101 citations · 894 across the 40 of their papers we have counts for
40 papers
An explicit four-corner dictionary for (2,p) minimal Liouville gravity
A. Alexandrov, V. Belavin
(2,p) minimal Liouville gravity admits four algebraic descriptions interrelated by dualities. On the Frobenius manifold (FM) side the theory is built either on the manifold…
Topological recursion, symplectic duality, and generalized fully simple maps
Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski +2
For a given spectral curve, we construct a family of symplectic dual spectral curves for which we prove an explicit formula expressing the -point functions produced by the topol…
Matrix models for the nested hypergeometric tau-functions
Alexander Alexandrov
We introduce and investigate a family of tau-functions of the 2D Toda hierarchy, which is a natural generalization of the hypergeometric family associated with Hurwitz numbers. For…
On W-operators and superintegrability for dessins d'enfant
Alexander Alexandrov
In this short note we identify a family of partition functions recently introduced by Wang, Liu, Zhang, and Zhao with certain specializations of the generating function for dessins…
A universal formula for the swap in topological recursion
Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski +2
We prove a recent conjecture of Borot et al. that a particular universal closed algebraic formula recovers the correlation differentials of topological recursion after the swap of…
On higher Brézin-Gross-Witten tau-functions
Alexander Alexandrov, Saswati Dhara
In this paper, we consider the higher Brézin--Gross--Witten tau-functions, given by the matrix integrals. For these tau-functions we construct the canonical Kac--Schwarz operators,…
Cut-and-join operators in cohomological field theory and topological recursion
Alexander Alexandrov
We construct a cubic cut-and-join operator description for the partition function of the Chekhov-Eynard-Orantin topological recursion for a local spectral curve with simple ramific…
A construction of open descendant potentials in all genera
Alexander Alexandrov, Alexey Basalaev, Alexandr Buryak
We present a construction of an open analogue of total descendant and total ancestor potentials via an "open version" of Givental's action. Our construction gives a genus expansion…
Cut-and-join operators for higher Weil-Petersson volumes
Alexander Alexandrov
In this paper, we construct the cut-and-join operator description for the generating functions of all intersection numbers of , , and classes on the moduli spaces $\overl…
KP integrability of triple Hodge integrals. III. Cut-and-join description, KdV reduction, and topological recursions
Alexander Alexandrov
In this paper, we continue our investigation of the triple Hodge integrals satisfying the Calabi-Yau condition. For the tau-functions, which generate these integrals, we derive the…
Elements of spin Hurwitz theory: closed algebraic formulas, blobbed topological recursion, and a proof of the Giacchetto-Kramer-Lewanski conjecture
Alexander Alexandrov, Sergey Shadrin
In this paper, we discuss the properties of the generating functions of spin Hurwitz numbers. In particular, for spin Hurwitz numbers with arbitrary ramification profiles, we const…
Generalized Brézin-Gross-Witten tau-function as a hypergeometric solution of the BKP hierarchy
Alexander Alexandrov
In this paper, we prove that the generalized Brézin-Gross-Witten tau-function is a hypergeometric solution of the BKP hierarchy with simple weight generating function. We claim tha…
Intersection numbers on and BKP hierarchy
Alexander Alexandrov
In their recent inspiring paper Mironov and Morozov claim a surprisingly simple expansion formula for the Kontsevich-Witten tau-function in terms of the Schur Q-functions. Here we…
KdV solves BKP
Alexander Alexandrov
In this note, we prove that any tau-function of the KdV hierarchy also solves the BKP hierarchy after a simple rescaling of times.
Matrix model for the total descendant potential of a simple singularity of type
Alexander Alexandrov, Todor Milanov
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 int…
KP integrability of triple Hodge integrals. II. Generalized Kontsevich matrix model
Alexander Alexandrov
In this paper we introduce a new family of the KP tau-functions. This family can be described by a deformation of the generalized Kontsevich matrix model. We prove that the simples…
KP integrability of triple Hodge integrals. I. From Givental group to hierarchy symmetries
Alexander Alexandrov
In this paper, we investigate a relation between the Givental group of rank one and the Heisenberg-Virasoro symmetry group of the KP hierarchy. We prove, that only a two-parameter…
Matrix model for the stationary sector of Gromov-Witten theory of
Alexander Alexandrov
In this paper we investigate the tau-functions for the stationary sector of Gromov-Witten theory of the complex projective line and its version, relative to one point. In particula…
From minimal gravity to open intersection theory
Alexander Alexandrov, Hisayoshi Muraki, Chaiho Rim
We investigated the relation between the two-dimensional minimal gravity (Lee-Yang series) with boundaries and open intersection theory. It is noted that the minimal gravity with b…
Buryak-Okounkov formula for the -point function and a new proof of the Witten conjecture
Alexander Alexandrov, Francisco Hernández Iglesias, Sergey Shadrin
We identify the formulas of Buryak and Okounkov for the n-point functions of the intersection numbers of psi-classes on the moduli spaces of curves. This allows us to combine the e…
Weighted Hurwitz numbers and topological recursion
A. Alexandrov, G. Chapuy, B. Eynard +1
The KP and 2D Toda tau-functions of hypergeometric type that serve as generating functions for weighted single and double Hurwitz numbers are related to the topological recursion p…
Fermionic approach to weighted Hurwitz numbers and topological recursion
A. Alexandrov, G. Chapuy, B. Eynard +1
A fermionic representation is given for all the quantities entering in the generating function approach to weighted Hurwitz numbers and topological recursion. This includes: KP and…
Refined open intersection numbers and the Kontsevich-Penner matrix model
Alexander Alexandrov, Alexandr Buryak, Ran J. Tessler
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, w…
Weighted Hurwitz numbers and topological recursion: an overview
A. Alexandrov, G. Chapuy, B. Eynard +1
Multiparametric families of hypergeometric -functions of KP or Toda type serve as generating functions for weighted Hurwitz numbers, providing weighted enumerations of branched…