Related papers: Tau-functions and monodromy symplectomorphisms

We prove that when Hodge theory survives on non-compact symplectic manifolds, a compact symplectic Lie group action having fixed points is necessarily Hamiltonian, provided the associated almost complex structure preserves the space of…

We introduce the concept of pseudo symplectic capacities which is a mild generalization of that of symplectic capacities. As a generalization of the Hofer-Zehnder capacity we construct a Hofer-Zehnder type pseudo symplectic capacity and…

After reviewing recent results on symplectic Lefschetz pencils and symplectic branched covers of CP^2, we describe a new construction of maps from symplectic manifolds of any dimension to CP^2 and the associated monodromy invariants. We…

It is shown that the multiplicative monoids of Brauer's centralizer algebras generated out of the basis are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself, and where, moreover, a kind of…

From the cohomological point of view the symplectomorphism group $Sympl (M)$ of a symplectic manifold is `` tamer'' than the diffeomorphism group. The existence of invariant polynomials in the Lie algebra $\frak {sympl }(M)$, the symplectic…

We consider random normal matrix and planar symplectic ensembles, which can be interpreted as two-dimensional Coulomb gases having determinantal and Pfaffian structures, respectively. For general radially symmetric potentials, we derive the…

We introduce the notion of a symplectic capacity relative to a coisotropic submanifold of a symplectic manifold, and we construct two examples of such capacities through modifications of the Hofer-Zehnder capacity. As a consequence, we…

We extend Poincar\'e's theory of orientation-preserving homeomorphisms from the circle to circloids with decomposable boundary. As special cases, this includes both decomposable cofrontiers and decomposable cobasin boundaries. More…

We consider the symplectic groupoid of pairs $(B, A)$ with $A$ real unipotent upper-triangular matrix and $B\in GL_n$ being such that $\tilde A=BAB^T$ is also a unipotent upper-triangular matrix. Fock and Chekhov defined a Poisson map of…

For one-matrix models with polynomial potentials, the explicit relationship between the partition function and the isomonodromic tau function for the 2x2 polynomial differential systems satisfied by the associated orthogonal polynomials is…

We investigate the random dynamics of rational maps on the Riemann sphere and the dynamics of semigroups of rational maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, in most cases, the chaos of the…

The special structures that arise in symplectic topology (particularly Gromov--Witten invariants and quantum homology) place as yet rather poorly understood restrictions on the topological properties of symplectomorphism groups. This…

We extend the famous convexity theorem of Atiyah, Guillemin and Sternberg to the case of non-Hamiltonian actions. We show that the image of a generalized momentum map is a bounded polytope times a vector space. We prove that this picture is…

Given an arrangement of hyperplanes in $\P^n$, possibly with non-normal crossings, we give a vanishing lemma for the cohomology of the sheaf of $q$-forms with logarithmic poles along our arrangement. We give a basis for the ideal $\cal J$…

Orthogonal and symplectic matrix integrals are investigated. It is shown that the matrix integrals can be considered as a $\tau$-function of the coupled KP hierarchy, whose solution can be expressed in terms of pfaffians.

Representation theory and the theory of symmetric functions have played a central role in Random Matrix Theory in the computation of quantities such as joint moments of traces and joint moments of characteristic polynomials of matrices…

We consider powers of the absolute value of the characteristic polynomial of Haar distributed random orthogonal or symplectic matrices, as well as powers of the exponential of its argument, as a random measure on the unit circle minus small…

The monodromy of torus bundles associated to completely integrable systems can be computed using geometric techniques (constructing homology cycles) or analytic arguments (computing discontinuities of abelian integrals). In this article we…

Given a collection of exact Lagrangians in a Liouville manifold, we construct a map from the Hochschild homology of the Fukaya category that they generate to symplectic cohomology. Whenever the identity in symplectic cohomology lies in the…

The automorphisms of the symmetrized polydisc $\mathbb G_n$ are well-known and are given in the coordinates of the polydisc in \cite{E:Z}. We find an explicit formula for the automorphisms of $\mathbb G_n$ in its own coordinates. If $\tau$…