Related papers: Equidistribution of Fekete points on complex manif…

We consider smooth, complete Riemannian manifolds which are exponentially locally doubling. Under a uniform Ricci curvature bound and a uniform lower bound on injectivity radius, we prove a Kato square root estimate for certain coercive…

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 prove an equidistribution theorem a la Bader-Muchnik for operator-valued measures associated with boundary representations in the context of discrete groups of isometries of CAT(-1) spaces thanks to an equidistribution theorem of T.…

This is an expanded version of [arXiv:1107.4836v1 [math.DS]]. Using techniques from [Chapter XI, The Selberg Trace Formula, in Eigenvalues in Riemannian Geometry, by Isaac Chavel], in which a differential-geometrically intrinsic treatment…

We prove effective equidistribution, with polynomial rate, for large closed orbits of semisimple groups on homogeneous spaces, under certain technical restrictions (notably, the acting group should have finite centralizer in the ambient…

It has recently been observed that, in contrast to the classical case, holomorphic structures on line bundles over the quantum projective line are not uniquely determined by degree. We formulate a fixed-point-theoretic framework for the…

Nevanlinna's unicity theorems have always held an important position in value distribution theory. The main purpose of this paper is to generalize the classical Nevanlinna's unicity theorems to non-compact complete Kahler manifolds with…

The purpose of this paper is to provide equations to model the evolution of effective diffusion over a Riemannian fiber bundle (under the hypothesis of infinite diffusion rate along compact fibers). These equations are obtained by…

We study the Fourier transform for compactly supported distributional sections of complex homogeneous vector bundles on symmetric spaces of non-compact type $X = G/K$. We prove a characterisation of their range. In fact, from Delorme's…

We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem by using intersection…

We construct an injective map from the set of holomorphic equivalence classes of neighborhoods $M$ of a compact complex manifold $C$ into ${\mathbb C}^m$ for some $m<\infty$ when $(TM)|_C$ is fixed and the normal bundle of $C$ in $M$ is…

We prove an effective equidistribution theorem for orbits of certain unipotent subgroups in arithmetic quotients of perfect Lie groups with a polynomial error term. Even for semisimple quotients, our result provides the first infinite…

We prove a homological characterization of $Q$-manifolds bundles over $C$-spaces. This provides a partial answer to Question QM22 from \cite{w}.

We introduce a natural way of associating oriented closed geodesics on the modular curve to elements of $(\mathbb{Z}/q\mathbb{Z})^\times$ and prove that the corresponding packets associated to sufficiently large subgroups equidistribute in…

We study the complex-analytic geometry of semi-positive holomorphic line bundles on compact K\"ahler manifolds. In one of our main results, for a $\mathbb{Q}$-effective line bundle satisfying a natural torsion-type assumption, we show the…

Using the notion of Levi form of a smooth distribution, we discuss the local and the global problem of existence of one horizontal section of a smooth vector bundle endowed with a horizontal distribution. The analysis will lead to the…

Results in the preliminary version have been strengthed. In addition, Batyrev's conjectural formula for quantum cohomology of projective bundles associated to direct sum of line bundles over $\Pee^n$ is partially verified.

Using a global version of the equivariant Chern character, we describe the complexified twisted equivariant K-theory of a space with a compact Lie group action in terms of fixed-point data. We apply this to the case of a compact Lie group…

We prove a structure theorem for compact aspherical Lorentz manifolds with abundant local symmetry. If M is a compact, aspherical, real-analytic, complete Lorentz manifold such that the isometry group of the universal cover has semisimple…

If a convex body $K \subset \mathbb{R}^n$ is covered by the union of convex bodies $C_1, \ldots, C_N$, multiple subadditivity questions can be asked. Two classical results regard the subadditivity of the width (the smallest distance between…