A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Reproduces basic supersymmetric QFTs using complexified graded algebraic geometry.
Reconstructs supersymmetry and supergravity in complexified Z/2-graded Algebraic Geometry.
Every finite dimensional real representation of a compact real semisimple Lie algebra determines a metric 2-step nilpotent Lie algebra and a corresponding simply connected metric 2-step nilpotent Lie group N. We study the differential geometry of N using representation theory of the complexified complex semisimple Lie …
We prove that a K-contact Lie group of dimension five or greater is the central extension of a symplectic Lie group by complexifying the Lie algebra and applying a result from complex contact geometry, namely, that, if the adjoint action of the complex Reeb vector field on a complex contact Lie algebra is diagonalizabl…
New representation of curves helps prove complex geometry result.
New classification of complex hypersurfaces in 3D.
Motivated by strong desire to understand the natural geometry of moduli spaces of hyperbolic monopoles, we introduce and study a new type of geometry: pluricomplex geometry. It is a generalisation of hypercomplex geometry: we still have a 2-sphere of complex structures, but they no longer behave like unit imaginary qua…
New algebraic description connects Fukaya category to bordered Floer homology.
This paper explores hyperkähler structures on specific orbits using different methods.
Given a compact Lie group, endowed with a bi-invariant Riemannian metric, its complexification inherits a Kaehler structure having twice the kinetic energy of the metric as its potential, and Kaehler reduction with reference to the adjoint action yields a stratified Kaehler structure on the resulting adjoint quotient. …
The paper describes orbits of parabolic subgroups in complexified actions.
Proves volume conjecture for double twist knots using complexified tetrahedrons.
Study of complexified Hermitian symmetric spaces and their structures.
We first investigate the geometry of orbits of the isotropy action on a semi-simple pseudo-Riemannian symmetric space by investigating the complexified action. Next we investigate the geometry of the orbits of Hermann type actions on the symmetric spaces. By considering two special Hermann type actions on the symmetric…
Study special complexified Kähler forms in mirror symmetry.
Extends K-energy to complexified Kähler classes for scalar curvature study.
Study norm-squared of momentum map in infinite dimensions with applications to symplectic geometry.
We identify two Frobenius manifolds obtained from two different differential Gerstenhaber-Batalin-Vilkovisky algebras on a compact Kaehler manifold. One is constructed on the Dolbeault cohomology, and the other on the de Rham cohomology. Our result can be considered as a generalization of the identification of the Dolb…
A venerable problem in combinatorics and geometry asks whether a given incidence relation may be realized by a configuration of points and lines. The classic version of this would ask for algebraic lines over some field or possibly real pseudolines: embedded circles (isotopic to ) in the real projective plane. In…
We study the geometry of complexified moduli spaces of special Lagrangian submanifolds in the complement of an anticanonical divisor in a compact Kahler manifold. In particular, we explore the connections between T-duality and mirror symmetry in concrete examples, and show how quantum corrections arise in this context.
Study on Hermitian Calabi functional in complexified orbits of symplectic manifolds.
Constructs maps from field theories to complexified K-theory and elliptic cohomology.
Defines Chern-Robinson connection on Robinson manifolds.
Analyzes Schouten square on specific Lie algebra extensions, revealing geometric and algebraic properties.
Representations of -algebras are realized on section spaces of holomorphic homogeneous vector bundles. The corresponding section spaces are investigated by means of a new notion of reproducing kernel, suitable for dealing with involutive diffeomorphisms defined on the base spaces of the bundles. Applications of th…
The paper describes Calabi-Yau structures and special Lagrangian submanifolds in complexified symmetric spaces.
For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary Clifford algebras, followed by quaternionic vectors as a special case. All results a…
We shall construct a natural Higgs bundle structure on the complexified Kähler cone of a compact Kähler manifold, which can be seen as an analogy of the classical Higgs bundle structure associated to a variation of Hodge structure. In the proof of the flat-ness of our Higgs bundle, we find a commutator identity that ca…
Simplified construction recovers Todd class using algebraic methods.
New combinatorial model for Milnor fibration using oriented matroids.
We consider principal fibre bundles with a given connection and construct almost complex structures on the total space if the adjoint bundle is isomorphic to the tangent bundle of the base. We derive the integrability condition. If the structure group is compact, then a choice of an ad-invariant inner product on its Li…
We propose an extension of the structure equation for constant mean curvature (CMC) surfaces in a three dimensional Riemannian space form to the associated CMC hierarchy of evolution equations by the higher-order commuting symmetries. Via the canonical formal Killing field, considered as an infinitely prolonged and loo…
The paper constructs homotopically non-trivial spheres in complexified spaces.
We introduce the category of holomorphic string algebroids, whose objects are Courant extensions of Atiyah Lie algebroids of holomorphic principal bundles, as considered by Bressler, and whose morphisms correspond to inner morphisms of the underlying holomorphic Courant algebroids in the sense of Severa. This category …
We study the Kaehler metric given by the logarithm of a cubic form on its complexified index cone. Under mirror symmetry, this metric should asymptotically correspond to the Weil-Petersson metric. Using the theory of special Kaehler manifolds, a proof of a curvature formula for this metric is given.
Null Kähler metrics are characterized by Painlevé I or II ODEs.
We study the boundary conditions in the topologically twisted Chern-Simons matter theories with the Lie 3-algebraic structure. We find that the supersymmetric boundary conditions and the gauge invariant boundary conditions can be unified as the complexified gauge invariant boundary conditions which lead to the supergro…
The reduced Burau representation of the braid group is obtained from the action of on the homology of an infinite cyclic cover of the disc with punctures. The group homology of braid groups with coefficients in the complexified reduced Burau representation is calculated. Our topolog…
Derives scalar curvature formula in generalized Kähler geometry.
Constructs simplified or complexified simplicial complexes.
In this sequel, employing more commutative algebra than that explored in \cite{CCJ}, we show that an isoparametric hypersurface with four principal curvatures and multiplicities in is one constructed by Ozeki-Takeuchi \cite[I]{OT} and Ferus-Karcher-Münzner \cite{FKM}, referred to collectively as of OT-…
Let be a finite dimensional complex vector space and $W\subseteq \GL(V)$ be a finite complex reflection group. Let $V^{\reg}$ be the complement in of the reflecting hyperplanes. We prove that $V^{\reg}$ is a space. This was predicted by a classical conjecture, originally stated by Brieskorn for complex…
The paper studies dynamics of rational maps using barycentric extensions and Berkovich spaces.
A complex Lie algebroid is a complex vector bundle over a smooth (real) manifold M with a bracket on sections and an anchor to the complexified tangent bundle of M which satisfy the usual Lie algebroid axioms. A proposal is made here to integrate analytic complex Lie algebroids by using analytic continuation to a compl…
Subharmonicity of Dirichlet energy proven for Kähler manifolds.
Surveying probabilistic real algebraic geometry.
Study shows certain toric arrangements have minimal topological complements.
We give a simple interpretation of the adapted complex structure of Lempert-Szoke and Guillemin-Stenzel: it is given by a polar decomposition of the complexified manifold. We then give a twistorial construction of an SO(3)-invariant hypercomplex structure on a neighbourhood of in , where is a real-analytic…