相关论文: Wall-crossings for Hassett descendant potentials

We resolve an open conjecture from algebraic geometry, which states that two generating functions for plane partition-like objects (the "box-counting" formulae for the Calabi-Yau topological vertices in Donaldson-Thomas theory and…

Using the connection between intersection theory on the Deligne-Mumford spaces and the edge scaling of the GUE matrix model (see math.CO/9903176, math.AG/0101147), we express the n-point functions for the intersection numbers as…

The goal of the paper is two-fold. At first, we attempt to give a survey of some recent applications of symmetric polynomials and divided differences to intersection theory. We discuss: polynomials universally supported on degeneracy loci;…

Let I and J be homogeneous ideals in a standard graded polynomial ring. We study upper bounds of the Hilbert function of the intersection of I and g(J), where g is a general change of coordinates. Our main result gives a generalization of…

In this paper we study the coefficients of the powers of an ordinary generating function and their properties. A new class of functions based on compositions of an integer $n$ is introduced and is termed composita. We present theorems about…

In a graph, the switching operation reverses adjacencies between a subset of vertices and the others. For a hereditary graph class $\mathcal{G}$, we are concerned with the maximum subclass and the minimum superclass of $\mathcal{G}$ that…

The Pixton class is a nonhomogeneous cohomology class on the moduli space of stable curves $\overline{\mathcal{M}}_{g,n}$, with nontrivial terms in degree $0,2,4,\ldots,2g$, whose top degree part coincides with the double ramification…

We show that there exists a simple generalization of Kazakov's multicritical one-matrix model, which interpolates between the various multicritical points of the model. The associated multicritical potential takes the form of a power series…

We construct a class of backgrounds with a warp factor and anti-de Sitter asymptotics, which are dual to boundary systems that have a ground state with a short-range two-point correlation function. The solutions of probe scalar fields on…

For a positive integer n and a subset S of [n-1], the descent polytope DP_S is the set of points x_1, ..., x_n in the n-dimensional unit cube [0,1]^n such that x_i >= x_{i+1} for i in S and x_i <= x_{i+1} otherwise. First, we express the…

We construct a Hermitian matrix model for the total descendant potential of a simple singularity of type D similar to the Kontsevich matrix model for the generating function of intersection numbers on the Deligne--Mumford moduli spaces…

This paper combines the post-Minkowskian expansion of general relativity with the language of intersection theory. Because of the nature of the soft limit inherent to the post-Minkowskian expansion, the intersection-based approach is of…

Starting from the moment sequences of classical orthogonal polynomials we derive the orthogonality purely algebraically. We consider also the moments of ($q=1$) classical orthogonal polynomials, and study those cases in which the…

We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble…

The weighted transition polynomial of a multimatroid is a generalization of the Tutte polynomial. By defining the activity of a skew class with respect to a basis in a multimatroid, we obtain an activities expansion for the weighted…

We construct a generalization of the theory of symmetric functions involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under the diagonal…

Original English Summary. - A systematic method of constructing potentials, for which the one-variable Schroedinger equation can be solved in terms of the hypergeometric (HGM) function, is presented. All the potentials, obtained by…

Gravitationally collapsed objects are known to be biased tracers of an underlying density contrast. Using symmetry arguments, generalised biasing schemes have recently been developed to relate the halo density contrast $\delta_h$ with the…

The decomposition into interaction subspaces is a hierarchical decomposition of the spaces of cylindrical functions of a finite product space, also called factor spaces. It is an important construction in graphical models and a standard way…

For a finite group $G$, let $\H_{g,G,\xi}$ be the stack of admissible $G$-covers $C\to D$ of stable curves with ramification data $\xi$, $g(C)=g$ and $g(D)=g'$. There are source and target morphisms $\phi\colon \H_{g,G,\xi}\to \M_{g,r}$ and…