Talks

There is observational evidence that the X-ray continuum source that creates the broad fluorescent emission lines in some Seyfert Galaxies may be compact and located at a few gravitational radii above the black hole. We consider two scenarios for the X-ray emission. The first possibility is that the X-rays may be produced by particles accelerated in an electrostatic gap at the base of a putative jet. However, our detailed study of the gap kinetic physics and scaling suggests that the energetics is not enough in these environments. The second possibility is that the compact X-ray emitting source may be powered by small scale flux tubes near the black hole that are attached to the orbiting accretion disk. Our force-free simulations show that the field linking the black hole and the disk can get twisted up by the differential rotation to form a magnetic tower. When the confinement provided by the field from the outer disk is strong, the built-up magnetic tower can quickly become kink unstable, which leads to continuous reconnection and dissipates most of the energy extracted from the rotating black hole. This could in principle power a hot X-ray emitting region above the black hole.

Bernstein operators are vertex operators that create and annihilate Schur polynomials. These operators play a significant role in the mathematical formulation of the Boson-Fermion correspondence due to Kac and Frenkel. The role of this correspondence in mathematical physics has been widely studied as it bridges the actions of the infinite Heisenberg and Clifford algebras on Fock space. Cautis and Sussan conjectured a categorification of this correspondence within the framework of Khovanov's Heisenberg category. I will discuss how to categorify the Bernstein operators and settle the Cautis-Sussan conjecture, thus proving a categorical Boson-Fermion correspondence.

The elliptic quantum (toroidal) group U_{q,p}(g) is an elliptic and dynamical analogue of the Drinfeld realization 
of the affine quantum (toroidal) group U_q(g). I will discuss an interesting connection of its representations with 
a geometry such as an identification of the elliptic weight functions derived by using  the vertex operators with 
the elliptic stable envelopes in [Aganagic-  Okounkov ’16] and correspondence between the Gelfand-Tsetlin bases 
of a finite dimensional representation of U_{q,p} with the fixed point classes in the equivariant elliptic cohomology.