Scientific Series

We will discuss some aspects of my recent preprint, joint with Victor Ginzburg, on Kostant-Whittaker reduction, a (deformation) quantization of restriction to a Kostant slice. We will explain how this functor can be used to prove conjectures of Ben-Zvi and Gunningham on parabolic induction, as well as a convolution exactness conjecture of Braverman and Kazhdan in the D-module setting. While this talk will occasionally reference facts from a talk I gave at Perimeter on other aspects of this preprint, the overlap and references will be minimal.

The physics of strongly correlated systems offers some of the most intriguing physics challenges such as competing orders or the emergence of dynamical composite degrees of freedom. Often, the resolution of these physics challenges is computationally hard, but can be simplified by a formulation in terms of the appropriate dynamical degrees of freedom.

Black hole X-ray binaries and Active Galactic Nuclei transition through a series of accretion states in a well-defined order. During a state transition, the accretion flow changes from a hot geometrically thick accretion flow, emitting a power-law–like hard spectrum to a geometrically thin, cool accretion flow, producing black-body–like soft spectrum. The hard intermediate accretion state present in the midst of a state transition is thought to be associated with the presence of both a hot geometrically thick component, termed the corona, and a cool, geometrically thin component of the accretion flow. The details concerning the geometry of the disk in the hard intermediate state are not agreed upon and numerous models have been proposed: In the “truncated disk” model, the accretion flow is geometrically thick and hot close to the black hole, while the outer regions of the flow are geometrically thin and cool. There are many open questions concerning the nature of truncated accretion disks: Which mechanisms generate the truncated disk structure? What sets the radius at which the disk truncates? How is the corona formed and what is its geometry? In this talk I present the first high-resolution 3D General Relativistic Magneto-Hydrodynamic (GRMHD) simulation and radiative GRMHD simulation modelling the self-consistent formation of a truncated accretion disk around a black hole.

Skein theory forms a once-categorified 3d TQFT and assigns skein algebras to surfaces and skein modules to 3-manifolds. Motivated by physics, these modules are expected to satisfy a certain holonomicity property, generalizing Witten's finiteness conjecture of skein modules. In this talk, we will recall the basic notions of skein theory as a deformation quantization theory, and then state and discuss the generalized Witten's finiteness conjecture.

Cosmic surveys offer a unique window into fundamental physics, particularly the physics of light particles such as neutrinos. As a striking example, the recent results from the Dark Energy Spectroscopic Instrument (DESI) have placed surprisingly stringent constraints on the sum of neutrino masses, nearly excluding the entire range of masses consistent with neutrino oscillation measurements. In this colloquium, I will review what we have learned about cosmic neutrinos from maps of the universe. I will then discuss this confusing situation, the status possible explanations for the current data, and the implications for Beyond the Standard Model physics.

The failure to calculate the vacuum energy remains a central problem in theoretical physics. In my talk I present a new understanding of the cosmological constant problem, grounded in the insight that vacuum energy density can be expressed in terms of phase space volume. Introduction of a UV-IR regularization implies a relationship between the vacuum energy and entropy. Combining this insight with the holographic bound on entropy then yields a bound on the cosmological constant consistent with observations. It follows that the universe is large, and the cosmological constant is naturally small, because the universe is filled with a large number of degrees of freedom. The talk is based on our papers Phys.Rev.D 107 (2023) 12, 126016; e-Print: 2212.00901 [hep-th] and Int.J.Mod.Phys.D 32 (2023) 14, 2342004; e-Print: 2303.17495 [hep-th].

Observations of gravitational waves from binary black-hole mergers provide a unique testbed for General Relativity in the strong-field regime. To extract the most information, many gravitational-wave signals can be used in concert to place constraints on theories beyond General Relativity. Although these hierarchical inference methods have allowed for more informative tests, careful consideration is needed when working with astrophysical observations. Assumptions about the underlying astrophysical population and the detectability of possible deviations can influence hierarchical analyses, potentially biasing the results. In this talk, I will address these key assumptions and discuss their mitigation. Finally, I will demonstrate how we can leverage the astrophysical nature of gravitational-wave observations to our advantage to empirically bound the curvature dependence of extensions to General Relativity.