59 citations · 223 across the 20 of their papers we have counts for
20 papers
Lagrangian correspondences of nonabelian Hodge type and shifted twistor structures
Jacob Kryczka, Yuuji Tanaka, Shing-Tung Yau
Classical nonabelian Hodge theory identifies Dolbeault and de Rham moduli spaces by providing a real-analytic isomorphism. In this paper, motivated by the Kapustin--Witten theory,…
A Polynomial Time Quantum Algorithm for Exponentially Large Scale Nonlinear Differential Equations via Hamiltonian Simulation
Yu Tanaka, Keisuke Fujii
Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientif…
The Blowup Formula for the Instanton Part of Vafa-Witten Invariants on Projective Surfaces
Nikolas Kuhn, Oliver Leigh, Yuuji Tanaka
We prove a blow-up formula for the generating series of virtual -genera for moduli spaces of sheaves on projective surfaces, which is related to a conjectured formula for topo…
A blowup formula for virtual enumerative invariants on projective surfaces
Nikolas Kuhn, Yuuji Tanaka
We apply virtual localization to the problem of finding blowup formulae for virtual sheaf-theoretic invariants on a smooth projective surface. This leads to a general procedure tha…
The Kapustin-Witten equations and nonabelian Hodge theory
Chih-Chung Liu, Steven Rayan, Yuuji Tanaka
Arising from a topological twist of super Yang-Mills theory are the Kapustin-Witten equations, a family of gauge-theoretic equations on a four-manifold parametriz…
Universal structures in -linear enumerative invariant theories
Jacob Gross, Dominic Joyce, Yuuji Tanaka
An enumerative invariant theory in Algebraic Geometry, Differential Geometry, or Representation Theory, is the study of invariants which 'count' -(semi)stable objects with f…
On orientations for gauge-theoretic moduli spaces
Dominic Joyce, Yuuji Tanaka, Markus Upmeier
Let be a compact manifold, a real elliptic operator on , a Lie group, a principal -bundle, and the infinite-dimensional moduli space of…
Vafa-Witten invariants for projective surfaces II: semistable case
Yuuji Tanaka, Richard P. Thomas
We propose a definition of Vafa-Witten invariants counting semistable Higgs pairs on a polarised surface. We use virtual localisation applied to Mochizuki/Joyce-Song pairs. For $K_…
Vafa-Witten invariants for projective surfaces I: stable case
Yuuji Tanaka, Richard P. Thomas
On a polarised surface, solutions of the Vafa-Witten equations correspond to certain polystable Higgs pairs. When stability and semistability coincide, the moduli space admits a sy…
On the singular sets of solutions to the Kapustin-Witten equations and the Vafa-Witten ones on compact Kähler surfaces
Yuuji Tanaka
This article finds a structure of singular sets on compact Kahler surfaces, which Taubes introduced in the studies of the asymptotic analysis of solutions to the Kapustin-Witten eq…
A perturbation and generic smoothness of the Vafa-Witten moduli spaces on closed symplectic four-manifolds
Yuuji Tanaka
We prove a Freed-Uhlenbeck style generic smoothness theorem for the moduli space of solutions to the Vafa--Witten equations on a closed symplectic four-manifold by using a method d…
Seiberg-Witten type equations on compact symplectic 6-manifolds
Yuuji Tanaka
In this article, we consider a gauge-theoretic equation on compact symplectic 6-manifolds, which forms an elliptic system after gauge fixing. This can be thought of as a higher-dim…
Stable sheaves with twisted sections and the Vafa-Witten equations on smooth projective surfaces
Yuuji Tanaka
This article describes a Hitchin-Kobayashi style correspondence for the Vafa-Witten equations on smooth projective surfaces. This is an equivalence between a suitable notion of sta…
Some boundedness properties of solutions to the Vafa-Witten equations on closed four-manifolds
Yuuji Tanaka
We consider a set of gauge-theoretic equations on closed oriented four-manifolds, which was introduced by Vafa and Witten. The equations involve a triple consisting of a connection…
A stability of vector bundles with twisted sections and the Donaldson-Thomas instantons on compact Kähler threefolds
Yuuji Tanaka
We consider a version of Hermitian-Einstein equation but perturbed by a Higgs field with a solution called a Donaldson-Thomas instanton on compact Kähler threefolds. The equation c…
A removal singularity theorem of the Donaldson-Thomas instantons on compact Kähler threefolds
Yuuji Tanaka
We consider a perturbed Hermitian-Einstein equation, which we call the Donaldson-Thomas equation, on compact Kähler threefolds. In arXiv:0805.2195, we analysed some analytic proper…
A construction of Spin(7)-instantons
Yuuji Tanaka
Joyce constructed examples of compact eight-manifolds with holonomy Spin(7), starting with a Calabi-Yau four-orbifold with isolated singular points of a special kind. That construc…
The Donaldson-Thomas instantons on compact Kahler threefolds and a convergence
Yuuji Tanaka
The contents of this article are now presented in the appendix of arXiv:0805.2195v2.
A weak compactness theorem of the Donaldson-Thomas instantons on compact Kähler threefolds
Yuuji Tanaka
In arXiv:0805.2192, we set up a gauge-theoretic equation on symplectic 6-manifolds, which is a version of the Hermitian-Einstein equation perturbed by Higgs fields, and call Donald…
On the moduli space of Donaldson-Thomas instantons
Yuuji Tanaka
In alignment with a programme by Donaldson and Thomas [DT], Thomas [Th] constructed a deformation invariant for smooth projective Calabi-Yau threefolds, which is now called the Don…