Related papers: Frameworks, Symmetry and Rigidity
We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…
For a system of partial differential equations admitting point, contact, or higher symmetries, the framework of invariant reduction systematically computes how invariant geometric structures, such as conservation laws, presymplectic…
In symplectic topology one uses elliptic methods to prove rigidity results about symplectic manifolds and solutions of Hamiltonian equations on them, where the most basic example is given by geodesics on Riemannian manifolds. Harmonic maps…
Many problems in areas such as compressive sensing and coding theory seek to design a set of equal-norm vectors with large angular separation. This idea is essentially equivalent to constructing a frame with low coherence. The elements of…
In this paper, we construct Hamilton-Jacobi equations for a great variety of mechanical systems (nonholonomic systems subjected to linear or affine constraints, dissipative systems subjected to external forces, time-dependent mechanical…
Let $g$ be a Riemannian metric for $\mathbf{R}^d$ ($d\geq 3$) which differs from the Euclidean metric only in a smooth and strictly convex bounded domain $M$. The lens rigidity problem is concerned with recovering the metric $g$ inside $M$…
We describe in this article a new code for evolving axisymmetric isolated systems in general relativity. Such systems are described by asymptotically flat space-times which have the property that they admit a conformal extension. We are…
This paper develops a mirror symmetry theory of Spencer cohomology within the geometric framework of constrained systems on principal bundles, revealing deep symmetric structures in constraint geometry. Based on compatible pairs…
The Reynolds equation, combined with the Elrod algorithm for including the effect of cavitation, resembles a nonlinear convection-diffusion-reaction (CDR) equation. Its solution by finite elements is prone to oscillations in…
This thesis is dedicated to the study of symmetries in reduced models of gravity, with some frozen degrees of freedom. We focus on the minisuperspace reduction whith a finite number of degrees of freedom. Minisuperspaces are treated as…
We find the symmetry generators for the Friedman equations emanating from a perfect fluid source, in the presence of a cosmological constant term. The relevant dynamics is seen to be governed by two coupled, first order ordinary…
Graded rings provide a natural algebraic framework for encoding symmetry via decompositions into homogeneous components indexed by a group, together with multiplication rules reflecting the group operation. Among graded rings, strongly…
Geometric number systems, obtained by extending the real number system to include new anticommuting square roots of +1 and -1, provide a royal road to higher mathematics by largely sidestepping the tedious languages of tensor analysis and…
We consider Abelian topological quantum field theories (TQFTs) in 3d and show that gaugings of invertible global symmetries naturally give rise to additive codes. These codes emerge as nonanomalous subgroups of the 1-form symmetry group,…
We prove that Whitehead's algorithm for solving the automorphism problem in a fixed free group $F_k$ has strongly linear time generic-case complexity. This is done by showing that the ``hard'' part of the algorithm terminates in linear time…
We elaborate the idea that the matrix models equipped with the gauge symmetry provide a natural framework to describe identical particles. After demonstrating the general prescription, we study an exactly solvable harmonic oscillator type…
We develop a framework that systematically casts the solvability and uniqueness conditions of linearized geometric boundary-value problems into cohomological terms. The theory is designed to be applicable without assumptions on the…
Affine metrics and its associated algebroid bundle are developed. Theses structures are applied to the general relativity and provide an structure for unification of gravity and electromagnetism. The final result is a field equation on the…
It is, by now, classical that lattices in higher rank semisimple groups have various rigidity properties. In this work, we add another such rigidity property to the list: uniform stability with respect to the family of unitary operators on…