Talks

In the coming decade, ground based CMB telescopes could face a substantial upgrade, to so-called CMB-S4. There are two main science drivers behind this initiative: B-modes, and neutrino mass, and I will focus on the latter. Thought of more generally, constraints on neutrinos can be thought of as generic tests of dark matter. I will discuss the prospects for CMB-S4 in the dark sector, with emphasis on searches for axions and neutrinos. It will be possible to detect percent level departures from standard cold dark matter at many sigma over a wide range of scales: a vast improvement over Planck (+ existing ground based). A large part of the improvement over Planck comes from precision lensing measurements at high multipole. I will briefly discuss some technical challenges in this measurement, based on modelling of dark matter clustering in the non-linear regime.

The study of isolated systems has been vastly successful in the context of vanishing cosmological constant, $\Lambda = 0$. However, there is no physically useful notion of asymptotics for the universe we inhabit with $\Lambda > 0$. The full non-linear framework is still under development, but some interesting results at the linearized level have been obtained. I will focus on the conceptual subtleties that arise at the linearized level and discuss the quadrupole formula for gravitational radiation.

A Coxeter category is a braided tensor category which carries an action of a generalised braid group $B_W$ on its objects. The axiomatics of a Coxeter category and the data defining the action of $B_W$ are similar in flavor to the associativity and commutativity constraints in a monoidal category, but arerelated to the coherence of a family of fiber functors.

We will show how to construct two examples of such structure on the integrable category $\matcal{O}$ representations of a symmetrisable Kac–Moody algebra $\mathfrak{g}$, the first one arising from the quantum group $U_\hbar(\mathfrak{g})$, and the second one encoding the monodromy of the KZ and Casimir connections of $\mathfrak{g}$.

The rigidity of this structure, proved in the framework of $\mathsf{PROP}$ categories, implies in particular that the monodromy of the Casimir connection is given by the quantum Weyl group operators of $U_\hbar(\mathfrak{g})$.

This is a joint work with Valerio Toledano Laredo.