV complete theory of quantum gravity. Large field axion inflation appears natural from the effective field theory perspective, but I argue that it is tuned from a quantum gravity perspective. The argument is based on the Weak Gravity Conjecture (WGC), a conjectural universal feature of quantum gravity that is present in all known string theory examples. In the process, I highlight recent progress in understanding the WGC and related conjectures about the charged spectrum of quantum gravity and discuss other potential applications, both formal and phenomenological.

It has long been wondered to what extent the observable properties of an inhomogeneous universe will be measurably different from a corresponding FLRW model. Here, we use tools from numerical relativity to study the properties of photons traversing an inhomogeneous universe. We evolve the full, unconstrained Einstein field equations for a spacetime containing dust, with a spectrum of long-wavelength density perturbations similar to the observed one. We then integrate the optical scalar equations along paths through this numerical spacetime, with all paths terminating at an observer situated similarly to ourselves, and construct the resulting Hubble diagrams.

I will talk about some connections among the GKZ (introduced by Gelfand-Kapranov-Zelevinsky) hypergeometric series, orbifold singularities of the system, and chain integrals in some geometry.  The GKZ hypergeometric series appeared in some very interesting contexts including arithmetic geometry, enumerative geometry and mathematical physics in the last few decades. I will report some new geometric realizations and interpretations of them.