Related papers: On the $\mathfrak{grt}$ hexagon symmetry
In this work, we state a general conjecture on the solvability of optimization problems via algorithms with linear convergence guarantees. We make a first step towards examining its correctness by fully characterizing the problems that are…
We introduce the notions of mixed resolutions and simplicial sections, and prove a theorem relating them. This result is used (in another paper) to study deformation quantization in algebraic geometry.
The connection between symmetries and linearizations of discrete-time dynamical systems is being inverstigated. It is shown, that existence of semigroup structures related to the vector field and having linear representations enables…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…
The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…
In this talk we present a division-algebra classification of the generalized supersymmetries admitting bosonic tensorial central charges. We show that for complex and quaternionic supersymmetries a whole class of compatible division-algebra…
We introduce the notion of difference equation defined on a structured set. The symmetry group of the structure determines the set of difference operators. All main notions in the theory of difference equations are introduced as invariants…
Detecting symmetry is crucial for effective object grasping for several reasons. Recognizing symmetrical features or axes within an object helps in developing efficient grasp strategies, as grasping along these axes typically results in a…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
We describe a convex relaxation for the Gilbert-Steiner problem both in $R^d$ and on manifolds, extending the framework proposed in [9], and we discuss its sharpness by means of calibration type arguments. The minimization of the resulting…
General relativity (GR) admits two alternative formulations with the same dynamics attributing the gravitational phenomena to torsion or nonmetricity of the manifold's connection. They lead, respectively, to the teleparallel equivalent of…
Linear time-varying differential-algebraic equations with symmetries are studied. The structures that we address are self-adjoint and skew-adjoint systems. Local and global canonical forms under congruence are presented and used to classify…
For the exterior algebra E over a vector space, we consider general maps E^a -> E(1)^b and general symmetric and skew-symmetric maps E^a -> E(1)^a and describe the associated exterior algebra resolutions. Using the theory of homogeneous…
In this review article we discuss four recent methods for computing Maurer-Cartan structure equations of symmetry groups of differential equations. Examples include solution of the contact equivalence problem for linear hyperbolic equations…
Variational and divergence symmetries are studied in this paper for linear equations of maximal symmetry in canonical form, and the associated first integrals are given in explicit form. All the main results obtained are formulated as…
We investigate the existence and the orthogonality of the generalized Jack symmetric functions which play an important role in the AGT relations. We show their orthogonality by deforming them to the generalized Macdonald symmetric…
We introduce complex intersection bodies and show that their properties and applications are similar to those of their real counterparts. In particular, we generalize Busemann's theorem to the complex case by proving that complex…
In this paper, a way of generalizing the tensor renormalization group(TRG) is proposed. Mathematically, the connection between patterns of tensor renormalization group and the concept of truncation sequence in polytope geometry is…
We determine all orthogonal transformations of a quadratic space over reals such that any orthogonal transformation which is conjugate to one of them in the linear group is conjugate in the orthogonal group.
We give a review of modern approaches to constructing formal solutions to integrable hierarchies of mathematical physics, whose coefficients are answers to various enumerative problems. The relationship between these approaches and…