arXiv research

Develops a finite construction for self-duality and related moduli spaces over Riemann surfaces.

QP perspective on Poisson-Lie T-duality topology changes.

New flows introduced for symplectic geometry.

Study $T$-duality on nilmanifolds using Lie algebras.

The paper explores symplectic geometry of Cartan-Hartogs domains.

The paper proves a duality theorem for conjugation-invariant norms and quasimorphisms.

Unified description of fluxes and T-duality via symplectic manifolds.

We prove that the cotangent of a double Lie groupoid S has itself a double groupoid structure with sides the duals of associated Lie algebroids, and double base the dual of the Lie algebroid of the core of S. Using this, we prove a result outlined by Weinstein in 1988, that the side groupoids of a general symplectic do…

Letters discuss results on Courant algebroids, including classification and reduction.

This paper explores 4-planes in Spin(7) manifolds with symplectic structures.

Given a six-dimensional symplectic manifold $(M, B)$, a nondegenerate, co-closed four-form $C$ introduces a dual symplectic structure $\widetilde{B} = *C$ independent of $B$ via the Hodge duality $*$. We show that the doubling of symplectic structures due to the Hodge duality results in two independent classes of nonc…

Let $G$ be a finite group and $\Y$ a $G$-gerbe over an orbifold $\B$. A disconnected orbifold $\hat{\Y}$ and a flat U(1)-gerbe $c$ on $\hat{\Y}$ is canonically constructed from $\Y$. Motivated by a proposal in physics, we study a mathematical duality between the geometry of the $G$-gerbe $\Y$ and the geometry of $\hat{…

Study connects complex and symplectic supersymmetric systems on SU(4)-structure backgrounds.

The paper explores properties of Coulomb branches in 3D SUSY gauge theories.

Study the symplectomorphism group of small rational 4-manifolds using curve decompositions.

We introduce the symplectic twistor operator $T_s$ in symplectic spin geometry, as a symplectic analogue of the twistor operator in Riemannian spin geometry. We focus on the real dimension 2 and compute the space of its solutions on ${\mathbb R}^2$. Our analysis is based on the techniques of metaplectic Howe duality.

The paper proves a generalized Lefschetz duality for a specific type of manifold.

The paper integrates supergravity with geometric and symplectic structures.

Symplectic spinors and their properties are analyzed for Hodge theory.

Holomorphic Lagrangian subvarieties are toric fibrations over their projections in special Kähler bases.

Global formulation of scalar and gauge field coupling for generalized duality structures.

We introduce certain homology and cohomology subgroups for any almost complex structure and study their pureness, fullness and duality properties. Motivated by a question of Donaldson, we use these groups to relate J-tamed symplectic cones and J-compatible symplectic cones over a large class of almost complex manifolds…

Unified geometric approach to quantum indeterminacy.

An Hermitian bounded symmetric domain in a complex vector space, given in its circled realization, is endowed with two natural symplectic forms: the flat form and the hyperbolic form. In a similar way, the ambient vector space is also endowed with two natural symplectic forms: the Fubini-Study form and the flat form. I…

Study cohomologies on manifolds with locally conformally symplectic structures.

New correspondence links fluxless to fluxy flag manifolds via T-duality.

Develops a new geometric formulation for abelian gauge theories.

We describe how generalized complex geometry, which interpolates between complex and symplectic geometry, is compatible with T-duality, a relation between quantum field theories discovered by physicists. T-duality relates topologically distinct torus bundles, and prescribes a method for transporting geometrical structu…

S-dual of Hamiltonian spaces connects to Langlands duality.

The geometry that is defined by the scalars in couplings of Einstein-Maxwell theories in N=2 supergravity in 4 dimensions is denoted as special Kaehler geometry. There are several equivalent definitions, the most elegant ones involve the symplectic duality group. The original construction used conformal symmetry, which…

Let $λ: \tilde{G}\to G$ be the non-trivial double covering of the symplectic group $G=Sp(V,ω)$ of the symplectic vector space $(V,ω)$ by the metaplectic group $\tilde{G}=Mp(V,ω).$ In this case, $λ$ is also a representation of $\tilde{G}$ on the vector space $V$ and thus, it gives rise to the representation of $\tilde{G…

Defines and examines morphisms of Courant algebroids with applications in physics.

Novel gauge-theoretic Floer homologies defined from 5d N=2 theory, linking 4, 3, and 2-manifolds.

The paper finds symplectic compactifications of coadjoint orbits.

Defines symplectic homology for Liouville cobordisms, satisfying Eilenberg-Steenrod axioms.

This thesis studies cluster varieties from surfaces and their properties.

Study of mixed equation combining gauge theory and symplectic geometry.

We establish a long exact sequence for Legendrian submanifolds L in P x R, where P is an exact symplectic manifold, which admit a Hamiltonian isotopy that displaces the projection of L off of itself. In this sequence, the singular homology H_* maps to linearized contact cohomology CH^* which maps to linearized contact …

We apply the results from the article Cahen, Schwachhöfer: Special symplectic connections, to the case of Bochner-Kaehler metrics. We obtain a (local) classification of these based on the orbit types of the adjoint action in $su(n,1)$. The relation between Sasaki and Bochner-Kaehler metrics in cone and transveral metri…

Projective resolves symplectic Steinberg module for number rings.

Complex geometry and symplectic geometry are mirrors in string theory. The recently developed generalised complex geometry interpolates between the two of them. On the other hand, the classical and quantum mechanics of a finite number of degrees of freedom are respectively described by a symplectic structure and a comp…

Summarizes geometric formulation of Einstein-Scalar-Maxwell theories.

Formulates a new class of gravity theories coupled to scalar and gauge fields.

Geometric formulation of 4D supergravity for mathematicians.

Study of Poisson manifolds of compact types with symplectic properties.

Gopakumar-Vafa large N duality is a correspondence between Chern-Simons invariants of a link in a 3-manifold and relative Gromov-Witten invariants of a 6-dimensional symplectic manifold relative to a Lagrangian submanifold. We address the correspondence between the Chern-Simons free energy of S^3 with no link and the G…

The paper explores geometric and topological properties of almost Kähler manifolds using harmonic theory.

Proves integrability of dispersionless Hirota type equations in 4D implies symplectic Monge-Ampere property.