Related papers: Symplectic leaves for generalized affine Grassmann…
The Darboux-Weinstein decomposition is a central result in the theory of Poisson (degenerate symplectic) varieties, which gives a local decomposition at a point as a product of the formal neighborhood of the symplectic leaf through the…
To a compact oriented surface of genus at most one with boundary, we associate a quantized $K$-theoretic Coulomb branch in the sense of Braverman, Finkelberg, and Nakajima. In the case where the surface is a three- or four-holed sphere or a…
Following Braverman-Finkelberg-Feigin-Rybnikov (arXiv:1008.3655), we study the convolution algebra of a handsaw quiver variety, a.k.a. a parabolic Laumon space, and a finite W-algebra of type A. This is a finite analog of the AGT conjecture…
We study deformations of symplectic structures on a smooth manifold $M$ via the quasi-Poisson theory. By a fact, we can deform a given symplectic structure $\omega $ to a new symplectic structure $\omega_t$ parametrized by some element $t$…
We prove a generalization of Kawai theorem for the case of orbifold Riemann surface. The computation is based on a formula for the differential of a holomorphic map from the cotangent bundle of the Teichm\"uller space to the…
A generalized cusp $C$ is diffeomorphic to $[0,\infty)$ times a closed Euclidean manifold. Geometrically $C$ is the quotient of a properly convex domain by a lattice, $\Gamma$, in one of a family of affine groups $G(\psi)$, parameterized by…
This article studies the symplectic cohomology of affine algebraic surfaces that admit a compactification by a normal crossings anticanonical divisor. Using a toroidal structure near the compactification divisor, we describe the complex…
We compute the quantum cohomology of symplectic flag manifolds. Symplectic flag manifolds can be described by non-abelian GLSMs with superpotential. Although the ring relations cannot be directly read off from the equations of motion on the…
Our paper develops a theory of Poisson slices and a uniform approach to their partial compactifications. The theory in question is loosely comparable to that of symplectic cross-sections in real symplectic geometry.
In this paper we develop the Hermitian refinement of symplectic Clifford analysis, by introducing a complex structure $\mathbb{J}$ on the canonical symplectic manifold $(\mathbb {R}^{2n},\omega_0)$. This gives rise to two symplectic Dirac…
The Kimura 3-parameter model on a tree of n leaves is one of the most used in phylogenetics. The affine algebraic variety W associated to it is a toric variety. We study its geometry and we prove that it is isomorphic to a geometric…
In this paper we use a diffeo-geometric framework based on manifolds that are locally modeled on "convenient" vector spaces to study the geometry of some infinite dimensional spaces. Given a finite dimensional symplectic manifold…
We consider aspherical manifolds with torsion-free virtually polycyclic fundamental groups, constructed by Baues. We prove that if those manifolds are cohomologically symplectic then they are symplectic. As a corollary we show that…
We initiate the study of the generalized quaternionic manifolds by classifying the generalized quaternionic vector spaces, and by giving two classes of nonclassical examples of such manifolds. Thus, we show that any complex symplectic…
The aim of this paper is to show that Lawson's foliation on the 5-sphere admits a smooth leafwise symplectic structure. The main part of the construction is to show that the Fermat type cubic surface admits an end-periodic symplectic…
In symplectic topology one uses elliptic methods to prove rigidity results about symplectic manifolds and solutions of Hamiltonian equations on them, where the most basic example is given by geodesics on Riemannian manifolds. Harmonic maps…
Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space of Kostant's slice. They have attracted a great deal of…
The closure of a Diximier sheet is the image of a generalized Grothendieck's simultaneous resolution. We show that the associated variety of simple affine vertex algebras is contained in the closure of the Diximier sheet when a…
We investigate generalised global symmetries in 3d $\mathcal{N}=4$ orthosymplectic quiver gauge theories. Using the superconformal index, we identify a $D_8$ categorical symmetry web in a class of theories featuring $\mathfrak{so}(2N)…
In this paper, we introduce Schubert decompositions for quiver Grassmannians and investigate example classes of quiver Grassmannians with a Schubert decomposition into affine spaces. The main theorem puts the cells of a Schubert…