Related papers: Subellipticity of some complex vector fields relat…

Making use of theory of differentiable stacks, we study symplectic vortex equations over a compact orbifold Riemann surface. We discuss the category of representable morphisms from a compact orbifold Riemann surface to a quotient stack.…

We discuss certain features of pseudo-Hermiticity and weak pseudo-Hermiticity conditions and point out that, contrary to a recent claim, there is no inconsistency if the correct orthogonality condition is used for the class of…

In this paper, we present algebraic tools to obtain normal forms of $\omega$-Hamiltonian vector fields under a semisymplectic action of a Lie group, by taking into account the symmetries and reversing symmetries of the vector field. The…

In this paper we characterize completely the global hypoellipticity and global solvability in the sense of Komatsu (of Roumieu and Beurling types) of constant-coefficients vector fields on compact Lie groups. We also analyze the influence…

The existence of a positive entire weak solution to a singular quasi-linear elliptic system with convection terms is established, chiefly through perturbation techniques, fixed point arguments, and a priori estimates. Some regularity…

We discuss the interplay between lagrangian distributions and connections in symplectic geometry, beginning with the traditional case of symplectic manifolds and then passing to the more general context of poly- and multisymplectic…

It is shown that the notion of W_\infty-algebra originally carried out over a (compact) Riemann surface can be extended to n complex dimensional (compact) manifolds within a symplectic geometrical setup. The relationships with the…

We provide a Plancherel decomposition for the space of symplectic bilinear forms of rank $2n$ over a local non-archimedean field $F$ in terms of that of $GL_n(F)$.

We establish the existence and uniqueness of variational solution to the nonlinear Neumann boundary problem for the $p^{th}$-Sub-Laplacian associated to a system of H\"ormander vector fields

A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a vector bundle structure on F, or, equivalently, from an Euler vector field. This is…

We study the topology of the regular loci of two complexified Hamiltonian integrable systems using the Zariski-van Kampen method. In particular, we show that the fundamental group of the regular locus for the complexified planar Kepler…

This work proposes to generalize certain results regarding some semilinear elliptic systems.

Let $\mathbb{W}$ be an irreducible subvariety a Hilbert scheme $Hilb_{p_W} (t) (\mathbb{P}^n )$. We show that under mild hypothesis there are polynomial formulas for the degrees of the loci of hypersurfaces in $\mathbb{P}^n$ with singular…

Hyperelliptic mapping class groups are defined either as the centralizers of hyperelliptic involutions inside mapping class groups of oriented surfaces of finite type or as the inverse images of these centralizers by the natural…

We discuss a correspondence between certain contact pairs on the one hand, and certain locally conformally symplectic forms on the other. In particular, we characterize these structures through suspensions of contactomorphisms. If the…

Boundary conditions for Bismut's hypoelliptic Laplacian which naturally correspond to Dirichlet and Neumann boundary conditions for Hodge Laplacians are considered. Those are related with specific boundary conditions for the differential…

Graph Laplacians on finite compact metric graphs are considered under the assumption that the matching conditions at the graph vertices are of either $\delta$ or $\delta'$ type. In either case, an infinite series of trace formulae which…

We give a quantization analysis to an elliptic system (Gelfand-Liouville type system) with Dirichlet condition. An application, we have a com-pactness result for an elliptic system with Lipschitz condition.

The Witten Laplacian corresponding to a Morse function on the circle is studied using methods of complex WKB and resurgent analysis. It is shown that under certain assumptions the low-lying eigenvalues of the Witten Laplacian are resurgent.

Let $Y$ be a smooth quasi-projective complex variety equipped with a simple normal crossings compactification. We show that integral points are potentially dense in the (relative) character varieties parametrizing $SL_2$-local systems on…