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The flow in a cylinder driven by time harmonic oscillations of the rotation rate, called longitudinal librations, is investigated. Using a theoretical approach and axisymmetric numerical simulations, we study two distinct phenomena…
Modular flow is a symmetry of the algebra of observables associated to spacetime regions. Being closely related to entanglement, it has played a key role in recent connections between information theory, QFT and gravity. However, little is…
The counterflow superfluidity (CSF) was predicted two decades ago. Counterintuitively, while both components in the CSF have fluidity, their correlated counterflow currents cancel out leading the overall system to an incompressible Mott…
The problem of boundary conditions in a supersymmetric theory of quantum cosmology is studied, with application to the one-loop prefactor in the quantum amplitude. Our background cosmological model is flat Euclidean space bounded by a…
We study the reconstruction of bulk operators in the entanglement wedge in terms of low energy operators localized in the respective boundary region. To leading order in $N$, the dual boundary operators are constructed from the modular flow…
In this paper, we present our general results about traversing flows on manifolds with boundary in the context of the flows on surfaces with boundary. We take advantage of the relative simplicity of $2D$-worlds to explain and popularize our…
In this article, we study the topology and bifurcations of the moduli space $\mathcal{M}_3$ of cubic Newton maps. It's a subspace of the moduli space of cubic rational maps, carrying the Riemann orbifold structure $(\mathbb{\widehat{C}},…
Given a conformal QFT local net of von Neumann algebras B_2 on the two-dimensional Minkowski spacetime with irreducible subnet A\otimes\A, where A is a completely rational net on the left/right light-ray, we show how to consistently add a…
In this paper we study a boundary value problem for the Ricci flow in the two dimensional ball endowed with a rotationally symmetric metric. We show short and long time existence results. We construct families of metrics for which the flow…
A four-dimensional Abelian gauge field can be coupled to a 3d CFT with a $U(1)$ symmetry living on a boundary. This coupling gives rise to a continuous family of boundary conformal field theories (BCFT) parametrized by the gauge coupling…
Let $D_t$, $t \in [0,1]$ be an arbitrary 1-parameter family of Dirac type operators on a two-dimensional disk with $m-1$ holes. Suppose that all operators $D_t$ have the same symbol, and that $D_1$ is conjugate to $D_0$ by a scalar gauge…
We measure, in two distinct ways, the extent to which the boundary region of moduli space contributes to the ``simple type'' condition of Donaldson theory. Using a geometric representative of \mu(pt), the boundary region of moduli space…
We develop a new boundary condition for the weak inverse mean curvature flow, which gives canonical and non-trivial solutions in bounded domains. Roughly speaking, the boundary of the domain serves as an outer obstacle, and the evolving…
In this paper we argue that boundary condition may run with energy scale. As an illustrative example, we consider one-dimensional quantum mechanics for a spinless particle that freely propagates in the bulk yet interacts only at the origin.…
The two known mechanisms for superflow are the gradient of the U(1) phase and the spin-orbit-gauge symmetry. We find the third mechanism, namely a spatial variation of the order-parameter morphology protected by a hidden su(2) symmetry in a…
We show that bulk quantities localized on a minimal surface homologous to a boundary region correspond in the CFT to operators that commute with the modular Hamiltonian associated with the boundary region. If two such minimal surfaces…
This is an expository article, explaining recent work by D. Groisser and myself [GS] on the extent to which the boundary region of moduli space contributes to the ``simple type'' condition of Donaldson theory. The presentation is intended…
We consider a model of axisymmetric flows for a free boundary vortex embedded in a statically stable fluid at rest. We identify the boundary of the vortex by solving a variational problem. Then, we reduce the analysis of the dynamics of the…
We study the short-time existence and regularity of solutions to a boundary value problem for the Ricci-DeTurck equation on a manifold with boundary. Using this, we prove the short-time existence and uniqueness of the Ricci flow prescribing…
We study the mixing processes inside a forced fountain using data from direct numerical simulation. The outer boundary of the fountain with the ambient is a turbulent/non-turbulent interface. Inside the fountain, two internal boundaries,…