Talks

I will give an overview of recent results on three-dimensional N=2 supersymmetric gauge theories placed on arbitrary half-BPS geometries. In particular, I will explain an explicit computation of the supersymmetric partition function on any Seifert three-manifold; such manifolds can have very intricate and interesting topology (for instance, a nice example is the Poincaré sphere) and can provide new interesting observables in 3d SCFTs. I will also discuss to which extent these results exhibit a generalisation of the 3d TQFT structure of Chern-Simons theory to non-topological (but supersymmetric) theories.
 

Bosonic ultra-light dark matter (ULDM) would form cored density distributions at the centres of galaxies. These cores admit analytic description as the lowest energy bound state solution ("soliton") of the Schrödinger-Poisson equations. Numerical simulations of ULDM galactic halos found empirical scaling relations between the mass of the large-scale host halo and the mass of the central soliton. 
We connect the simulation results of different groups to basic properties of the soliton. Importantly, simulations imply that the specific kinetic energy in the soliton and in the host halo should be approximately equal. This relation predicts that the peak circular velocity, measured for the host halo in the outskirts of the galaxy, should repeat itself in the central region. Contrasting this prediction to the measured rotation curves of low surface-brightness galaxies, we show that ULDM in the mass range m ~ 10⁻²²-10⁻²¹ eV, which has been invoked as a possible solution of small-scale puzzles of ΛCDM, is in tension with the data. We discuss the potential of detailed dynamical modelling of the Milky Way and other well-resolved galaxies to probe ULDM up to m ~ 10⁻¹⁹ eV.

I'll discuss recent work on finding time-dependent solutions of a black hole interacting with a scalar field. I'll discuss two distinct cases where the back-reaction of the scalar can be found. First, in the case that the scalar is slowly rolling (such as in inflation) the scalar field can be found in terms of super-advanced time coordinate, regular on both horizons. The scalar back-reacts on the geometry, with the black hole accreting and growing more or less as expected. The second case I'll describe briefly is scalar hair in modified gravity - giving a scalar-dressed rotating black hole that is finite on both horizons. 

The Heisenberg algebra plays a vital role in many areas of mathematics and physics.  We will describe a family of quantum Heisenberg categories, depending on a choice of central charge, that categorify this algebra.  When the central charge is nonzero, these categories act on modules for cyclotomic quotients of the affine Hecke algebra.  In central charge zero, we obtain an affinization of the HOMFLY-PT skein category, which acts on modules for $U_q(\mathfrak{gl}_n)$.  We will also discuss how the categories can be generalized by adding a Frobenius superalgebra into the construction.  This is joint work with Jon Brundan and Ben Webster.