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Given a reduced analytic space $Y$ we introduce a class of {\it nice} cycles, including all effective $\mathbb{Q}$-Cartier divisors. Equidimensional nice cycles that intersect properly allow for a natural intersection product. Using…
In some insulators, corner charges are fractionally quantized, due to the topological invariant called a filling anomaly. The previous theories of fractional corner charges have been mostly limited to two-dimensional systems. In three…
Varying the curvature, quantum phase transitions are investigated in holographic confining QFTs defined on a fixed constant positive curvature background. We find a competition between two branches of solutions and a phase transition as one…
We consider C^r-diffeomorphisms of a compact smooth manifold having a pair of robust heterodimensional cycles where r is a positive integer or infinity. We prove that if certain conditions about the signatures of non-linearities and…
The Separatrix Theorem of C. Camacho and P. Sad guarantees the existence of invariant curve (separatrix) passing through the singularity of germ of holomorphic foliation on complex surface, when the surface underlying the foliation is…
A defining property of metals is the existence of a Fermi surface: for two dimensions, a continuous contour in momentum space which separates occupied from unoccupied states. In this paper, I discuss angle resolved photoemission data on the…
We study finite density QCD in an approximation in which the interaction between quarks is modelled on that induced by instantons. We sketch the mechanism by which chiral symmetry restoration at finite density occurs in this model. At all…
Metals typically have multiple Fermi surface sheets, and when they enter the superconducting state, some electrons on these sheets may remain uncondensed, or their superconducting pairs can be rapidly destroyed by a magnetic field.…
The surface states of 3D topological insulators in general have negligible quantum oscillations when the chemical potential is tuned to the Dirac points. In contrast, we find that topological Kondo insulators can support surface states with…
This article is concerned with the geometry of germs of real analytic surfaces in $(\mathbb{C}^2,0)$ having an isolated Cauchy-Riemann (CR) singularity at the origin. These are perturbations of {\it Bishop quadrics}. There are two kinds of…
Liquid crystals with molecules constrained to the tangent bundle of a curved surface show interesting phenomena resulting from the tight coupling of the elastic and bulk free energies of the liquid crystal with geometric properties of the…
Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and…
We investigate the phase diagram of a fluid of hard-core disks confined to the surface of a sphere and whose interaction potential contains a short-range attraction followed by a long-range repulsive tail (SALR). Based on previous works in…
At model water--vapor and water--solid interfaces, molecular ordering leads to charge oscillations and, thereby, to a spatially varying electrostatic potential. Atomistic simulations indicate that such ordering leads to an electric…
We study the transition between sharp and smooth density distributions at the edges of Quantum Hall Liquids in the presence of interactions. We find that, for strong confining potentials, the edge of a $\nu=1$ liquid is described by the…
Quantum crystals abound in the whole range of solid-state species. Below a certain threshold temperature the physical behavior of rare gases (4He and Ne), molecular solids (H2 and CH4), and some ionic (LiH), covalent (graphite), and…
A tetragonal canonical curve is the complete intersection of two divisors on a scroll. The equations can be written in `rolling factors' format. For such homogeneous ideals we give methods to compute infinitesimal deformations. Deformations…
The folklore tradition about the QCD phase diagram is that at the chiral restoration phase transition at finite density hadrons are deconfined and there appears the quark matter. We address this question within the only known exactly…
We calculate the grand canonical partition function at the one-loop level for scalar quantum electrodynamics at finite temperature and chemical potential. A classical background charge density with a charge opposite that of the scalars…
According to Dirac, fundamental laws of Classical Mechanics should be recovered by means of an "appropriate limit" of Quantum Mechanics. In the same spirit it is reasonable to enquire about the fundamental geometric structures of Classical…