Related papers: Research problems on relations between Nijenhuis g…
These are lecture notes for five lectures given at MPI Leipzig in May 2024. We study the moduli space M_{0,n} of n distinct points on P^1 as a positive geometry and a binary geometry. We develop mathematical formalism to study…
The algebraic structure of the integrable mixed mKdV/sinh-Gordon model is discussed and \textit{}extended to the AKNS/Lund-Regge model and to its corresponding supersymmetric versions. The integrability of the models is guaranteed from the…
The relation between two--dimensional integrable systems and four--dimen\-sional self--dual Yang--Mills equations is considered. Within the twistor description and the zero--curvature representation a method is given to associate self--dual…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
Science meets Engineering in Deep Learning took place in Vancouver as part of the Workshop section of NeurIPS 2019. As organizers of the workshop, we created the following report in an attempt to isolate emerging topics and recurring themes…
This paper shows the complementary roles of mathematical and engineering points of view when dealing with truss analysis problems involving systems of linear equations and inequalities. After the compatibility condition and the mathematical…
On June 5, 2007 the second author delivered a talk at the Journees de l'Institut Elie Cartan entitled "Finite symmetry groups in complex geometry". This paper begins with an expanded version of that talk which, in the spirit of the…
The object of this expository work is to try to unveil the topological/geometric intuition behind the theory of free groups and their automorphism and outer automorphism groups. The method we follow is to focus on a series of problems in…
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
We use ideas on integrability in higher dimensions to define Lorentz invariant field theories with an infinite number of local conserved currents. The models considered have a two dimensional target space. Requiring the existence of…
We discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry.
I review the current status of structure formation bounds on neutrino properties such as mass and energy density. I also discuss future cosmological bounds as well as a variety of different scenarios for reconciling cosmology with the…
The purpose of this manuscript is to review my recent activity on three main research topics. The first concerns the nature of low temperature amorphous solids and their relation with the spin glass transition in a magnetic field. This is…
We present an intuitive diagrammatic representation of a new class of integrable $\s$-models. It is shown that to any given diagram corresponds an integrable theory that couples $N$ WZW models with a certain number of each of the following…
For construction and classification of the natural integrable systems we propose to use a criterion of separability in Darboux--Nijenhuis coordinates, which can be tested without an a priori explicit knowledge of these coordinates.
These notes represent the transcript of three, 90 minute lectures given by the second author at the CRM in Barcelona in 2021 as part of the "Higher Structures and Operadic Calculus" workshop. The goal of the series was to introduce and…
In this paper, we proposed an procedure to construct the completion of the integrable system by adding a perturbation to the generalized matrix problem, which can be used to continuous integrable couplings, discrete integrable couplings and…
We collect some open problems about minimal presentations of numerical semigroups and, more generally, about defining ideals and free resolutions of their semigroup rings and associated graded rings. We emphasize both long-standing problems…
We construct a weight matrix for the 3D Ising model satisfying the so-called twisted tetrahedron equation. The result is based on the theory of the n-simplicial complex and the invented recursion procedure on the space of n-simplex…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…