Related papers: The asymptotic shape theorem for generalized first…

We present some new Stokes' type theorems on complete non-compact manifolds that extend, in different directions, previous work by Gaffney and Karp and also the so called Kelvin-Nevanlinna-Royden criterion for (p-)parabolicity. Applications…

A beautiful theorem of Zeckendorf states that every positive integer has a unique decomposition as a sum of non-adjacent Fibonacci numbers. Such decompositions exist more generally, and much is known about them. First, for any positive…

We prove a generalized mirror conjecture for non-negative complete intersections in symplectic toric manifolds. Namely, we express solutions of the PDE system describing quantum cohomology of such a manifold in terms of suitable…

The main result of this paper is that two large collections of ergodic measure preserving systems, the Odometer Based and the Circular Systems have the same global structure with respect to joinings. The classes are canonically isomorphic…

We prove a prime geodesic theorem for compact quotients of affine buildings and apply it to get class number asymptotics for global fields of positive characteristic.

Recently, many results have been established drawing a parallel between Bernoulli percolation and models given by levels of smooth Gaussian fields with unbounded, strongly decaying correlation. In a previous work with D. Gayet , we started…

First-passage percolation is a random growth model which has a metric structure. An infinite geodesic is an infinite sequence whose all sub-sequences are shortest paths. One of the important quantity is the number of infinite geodesics…

We prove mean and pointwise ergodic theorems for general families of averages on a semisimple algebraic (or S-algebraic) group G, together with an explicit rate of convergence when the action has a spectral gap. Given any lattice in G, we…

The classical construction of the symplectic structure on the space of geodesic trajectories via Hamiltonian reduction fails in the pseudo-Riemannian setting due to a dimensional mismatch created by the null geodesics. This paper proposes a…

We introduce the group-compact coarse structure on a Hausdorff topological group in the context of coarse structures on an abstract group which are compatible with the group operations. We develop asymptotic dimension theory for the…

We prove asymptotic 0-1 Laws satisfied by diagrams of unimodal sequences of positive integers. These diagrams consist of columns of squares in the plane, and the upper boundary is called the shape. For various types, we show that, as the…

Let E be a transitive Courant algebroid with scalar product of neutral signature. A generalized almost complex structure \mathcal J on E is a skew-symmetric smooth field of endomorphisms of E which squares to minus the identity. We say that…

In this paper we prove a general structure theorem for relatively hyperbolic groups (with arbitrary peripheral subgroups) acting naive convex co-compactly on properly convex domains in real projective space. We also establish a…

Motivated by the shape invariance condition in supersymmetric quantum mechanics, we develop an algebraic framework for shape invariant Hamiltonians with a general change of parameters. This approach involves nonlinear generalizations of Lie…

We introduce and study a class of abstract continuous action minimization problems that generalize continuous first and last passage percolation. In this class of models a limit shape exists. Our main result provides a framework under which…

The main goal of the paper is to prove convergence in norm and pointwise almost everywhere on $L^p$, $p\in (1,\infty)$, for certain multiparameter polynomial ergodic averages in the spirit of Dunford and Zygmund for continuous flows. We…

Generalizations of Redfield's master theorem and superposition theorem are proved by using decomposition of the tensor product of several induced monomial representations of the symmetric group $S_d$ into transitive constituents. As direct…

We provide, among other things: (i) a Bousfield--Kan formula for colimits in $\infty$-categories (generalizing the 1-categorical formula for a colimit as a coequalizer of maps between coproducts); (ii) $\infty$-categorical generalizations…

We derive a generalized Stokes' theorem, valid in any dimension and for arbitrary loops, even if self intersecting or knotted. The generalized theorem does not involve an auxiliary surface, but inherits a higher rank gauge symmetry from the…

We construct classes of ${\cal N}=1$ superconformal theories elements of which are labeled by punctured Riemann surfaces. Degenerations of the surfaces correspond, in some cases, to weak coupling limits. Different classes are labeled by two…