Related papers: $\delta$-Forms on Lubin--Tate Space

We form a generating series of regularized volumes of intersections of special cycles on a non-compact unitary Shimura variety with a fixed base change cycle. We show that it is a Hilbert modular form by identifying it with a theta…

In nature, barchan dunes typically exist as members of larger fields that display striking, enigmatic structures that cannot be readily explained by examining the dynamics at the scale of single dunes, or by appealing to patterns in…

Here we obtain bounds on the spectrum of that operator whose inverse, when it exists, gives the Green's function. We consider the wide of physical problems that can be cast in a form where a constitutive equation ${\bf J}({\bf x})={\bf…

Starting from a very general trace-form entropy, we introduce a pair of algebraic structures endowed by a generalized sum and a generalized product. These algebras form, respectively, two Abelian fields in the realm of the complex numbers…

Let $K$ be a complete, algebraically closed non-archimedean field with ring of integers $K^\circ$ and let $X$ be a $K$-variety. We associate to the data of a strictly semistable $K^\circ$-model $\mathscr X$ of $X$ plus a suitable horizontal…

This paper provides an overview of recent progress on the interplay between tropical geometry and non-archimedean analytic geometry in the sense of Berkovich. After briefly discussing results by Baker, Payne and Rabinoff in the case of…

The theta correspondence has been an important tool in studying cycles in locally symmetric spaces of orthogonal type. We generalize the Kudla-Millson relation between intersection numbers of cycles and Fourier coefficients of Siegel…

We give a complete theta expression of a pair of Hermitian modular forms as an inverse period mapping of lattice polarized $K3$ surfaces. Our result gives a non-trivial relation among moduli of $K3$ surfaces, theta functions and the finite…

Deformation theory for 2-dimensional dynamical triangulations with N vertices is discussed by exploiting the geometry of the moduli space of Euclidean polygons. Such an analysis provides an explicit connection among Regge surfaces,…

After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…

We prove a general finiteness statement for the ordered abelian group of tropical functions on skeleta in Berkovich analytifications of algebraic varieties. Our approach consists in working in the framework of stable completions of…

Let $F_g(t)$ be the generating function of intersection numbers on the moduli spaces $\bar{\mathcal{M}}_{g,n}$ of complex curves of genus $g$. As by-product of a complete solution of all non-planar correlation functions of the renormalised…

We derive some explicit expressions for correlators on Grassmannian G_r(C^n) as well as on the moduli space of holomorphic maps, of a fixed degree d, from sphere into the Grassmannian. Correlators obtained on the Grassmannain are a first…

We construct a combinatorial moduli space closely related to the KSV-compactification of the moduli space of bordered marked Riemann surfaces. The open part arises from symmetric metric ribbon graphs. The compactification is obtained by…

The Coleman power series defined on a Lubin-Tate tower of extensions over $K$ are compatible with respect to two formal group laws: the multiplicative formal group law and some Lubin-Tate formal group law defined over $\mathcal{O}_K$. We…

We study $t$-intersecting and $t$-cross-intersecting families of $k$-dimensional subspaces in finite vector spaces of dimension $n$. We show that all large $t$-intersecting families admit a governing low-dimensional structure for $n \ge…

Recently, the equivalence between the \delta N and covariant formalisms has been shown (Suyama et al. 2012), but they essentially assumed Einstein gravity in their proof. They showed that the evolution equation of the curvature covector in…

In [1] the authors showed some basic properties of a pre-order that arose in combinatorial number theory, namely the finite embeddability between sets of natural numbers, and they presented its generalization to ultrafilters, which is…

We define the tropical moduli space of covers of a tropical line in the plane as weighted abstract polyhedral complex, and the tropical branch map recording the images of the simple ramifications. Our main result is the invariance of the…

A resolution of the intersection of a finite number of subgroups of an abelian group by means of their sums is constructed, provided the lattice generated by these subgroups is distributive. This is used for detecting singularities of…