相关论文: An effective Deligne's equidistribution theorem

We extend the famous Erd\H{o}s-Szekeres theorem to $k$-flats in ${\mathbb{R}^d}$

We prove a Lichnerowicz type vanishing theorem for non-compact spin manifolds admiting proper cocompact actions. This extends a previous result of Ziran Liu who proves it for the case where the acting group is unimodular.

We introduce abstract net spaces on directed sets and prove their embedding and interpolation properties. Typical examples of interest are lattices of irreducible unitary representations of compact Lie groups and of class I representations…

We consider twisted equivariant K--theory for actions of a compact Lie group $G$ on a space $X$ where all the isotropy subgroups are connected and of maximal rank. We show that the associated rational spectral sequence \`a la Segal has a…

The aim of the present paper is to provide a comprehensive introduction to some algebraic and geometric aspects of real representations of compact Lie groups, as well as some results concerning isotropy strata and restriction of invariants.

We present a quantitative version of Bilu's theorem on the limit distribution of Galois orbits of sequences of points of small height in the $N$-dimensional algebraic torus. Our result gives, for a given point, an explicit bound for the…

We prove a Freiman-type theorem for locally compact abelian groups. If A is a subset of a locally compact abelian group with Haar measure m and m(nA) < n^dm(A) for all n>d log d then we describe A in a way which is tight up to logarithmic…

Hardy's type uncertainty principle on connected nilpotent Lie groups for the Fourier transform is proved. An analogue of Hardy's theorem for Gabor transform has been established for connected and simply connected nilpotent Lie groups.…

We show that the description of Deligne--Beilinson cohomology is improved by using log Hodge theory. We consider the log relative version of it, and also present a fundamental conjecture in log Hodge theory.

In this short note we give a proof of the refined version of the uniform invariant approximation property for compact (non-commutative) groups following the Bourgain's approach.

We upgrade Howard's divisibility towards Perrin-Riou's Heegner point main conjecture to the predicted equality. Contrary to previous works in this direction, our main result allows for the classical Heegner hypothesis and non-squarefree…

Let G/H be a reductive symmetric space and K a maximal compact subgroup of G. We study Fourier transforms of compactly supported K-finite distributions on G/H and characterize the image of the space of such distributions.

We prove a uniform effective density theorem as well as an effective counting result for a generic system comprising a polynomial with a mild homogeneous condition and several linear forms using Roger's second moment formula for the Siegel…

We determine the rational divisor class group of the moduli spaces of smooth pointed hyperelliptic curves and of their Deligne-Mumford compactification, over the field of complex numbers.

This note presents some equalities in law for $Z_N:=\det(\Id-G)$, where $G$ is an element of a subgroup of the set of unitary matrices of size $N$, endowed with its unique probability Haar measure. Indeed, under some general conditions,…

We discuss a very general Kirillov Theory for the representations of certain nilpotent groups which gives a combined view an many known examples from the literature.

We study the dynamics of $SL_{2}(\mathbb{R})$ on the stratum of translation surfaces $\mathcal{H}(2)$. Especially, we obtain effective density theorems on $\mathcal{H}(2)$ for orbits of the upper triangular subgroup $P$ of…

We use Reznick's Theorem for positive homogeneous polynomials to prove an elliptic regularity result for representations of enveloping algebras of Lie algebras. This allows us to relax a technical condition for a sum of squares…

In this paper, we present a novel proof of the uniform Bogomolov conjecture for algebraic tori. To do this, we introduce a definition of non-degenerate subvarieties applicable to a family of algebraic tori and establish an equidistribution…

We consider isometric actions of lattices in semisimple algebraic groups on (possibly non-compact) homogeneous spaces with (possibly infinite) invariant Radon measure. We assume that the action has a dense orbit, and demonstrate two novel…