Related papers: A quantized Riemann-Hilbert problem in Donaldson-T…
We study a class of Riemann-Hilbert problems arising naturally in Donaldson-Thomas theory. In certain special cases we show that these problems have unique solutions which can be written explicitly as products of gamma functions. We briefly…
We study the quantum Riemann-Hilbert problems determined by the refined Donaldson-Thomas theory on the resolved conifold. Using the solutions to classical Riemann-Hilbert problems by Beidgeland, we give explicit solutions in terms of…
We study the Riemann-Hilbert problems associated to the Donaldson-Thomas theory of the resolved conifold. We give explicit solutions in terms of the Barnes double and triple sine functions. We show that the corresponding tau function is a…
The local Donaldson-Thomas theory of curves is solved by localization and degeneration methods. The results complete a triangle of equivalences relating Gromov-Witten theory, Donaldson-Thomas theory, and the quantum cohomology of the…
We study the Riemann-Hilbert problem attached to an uncoupled BPS structure proposed by Bridgeland in "Riemann-Hilbert problems from Donaldson-Thomas theory". We show that it has "essentially" unique meromorphic solutions given by a product…
This paper is a continuation of author's previous work arXiv:1911.07949, where we defined Donaldson-Thomas invariants of quantum Fermat threefolds. In this paper, we study the generic quantum Fermat threefold. We give explicit local models…
The Hamiltonian approach to the theory of dual isomonodromic deformations is developed within the framework of rational classical R-matrix structures on loop algebras. Particular solutions to the isomonodromic deformation equations…
We consider a perturbed Hermitian-Einstein equation, which we call the Donaldson-Thomas equation, on compact K\"ahler threefolds. In arXiv:0805.2195, we analysed some analytic properties of solutions to the equation, in particular, we…
A new concept of meromorphic $\Sigma$-factorization, for H\"{o}lder continuous functions defined on a contour $\Gamma$ that is the pullback of $\dot{\mathbb{R}}$ (or the unit circle) in a Riemann surface $\Sigma$ of genus 1, is introduced…
We perform a resurgence analysis of the perturbative partition functions of orientifolded conifolds and obtain the full nonperturbative partition functions in terms of multiple sine functions. We derive the unoriented Donaldson--Thomas…
We revisit the Riemann-Hilbert problem determined by Donaldson-Thomas invariants for the resolved conifold and for other small crepant resolutions. While this problem can be recast as a system of TBA-type equations in the conformal limit,…
Integrals of characteristic classes of tautological sheaves on the Hilbert scheme of points on a surface frequently arise in enumerative problems. We use the K-theoretic Donaldson-Thomas theory of certain toric Calabi-Yau threefolds to…
In recent years, a version of enumerative geometry over arbitrary fields has been developed and studied by Kass-Wickelgren, Levine, and others, in which the counts obtained are not integers but quadratic forms. Aiming to understand the…
We apply a perturbative technique to study classical Liouville theory on the torus. After mapping the problem on the cut-plane we give the perturbative treatment for a weak source. When the torus reduces to the square the problem is exactly…
We solve the $K$-theoretically refined Donaldson-Thomas theory of local curves. Our results avoid degeneration techniques, but rather exploit direct localisation methods to reduce the refined Donaldson-Thomas partition function to the…
This paper concerns the cohomological aspects of Donaldson-Thomas theory for Jacobi algebras and the associated cohomological Hall algebra, introduced by Kontsevich and Soibelman. We prove the Hodge-theoretic categorification of the…
We study the relative Donaldson-Thomas theory of A_n x P^1, where A_n is the surface resolution of a type A_n singularity. The action of divisor operators in the theory is expressed in terms of operators of the affine algebra \hat{gl}(n+1)…
We discuss here basic properties of the quantum differential equation of the Hilbert scheme of points in the plane. Our emphasis is on intertwining operators (which shift equivariant parameters) and their applications. In particular, we…
The theory of holomorphic functions of several complex variables is applied in proving a multidimensional variant of a theorem involving an exponential boundedness criterion for the classical moment problem. A theorem of Petersen concerning…
We begin the study of categorifications of Donaldson-Thomas invariants associated with Hilbert schemes of points on the three-dimensional affine space, which we call DT categories. The DT category is defined to be the category of matrix…