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In classical General Relativity (GR), an observer falling into an astrophysical black hole (BH) is not expected to experience anything dramatic as she crosses the event horizon. However, tentative resolutions to problems in quantum gravity, such as the cosmological constant problem or the black hole information paradox, invoke significant departures from classicality in the vicinity of the horizon. I outline theoretical and phenomenological arguments for these departures. I will then discuss the tentative observational evidence for Planck-scale structure near BH horizons, seen as "echoes" in LIGO gravitational wave observations,  which has now been found by three independent groups. Finally, I present preliminary analysis which strongly suggest formation of a highly spinning black hole within 0.5 second of GW170817 binary neutron star merger, based on prominent echoes in the LIGO strain data. 

Let be a complex semisimple algebraic group of adjoint type and the wonderful compacti
cation. We show that the closure in \overline{G} of the centralizer of a regular nilpotent is isomorphic to the Peterson variety. We generalize this result to show that for any regular , the closure of the centralizer in is isomorphic to the closure of a general -orbit in the flag variety. We consider the family of all such centralizer closures, which is a partial compactication of the universal centralizer. We show that it has a natural log-symplectic Poisson structure that extends the usual symplectic structure on the universal centralizer.

In this talk, I'd like to explain how quantum integrability and (q-deformed) W-algebraic structure arise from the moduli space of quiver gauge theory. It'll be also shown that our construction gives rise to a new family of W-algebras. 

We are fortunate to live in an era of great discoveries in particle physics and cosmology, and most of the theoretical understanding that made this possibile is based on effective field theories. In this talk, I will show how these powerful techniques can be applied across the spectrum of theoretical physics, and allow us to draw unexpected connections among very different systems. To illustrate this, I will discuss two interesting but very different phenomena, and show how they can both be described using a point-like particle effective theory. The first phenomenon I will consider is superradiance---a dissipative phenomenon by which a spinning object can amplify the intensity of scattered radiation, or be unstable by creation of particles in a bound state. This phenomenon is particularly interesting when applied to spinning black holes, and in this context it has recently received significant attention as a possible probe of ultra-light particle beyond the Standard Model. The second phenomenon I will discuss is the existence of roton excitations in superfluid He4. By treating rotons as point-like particles--albeit of a very special kind--I will write down an effective theory that describes the motion of rotons in the medium at equilibrium as well as their couplings to sound waves and generic fluid flows. This approach allows us to correct classic results by Landau and Khalatnikov on roton-phonon scattering, and to pose and answer the intriguing question: do rotons sink or float?