Related papers: $\hbar$-Riemann-Hilbert correspondence

We describe an $A_\infty$-quasi-equivalence of dg-categories between the first authors' $\mathcal{P}_{\mathcal{A}}$ ---the category of category of prefect $A^0$-modules with flat $\Z$-connection, corresponding to the de Rham dga…

We establish a Kobayashi-Hitchin correspondence between solutions of the extended Bogomolny equation with a Dirac type singularity and Hecke modifications of Higgs bundles. This correspondence was conjectured by Witten and plays an…

We leverage the results of the prequel in combination with a theorem of D. Orlov to yield some results in Hodge theory of derived categories of factorizations and derived categories of coherent sheaves on varieties. In particular, we…

This is a survey on our recent works which reveal new relationships among deformation quantization, geometric quantization, Berezin-Toeplitz quantization and BV quantization on K\"ahler manifolds.

The Dolbeault resolution of the sheaf of holomorphic vector fields $Lie$ on a complex manifold $M$ relates $Lie$ to a sheaf of differential graded Lie algebras, known as the Fr\"olicher-Nijenhuis algebra $g$. We establish - following B. L.…

We give an explicit combinatorial description of the deformation theory of the Abelian category of (quasi)coherent sheaves on any separated Noetherian scheme $X$ via the deformation theory of path algebras of quivers with relations, by…

We study the relationship between the equations of first order Lagrangian field theory on fiber bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. The…

We prove an analogue of the Kobayashi-Hitchin correspondence oncompact connected 3-folds that is fibered on orbifold Riemann surfaces and satisfy an integrability condition, which contains compact connected Sasakian 3-folds. We define…

This paper continues our study of the sheaf associated to K\"ahler differentials in the cdh-topology and its cousins, in positive characteristic, without assuming resolution of singularities. The picture for the sheaves themselves is now…

Kazhdan and Lusztig identified the affine Hecke algebra $\mathcal{H}$ with an equivariant $K$-group of the Steinberg variety, and applied this to prove the Deligne-Langlands conjecture, i.e., the local Langlands parametrization of…

The article is a contribution to the local theory of geometric Langlands correspondence. The main result is a categorification of the isomorphism between the (extended) affine Hecke algebra, thought of as an algebra of Iwahori bi-invariant…

Various algebraic structures have recently appeared in a parallel way in the framework of Hilbert schemes of points on a surface and respectively in the framework of equivariant K-theory [N1,Gr,S2,W], but direct connections are yet to be…

Motivated by the existence of bi-Hamiltonian classical systems and the correspondence principle, in this paper we analyze the problem of finding Hermitian scalar products which turn a given flow on a Hilbert space into a unitary one. We…

In this paper after recalling some essential tools concerning the theory of differential forms in the Cartan, Hodge and Clifford bundles over a Riemannian or Riemann-Cartan space or a Lorentzian or Riemann-Cartan spacetime we solve with…

In [arXiv:2109.13991], the author explained a relation between enhanced ind-sheaves and enhanced subanalytic sheaves. In this paper, we shall define C-constructability for enhanced subanalytic sheaves which was announced in…

The geometric Satake correspondence provides an equivalence of categories between the Satake category of spherical perverse sheaves on the affine Grassmannian and the category of representations of the dual group. In this note, we define a…

We study the images of tautological bundles on Hilbert schemes of points on surfaces and their wedge powers under the derived McKay correspondence. The main observation of the paper is that using a derived equivalence differing slightly…

We categorify the R-matrix isomorphism between tensor products of minuscule representations of U_q(sl(n)) by constructing an equivalence between the derived categories of coherent sheaves on the corresponding convolution products in the…

We show that the bicategory of proper correspondences is the Dwyer-Kan localisation of the category of C*-algebras at a certain class of *-homomorphisms.

We (re)consider how the Fukaya category of a Lefschetz fibration is related to that of the fibre. The distinguishing feature of the approach here is a more direct identification of the bimodule homomorphism involved.