Related papers: Quiver Grassmannians associated to nilpotent cycli…

Any moduli space of representations of a quiver (possibly with oriented cycles) has an embedding as a dense open subvariety into a moduli space of representations of a bipartite quiver having the same type of singularities. A connected…

This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class…

We give a construction of the moduli space of stable maps to the classifying stack B\mu_r of a cyclic group by a sequence of r-th root constructions on M_{0, n}. We prove a closed formula for the total Chern class of \mu_r-eigenspaces of…

For any acyclic quiver, we establish a family of structure isomorphisms for its cohomological Hall algebra (CoHA). The family is parameterized by partitions of the quiver into Dynkin subquivers. For each such partition, we write the domain…

In the classification theorems of Vinberg and Yakimova for commutative nilmanifolds, the relevant nilpotent groups have a very surprising analytic property. The manifolds are of the form $G/K = N \rtimes K/K$ where, in all but three cases,…

Let T be a compact torus and X a nice compact T-space (say a manifold or variety). We introduce a functor assigning to X a "GKM-sheaf" F_X over a "GKM-hypergraph" G_X. Under the condition that X is equivariantly formal, the ring of global…

We treat the topic of the closures of the nilpotent orbits of the Lie algebras of Exceptional groups through their descriptions as moduli spaces, in terms of Hilbert series and the highest weight generating functions for their…

Given the complement of a hyperplane arrangement, let $\Gamma$ be the closure of the graph of the map inverting each of its defining linear forms. The characteristic polynomial manifests itself in the Hilbert series of $\Gamma$ in two…

We construct natural extensions of the Kudla--Millson generating series of cohomology classes of special cycles in compactified unitary Shimura varieties of signature $(n+1,1)$ and prove that they are holomorphic Hermitian modular forms.…

Let $Y$ be a CW-complex with a single 0-cell, $K$ its Kan group, a model for the loop space of $Y$, and let $G$ be a compact, connected Lie group. We give an explicit finite dimensional construction of generators of the equivariant…

In this article we describe relations of the topology of closed 1-forms to the group theoretic invariants of Bieri-Neumann-Strebel-Renz. Starting with a survey, we extend these Sigma invariants to finite CW- complexes and show that many…

We calculate the deformed and non-deformed cohomological Hall algebra (CoHA) of the preprojective algebra for the case of cyclic quivers by studying the Kontsevich-Soibelman CoHA and using tools from cohomological Donaldson-Thomas theory.…

This paper presents analogous results of Hua [7][8] on numbers of representations of quivers over finite fields which respect nilpotent relations under certain assumptions. A closed formula which counts isomorphism classes of absolutely…

We introduce the notion of equivariant basic cohomology for singular Riemannian foliations with transverse infinitesimal actions, and prove some elementary properties such as its invariance under homotopies. For the particular case of…

Under Poincar\'e duality, a smooth map of compact oriented manifolds induces a pushforward map in cohomology, called the "Gysin map." It plays an important role in enumerative geometry. Using the equivariant localization formula, the author…

Given a quiver, we consider its cohomological Hall algebra (CoHA) as well as CoHA modules built of cohomology groups of non-commutative Hilbert schemes. We investigate cell decompositions of non-commutative Hilbert schemes and the…

We investigate the structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group. We work with square integrable representations, and we show that they are those for which we can construct an…

We combine recent developments on weakly symmetric pseudo--riemannian nilmanifolds with with geometric methods for construction of unitary representations on square integrable Dolbeault cohomology spaces. This runs parallel to construction…

We consider two types of nilpotent invariants associated to smooth representations, namely generalized Whittaker models, and associated characters (in the case of a real reductive group). We survey some recent results on the behavior of…

We study a class of algebras with non-Lie commutation relations whose symplectic leaves are surfaces of revolution: a cylinder or a torus. Over each of such surfaces we introduce a family of complex structures and Hilbert spaces of…