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In graph theory there are intimate connections between the expansion properties of a graph and the spectrum of its Laplacian. In this paper we define a notion of combinatorial expansion for simplicial complexes of general dimension, and…
We construct a functor that associates to any dg cooperad of dg commutative algebras (satisfying some conditions) an augmented commutative algebra. When applied to the cohomology operad of Francis Brown's moduli spaces it produces an…
The analytic contribution to the low energy expansion of Type II string amplitudes at genus-one is a power series in space-time derivatives with coefficients that are determined by integrals of modular functions over the complex structure…
We survey three settings in which dimensions of intersection cohomology groups of algebraic varieties provide deep combinatorial and representation-theoretic information, and computations of the groups themselves have been made using…
The general idea of this paper is to start from a classical integrable (partial differential) equation which arises as a compatibility condition for a matrix linear differential problem. For definitiveness' sake, a generalised sinh-Gordon…
We introduce families of decorations of a same topological space, as well as a family of sheaves over such decorated spaces. Making those families a directed system leads to the concept of emerald over a space. For the configuration space…
A group-theoretical structure in a perturbative expansion of the Wilson loops in the 3d Chern-Simons theory with $SU(N)$ gauge group is studied in symmetric approach. A special basis in the center of the universal enveloping algebra…
In this paper, convergence results in a multivariate setting have been proved for a family of neural network operators of the max-product type. In particular, the coefficients expressed by Kantorovich type means allow to treat the theory in…
A strong-coupling expansion for models of correlated electrons in any dimension is presented. The method is applied to the Hubbard model in $d$ dimensions and compared with numerical results in $d=1$. Third order expansion of the Green…
We prove the structure theorem of the intersection complexes of toric varieties in the category of mixed Hodge modules. This theorem is due to Bernstein, Khovanskii and MacPherson for the underlying complexes with rational coefficients. As…
We study the reduced density matrix of the $\mathfrak{sl}_3$-invariant fundamental exchange model by means of a novel reduced quantum Knizhnik-Zamolodchikov equation. This gives us insight into the algebraic structure and explicit results…
Our main aim is to investigate the approximation properties for the summation integral type operators in a statistical sense. In this regard, we prove the statistical convergence theorem using well known Korovkin theorem and the degree of…
We introduce and study a family of integral operators in the Kantorovich sense for functions acting on locally compact topological groups. We obtain convergence results for the above operators with respect to the pointwise and uniform…
We investigate a class of models in 1+1 dimensions with four fermion interaction term. At each order of the perturbation expansion, the models are ultraviolet finite and Lorentz non-invariant. We show that for certain privileged values of…
We analyze a new family of weighted double Hurwitz numbers that was introduced as a notable example in the context of the $x-y$ duality for logarithmic topological recursion. We use this family to systematically demonstrate, refine and…
We propose an advanced Chebyshev expansion method for the numerical calculation of linear response functions at finite temperature. Its high stability and the small required resources allow for a comprehensive study of the optical…
We show that introducing a periodic time coordinate in the models of Penner-Kontsevich type generalizes the corresponding constructions to the case of the moduli space ${\cal S}_{gn}^k$ of curves $C$ with homology chains $\gamma\in…
For any (possibly singular) hyperelliptic curve, we give the definition of a hyperelliptic refined spectral curve and the hyperelliptic refined topological recursion, generalising the formulation for a special class of genus-zero curves by…
We provide a general method for computing rational Chow rings of moduli of smooth complete intersections. We specialize this result in different ways: to compute the integral Picard group of the associated stack ; to obtain an explicit…
We analyze the static and dynamical properties of a one-dimensional topological lattice, the fermionic Su-Schrieffer-Heeger model, in the presence of on-site interactions. Based on a study of charge and spin correlation functions, we…