Related papers: Rigidity of differential operators and Chern numbe…

In this paper we investigate the $L^p$-boundedness of certain classes of periodic pseudo-differential operators. The operators considered arise from the study of symbols on $\mathbb{T}^n\times\mathbb{Z}^n$ with limited regularity.

In this paper we give explicit formulas of differential characteristic classes of principal $G$-bundles with connections and prove their expected properties. In particular, we obtain explicit formulas for differential Chern classes,…

In this paper the authors study quotients of the product of elliptic curves by a rigid diagonal action of a finite group $G$. It is shown that only for $G = \operatorname{He(3)}, \mathbb Z_3^2$, and only for dimension $\geq 4$ such an…

We prove some uniform and pointwise gradient estimates for the Dirichlet and the Neumann evolution operators $G_{\mathcal{D}}(t,s)$ and $G_{\mathcal{N}}(t,s)$ associated with a class of nonautonomous elliptic operators $\A(t)$ with…

Let ${\mathfrak o}$ be a complete discrete valuation ring of mixed characteristic $(0,p)$ and ${\mathfrak X}_0$ a smooth formal scheme over the formal spectrum of ${\mathfrak o}$. Given an admissible formal blow-up ${\mathfrak X}$ of…

Progress along the line of a previous article are reported. One main point is to include chiral operators with fractional quantum group spins (fourth or sixth of integers) which are needed to achieve modular invariance. We extend the study…

This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin…

We study the contraction semigroups of elliptic quadratic differential operators. Elliptic quadratic differential operators are the non-selfadjoint operators defined in the Weyl quantization by complex-valued elliptic quadratic symbols. We…

In this paper we develop the generalised Schur theory offered in the recent paper by the second author in dimension one case, and apply it to obtain a new explicit parametrisation of torsion free rank one sheaves on projective irreducible…

We say that a system of differential equations d^2x(t)/dt^2=Adx(t)/dt+Bx(t)+Cu(t), in which A and B are m-by-m complex matrices and C is an m-by-n complex matrix, is rigid if it can be reduced by substitutions x(t)=Sy(t),…

The present paper establishes a certain duality between the Dirichlet and Regularity problems for elliptic operators with $t$-independent complex bounded measurable coefficients ($t$ being the transversal direction to the boundary). To be…

We consider singular integral operators and maximal singular integral operators with rough kernels on homogeneous groups. We prove certain estimates for the operators that imply $L^p$ boundedness of them by an extrapolation argument under a…

In this expository paper we answer two fundamental questions concerning discrete magnetic Schr\"odinger operator associated with weighted graphs. We discuss when formal expressions of such operators give rise to self-adjoint operators,…

Chiral differential operators (CDOs) are closely related to string geometry and the quantum theory of two-dimensional sigma models. This paper investigates two topics about CDOs on smooth manifolds. In the first half, we study how a Lie…

We consider one-dimensional inhomogeneous parabolic equations with higher-order elliptic differential operators subject to periodic boundary conditions. In our main result we show that the property of continuous maximal regularity is…

In this paper, we obtain new Carleman estimates for a class of variable coefficient degenerate elliptic operators whose constant coefficient model at one point is the so called Baouendi-Grushin operator. This generalizes the results…

Motivic integration and MacPherson's transformation are combined in this paper to construct a theory of "stringy" Chern classes for singular varieties. These classes enjoy strong birational invariance properties, and their definition…

In our previous works, we introduced, for each (super)manifold, a commutative algebra of densities. It is endowed with a natural invariant scalar product. In this paper, we study geometry of differential operators of second order on this…

Let C be a triangulated category with a Serre functor S and X a non-zero contravariantly finite rigid subcategory of C. Then X is cluster tilting if and only if the quotient category C/X is abelian and S(X)=X[2]. As an application, this…

Let A be a commutative ring, B a commutative A-algebra and M a complex of B-modules. We begin by constructing the square Sq_{B/A} M, which is also a complex of B-modules. The squaring operation is a quadratic functor, and its construction…