Related papers: KP integrability of non-perturbative differentials
For perturbations of integrable Hamiltonians systems, the Nekhoroshev theorem shows that all solutions are stable for an exponentially long interval of time, provided the integrable part satisfies a steepness condition and the system is…
The analytic proof of mode stability of the Kerr black hole was provided by Whiting. In his proof, the construction of a conserved quantity for unstable mode was crucial. We extend the method of the analysis for the Kerr-de Sitter geometry.…
There are well-known constructions of integrable systems which are chains of infinitely many copies of the equations of the KP hierarchy ``glued'' together with some additional variables, e.g., the modified KP hierarchy. Another…
We review the integration of the KP hierarchy in several non-standard contexts. Specifically, we consider KP in the following associative differential algebras: an algebra equipped with a nilpotent derivation; an algebra of functions…
We show that the solution space of the noncommutative KP hierarchy is the same as that of the commutative KP hierarchy owing to the Birkhoff decomposition of groups over the noncommutative algebra. The noncommutative Toda hierarchy is…
We revisit the construction of stable envelopes in equivariant elliptic cohomology [arXiv:1604.00423] and give a direct inductive proof of their existence and uniqueness in a rather general situation. We also discuss the specialization of…
In this paper, we investigate perturbations of linear integrable Hamiltonian systems, with the aim of establishing results in the spirit of the KAM theorem (preservation of invariant tori), the Nekhoroshev theorem (stability of the action…
We propose and analyze a new family of nonconforming finite elements for the three-dimensional quad-curl problem. The proposed finite element spaces are subspaces of $\pmb{H}(\mathrm{curl})$, but not of…
We present a mathematical proof of the Aganagic-Dijkgraaf-Klemm-Mari\~no-Vafa Conjecture proposed in 2006, which states that the generating function of the topological vertex, i.e., the generating function of the open Gromov-Witten…
Demailly proved that on a smooth compact K\"ahler manifold the distribution defined by a holomorphic $p$-form with values in an anti-pseudoeffective line bundle is always integrable. We generalise his result to compact K\"ahler spaces with…
We obtain new invariants of topological link concordance and homology cobordism of 3-manifolds from Hirzebruch-type intersection form defects of towers of iterated p-covers. Our invariants can extract geometric information from an arbitrary…
Based on the Kupershmidt deformation for any integrable bi-Hamiltonian systems presented in [4], we propose the generalized Kupershmidt deformation to construct new systems from integrable bi-Hamiltonian systems, which provides a…
We study the K-stability of a polarised variety with non-reductive automorphism group. We associate a canonical filtration of the co-ordinate ring to each variety of this kind, which destabilises the variety in several examples which we…
When a solution to an abstract inverse linear problem on Hilbert space is approximable by finite linear combinations of vectors from the cyclic subspace associated with the datum and with the linear operator of the problem, the solution is…
We give a precise characterization when a compact homogeneous CR-solvmanifold is CR-embeddable in a Kahler manifold. Equivalently this gives a non-Kahler criterion for complex manifolds containing CR-solvmanifolds not satisfying these…
The non-chiral edge excitations of quantum spin Hall systems and topological insulators are described by means of their partition function. The stability of topological phases protected by time-reversal symmetry is rediscussed in this…
Motivated by the Lagrange top coupled to an oscillator, we consider the quasi-periodic Hamiltonian Hopf bifurcation. To this end, we develop the normal linear stability theory of an invariant torus with a generic (i.e., non-semisimple)…
In this paper, we prove a stability result for the non-K\"ahler geometry of locally conformally K\"ahler (lcK) spaces with singularities. Specifically, we find sufficient conditions under which the image of an lcK space by a holomorphic…
The recent focus on deformations of algebras called quantum algebras can be attributed to the fact that they appear to be the basic algebraic structures underlying an amazingly diverse set of physical situations. To date many interesting…
We prove the conjecture of Do and Karev that the monotone orbifold Hurwitz numbers satisfy the Chekhov-Eynard-Orantin topological recursion.