Related papers: Topological expansion in the cubic random matrix m…

We use the Riemann-Hilbert approach, together with string and Toda equations, to study the topological expansion in the quartic random matrix model. The coefficients of the topological expansion are generating functions for the numbers…

In this article, we compute the topological expansion of all possible mixed-traces in a hermitian two matrix model. In other words we give a recipe to compute the number of discrete surfaces of given genus, carrying an Ising model, and with…

We use the explicit relation between genus filtrated $s$-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich--Penner matrix model (KPMM), which is the generating function for volumes of discretized…

We continue the investigation of the connection between the genus expansion of matrix models and the $\hbar$ expansion of integrable hierarchies started in arXiv:2008.06416. In this paper, we focus on the $B$KP hierarchy, which corresponds…

We construct {\it Topological Elliptic Genera}, homotopy-theoretic refinements of the elliptic genera for $SU$-manifolds and variants including the Witten-Landweber-Ochanine genus. The codomains are genuinely $G$-equivariant Topological…

We prove the topological expansion for the cubic log-gas partition function \[ Z_N(t)= \int_\Gamma\cdots\int_\Gamma\prod_{1\leq j<k\leq N}(z_j-z_k)^2 \prod_{k=1}^Ne^{-N\left(-\frac{z^3}{3}+tz\right)}\mathrm dz_1\cdots \mathrm dz_N, \] where…

We use a combinatorial interpretation of the coefficients of zonal Kerov polynomials as a number of unoriented maps to derive an explicit formula for the coefficients in genus one.

We quantify the topological expansion properties of bounded degree simplicial complexes in terms of a family of sublinear functions, in analogy with the separation profile of Benjamini-Schramm-Tim\'ar for classical expansion of bounded…

We consider the geodesic flow of a compact connected rank 1 surface. We prove a formula for the topological pressure as the exponential growth rate of rank 1 periodic geodesics generalizing a previous result of K. Gelfert and B. Schapira…

In this paper, we present a probabilistic extension of the Fubini polynomials and numbers associated with a random variable satisfying some appropriate moment conditions. We obtain the exponential generating function and an integral…

We present a systematic short time expansion for the generating function of the one point height probability distribution for the KPZ equation with droplet initial condition, which goes much beyond previous studies. The expansion is checked…

Since the work of Mirzakhani and Petri on random hyperbolic surfaces of large genus, length statistics of closed geodesics have been studied extensively. We focus on the case of random hyperbolic surfaces with cusps, the number of which…

We obtain a simple, recursive presentation of the tautological (\kappa, \psi, and \lambda) classes on the moduli space of curves in genus zero and one in terms of boundary strata (graphs). We derive differential equations for the generating…

We present a genus expansion-type expression for the expected values of products of traces of expressions involving Haar-distributed orthogonal matrices. As with other real genus expansions, nonorientable surfaces appear, in addition to the…

We present a unified approach to studying certain non-linear random matrix ensembles and associated random neural networks at initialization. This begins with a novel series expansion for neural networks which generalizes Fa\'a di Bruno's…

We present a method to compute the genus expansion of the free energy of Hermitian matrix models from the large N expansion of the recurrence coefficients of the associated family of orthogonal polynomials. The method is based on the…

We study the role of the topology of the background space on the one-dimensional Kardar-Parisi-Zhang (KPZ) universality class. To do so, we study the growth of balls on disordered 2D manifolds with random Riemannian metrics, generated by…

A study of the intersection theory on the moduli space of Riemann surfaces with boundary was recently initiated in a work of R. Pandharipande, J. P. Solomon and the third author, where they introduced open intersection numbers in genus 0.…

We use tropical and nonarchimedean geometry to study the moduli space of genus $0$ stable maps to $\mathbb{P}^1$ relative to two points. This space is exhibited as a tropical compactification in a toric variety. Moreover, the fan of this…

Let $M = \mathbb{B}^2 / \Gamma$ be a smooth ball quotient of finite volume with first betti number $b_1(M)$ and let $\mathcal{E}(M) \ge 0$ be the number of cusps (i.e., topological ends) of $M$. We study the growth rates that are possible…