Related papers: Integrability and geometry of the Wynn recurrence
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We consider a Frobenius structure associated with the dispersionless Kadomtsev-Petviashvili equation. This is done, essentially, by applying a continuous analogue of the finite dimensional theory in the space of Schwartz functions on the…
In this paper, we aim at recovering an undirected weighted graph of $N$ vertices from the knowledge of a perturbed version of the eigenspaces of its adjacency matrix $W$. For instance, this situation arises for stationary signals on graphs…
A recurrence equation is a discrete integrable equation whose solutions are all periodic and the period is fixed. We show that infinitely many recurrence equations can be derived from the information about invariant varieties of periodic…
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Perturbations of $WD_n$ and $W_3$ conformal theories which generalize the $(1,2)$ perturbations of conformal minimal models are shown to be integrable by counting argument. $A_{2n-1,q}^{(2)}$ and $D_{4,q}^ {(3)}$ symmetries of corresponding…
The path integral description of the Wess-Zumino-Witten $\to$ Liouville reduction is formulated in a manner that exhibits the conformal invariance explicitly at each stage of the reduction process. The description requires a conformally…
\textit{Dessins d'enfants} (hypermaps) are useful to describe algebraic properties of the Riemann surfaces they are embedded in. In general, it is not easy to describe algebraic properties of the surface of the embedding starting from the…
The Frobenius-Schwinger-Dyson equations are a rather high-brow abstract nonsense type of equations describing n-point functions of arbitrarily high composite insertions. It is not clear how to solve or even find approximate solutions of…
We study a variety of questions centered around the computation of cohomology of line bundles on the incidence correspondence (the partial flag variety parametrizing pairs consisting of a point in projective space and a hyperplane…
We consider orthogonal polynomials p_n with respect to an exponential weight function w(x) = exp(-P(x)). The related equations for the recurrence coefficients have been explored by many people, starting essentially with Laguerre [49], in…
We construct some explicit quasihomogeneous algebraic solutions to the associativity (WDVV) equations by using analytical methods of the finite gap integration theory. These solutions are expanded in the uniform way to non-semisimple…
This thesis is devoted to some particular aspects of integrability in $4d$ SUSY gauge theories. Taking advantage of the integrable structures emergent in the theory, non-local observables such as null polygonal Wilson loops are studied in…
The quantum form of the Poincar\'e recurrence theorem stipulates that a system with a time-independent Hamiltonian and discrete energy levels returns arbitrarily close to its initial state in a finite time. Qubit systems, being highly…
Inductive bias refers to restrictions on the hypothesis class that enable a learning method to generalize effectively from limited data. A canonical example in control is linearity, which underpins low sample-complexity guarantees for…
Twisted symmetries, widely studied in the last decade, proved to be as effective as standard ones in the analysis and reduction of nonlinear equations. We explain this effectiveness in terms of a Lie-Frobenius reduction; this requires to…
This paper aims to present a general idea for description of spatially finite physical objects with a consistent nontrivial translational-rotational dynamical structure and evolution as a whole, making use of the mathematical concepts and…
In this introductory paper we study nearly Frobenius algebras which are generalizations of the concept of a Frobenius algebra which appear naturally in topology: nearly Frobenius algebras have no traces (co-units). We survey the most basic…
String equations related to 2D gravity seem to provide, quite naturally and systematically, integrable kernels, in the sense of Its-Izergin-Korepin and Slavnov. Some of these kernels (besides the "classical" examples of Airy and Pearcey)…
Let $F$ be a non-Archimedean locally compact field and let $D$ be a central division algebra over $F$. Let $\pi_1$ and $\pi_2$ be respectively two smooth irreducible representations of ${\rm GL}(n_1,D)$ and ${\rm GL}(n_2,F)$, $n_1, n_2 \geq…