42 citations · 322 across the 32 of their papers we have counts for
31 papers · 1 filter
Quasi-modularity of -traces and integrals over Hilbert schemes
Killian Hong-Minh, Sergey Mozgovoy
We study quasi-modularity of normalized -traces on bosonic Fock spaces associated with finite-dimensional quadratic spaces and superspaces. For a natural class of operators obta…
Wall-crossing structures on surfaces
Sergey Mozgovoy
Families of Bridgeland stability conditions induce families of stability data, wall-crossing structures and scattering diagrams on the motivic Hall algebra. These structures can be…
Tautological bases of CoHA modules
Hans Franzen, Sergey Mozgovoy
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 decompo…
DT invariants from vertex algebras
Vladimir Dotsenko, Sergey Mozgovoy
We obtain a new interpretation of the cohomological Hall algebra of a symmetric quiver in the context of the theory of vertex algebras. Namely, we show that the…
Donaldson-Thomas invariants for 3-Calabi-Yau varieties of dihedral quotient type
Sergey Mozgovoy, Markus Reineke
We compute motivic Donaldson-Thomas invariants for crepant resolutions of quotients of affine three-space by even dihedral groups in terms of an affine type D root system, using do…
Operadic approach to wall-crossing
Sergey Mozgovoy
Wall-crossing phenomena are ubiquitous in many problems of algebraic geometry and theoretical physics. Various ways to encode the relevant information and the need to track the cha…
Motivic classes of Quot-schemes on surfaces
Sergey Mozgovoy
Given a locally free coherent sheaf on a smooth algebraic surface, we consider the Quot-scheme parametrizing zero-dimensional quotients of the sheaf and find the corresponding moti…
Translation quiver varieties
Sergey Mozgovoy
We introduce a framework of translation quiver varieties which includes Nakajima quiver varieties as well as their graded and cyclic versions. An important feature of translation q…
Commuting matrices and volumes of linear stacks
Sergey Mozgovoy
A conjecture by Higman asserts that the number of conjugacy classes in the unipotent group of upper triangular matrices over a finite field depends polynomially on the number of el…
Counting twisted Higgs bundles
Sergey Mozgovoy, Ronan O'Gorman
We count invariants of the moduli spaces of twisted Higgs bundles on a smooth projective curve.
Counting Higgs bundles and type A quiver bundles
Sergey Mozgovoy, Olivier Schiffmann
We prove a closed formula counting semistable twisted (or meromorphic) Higgs bundles of fixed rank and degree over a smooth projective curve of genus g, defined over a finite field…
Intersection cohomology of moduli spaces of sheaves on surfaces
Jan Manschot, Sergey Mozgovoy
We study intersection cohomology of moduli spaces of semistable vector bundles on a complex algebraic surface. Our main result relates intersection Poincare polynomials of the modu…
Higgs bundles over P^1 and quiver representations
Sergey Mozgovoy
In this note we prove a new explicit formula for the invariants of moduli spaces of twisted Higgs bundles over P^1 and we relate these invariants to the invariants of moduli spaces…
Intersection cohomology of moduli spaces of vector bundles over curves
Sergey Mozgovoy, Markus Reineke
We compute the intersection cohomology of the moduli spaces of semistable vector bundles having rank and degree over a curve. We do this by relating the Hodge-Del…
Counting Higgs bundles
Sergey Mozgovoy, Olivier Schiffmann
We prove a closed formula counting semistable twisted Higgs bundles of fixed rank and degree over a smooth projective curve defined over a finite field. We also prove a formula for…
Arithmetic of character varieties of free groups
Sergey Mozgovoy, Markus Reineke
Via counting over finite fields, we derive explicit formulas for the E-polynomials and Euler characteristics of GL(d)- and PGL(d)-character varieties of free groups. We prove a pos…
Moduli spaces of stable pairs and non-abelian zeta functions of curves via wall-crossing
Sergey Mozgovoy, Markus Reineke
In this paper we study and relate the non-abelian zeta functions introduced by Weng and invariants of the moduli spaces of arbitrary rank stable pairs over curves. We prove a wall-…
Invariants of moduli spaces of stable sheaves on ruled surfaces
Sergey Mozgovoy
We compute Betti numbers of the moduli spaces of arbitrary rank stable sheaves on ruled surfaces. Our result generalizes the formula of Goettsche for rank one sheaves and the formu…
Abelian quiver invariants and marginal wall-crossing
Sergey Mozgovoy, Markus Reineke
We prove the equivalence of (a slightly modified version of) the wall-crossing formula of Manschot, Pioline and Sen and the wall-crossing formula of Kontsevich and Soibelman. The f…
Motivic Donaldson-Thomas invariants and McKay correspondence
Sergey Mozgovoy
Let be a finite group. We compute motivic Pandharipande-Thomas and Donaldson-Thomas invariants of the crepant resolution of …
Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex
Andrew Morrison, Sergey Mozgovoy, Kentaro Nagao +1
We compute the motivic Donaldson-Thomas theory of the resolved conifold, in all chambers of the space of stability conditions of the corresponding quiver. The answer is a product f…
Solutions of the motivic ADHM recursion formula
Sergey Mozgovoy
We give an explicit solution of the ADHM recursion formula conjectured by Chuang, Diaconescu, and Pan. This solution is closely related to the formula for the Hodge polynomials of…
Wall-crossing formulas for framed objects
Sergey Mozgovoy
We prove wall-crossing formulas for the motivic invariants of the moduli spaces of framed objects in the ind-constructible abelian categories. Developed techniques are applied in t…
Motivic Donaldson-Thomas invariants and Kac conjecture
Sergey Mozgovoy
We derive some combinatorial consequences from the positivity of Donaldson-Thomas invariants for symmetric quivers conjectured by Kontsevich and Soibelman and proved recently by Ef…