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We examine various examples of horosymmetric manifolds which exhibit interesting properties with respect to canonical metrics. In particular, we determine when the blow-up of a quadric along a linear subquadric admits K\"ahler-Einstein…
We present a framework to systematically address topological phases when finer partitionings of bands are taken into account, rather than only considering the two subspaces spanned by valence and conduction bands. Focusing on…
We give a purely algebraic construction of a cohomological field theory associated with a quasihomogeneous isolated hypersurface singularity W and a subgroup G of the diagonal group of symmetries of W. This theory can be viewed as an…
We study a tachyon model with non-minimal derivative coupling to gravity in the Friedmann-Robertson-Walker flat cosmology. We propose the special re-definition of the tachyon field which allows us to represent tachyon field equation…
We construct well-formed and quasismooth terminal Fano 4-folds of index 1 in low codimension containing at worst isolated orbifold points. We provide a certain classification of these varieties where their images under the anitcanonical…
Given a homogeneous component of an exterior algebra, we characterize those subspaces in which every nonzero element is decomposable. In geometric terms, this corresponds to characterizing the projective linear subvarieties of the Grassmann…
A general field-theoretical description of many-fermion systems, with or without quenched disorder, is developed. Starting from the Grassmannian action for interacting fermions, we first bosonize the theory by introducing composite matrix…
I solve a quantum chain whose Hamiltonian is comprised solely of local four-fermi operators by constructing free-fermion raising and lowering operators. The free-fermion operators are both non-local and highly non-linear in the local…
Equivalence classes of $n$-point configurations in Euclidean, Hermitian, and quaternionic spaces are related, respectively, to classical determinantal varieties of symmetric, general, and skew-symmetric bilinear forms. Cayley-Menger…
The coherent superposition of non-orthogonal fermionic Gaussian states has been shown to be an efficient approximation to the ground states of quantum impurity problems [Bravyi and Gosset,Comm. Math. Phys.,356 451 (2017)]. We present a…
Multi-frequency forcing of systems undergoing a Hopf bifurcation to spatially homogeneous oscillations is investigated using a complex Ginzburg-Landau equation that systematically captures weak forcing functions that simultaneously hit the…
Non-anticommutative Grassmann coordinates in four-dimensional twist-deformed N=1 Euclidean superspace are decomposed into geometrical ones and quantum shift operators. This decomposition leads to the mapping from the commutative to the…
In this paper we compute the cohomology of the Fano varieties of $k$-planes in the smooth complete intersection of two quadrics in $\mathbb{P}^{2g+1}$, using Springer theory for symmetric spaces.
We introduce a system combining the quadratic self-attractive or composite quadratic-cubic nonlinearity, acting in the combination with the fractional diffraction, which is characterized by its L\'{e}vy index $\alpha $. The model applies to…
We study vacua, walls and three-pronged junctions of mass-deformed nonlinear sigma models on $SO(2N)/U(N)$ and $Sp(N)/U(N)$ for generic $N$. We review and discuss the on-shell component Lagrangians of the ${\mathcal{N}}=2$ nonlinear sigma…
Given a unitary fusion category, one can define the Hilbert space of a so-called ``anyonic spin-chain'' and nearest neighbor Hamiltonians providing a real-time evolution. There is considerable evidence that suitable scaling limits of such…
Gapless topological phases of matter may host emergent quasiparticle excitations which have no analog in quantum field theory. This is the case of so called triple point fermions (TPF), quasiparticle excitations protected by crystal…
We study the PI degree of various quantum algebras at roots of unity, including quantum Grassmannians, quantum Schubert varieties, partition subalgebras, and their associated quantum affine spaces. By a theorem of De Concini and Procesi,…
We set up an algebraic framework for the study of pseudoholomorphic discs bounding nonorientable Lagrangians, as well as equivariant extensions of such structures arising from a torus action. First, we define unital cyclic twisted…
We give a conjectural formula for sheaves supported on (irreducible) conormal varieties inside the cotangent bundle of the Grassmannian, such that their equivariant $K$-class is given by the partition function of an integrable loop model,…