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The tenfold classification provides a powerful framework for organizing topological phases of matter based on symmetry and spatial dimension. However, it does not offer a systematic method for transitioning between classes or engineering…
For one-dimensional systems of conservation laws admitting two additional conservation laws we assign a ruled surface of codimension two in projective space. We call two such systems dual if the corresponding ruled surfaces are dual. We…
Many elastic structures exhibit rapid shape transitions between two possible equilibrium states: umbrellas become inverted in strong wind and hopper popper toys jump when turned inside-out. This snap-through is a general motif for the…
The discovery of two-dimensional topological photonic systems has transformed our views on electromagnetic propagation and scattering of classical waves, and a quest for similar states in three dimensions, known to exist in condensed matter…
Time dependence is a universal phenomenon in nature, and a variety of mathematical models in terms of dynamical systems have been developed to understand the time-dependent behavior of real-world problems. Originally constructed to analyze…
D-instantons of Type IIB string theory are Ramond-Ramond counterpart of Giddings-Strominger wormholes connecting two asymptotic regions of spacetime. Such wormholes, according to Coleman, might lead to spacetime topology change,…
We prove a version of de Rham and Hyodo-Kato flip-flopping for dual towers of rigid analytic spaces including those coming from dual basic local Shimura varieties. The main tool are comparison theorems expressing the two cohomologies as…
Three-dimensional double-diffusive convection in a horizontally infinite layer of an uncompressible fluid interacting with horizontal vorticity field is considered in the neighborhood of Hopf bifurcation points. A family of amplitude…
Several interesting physical systems, such as the Lovelock extension of General Relativity in higher dimensions, classical time crystals, k-essence fields, Horndeski theories, compressible fluids, and nonlinear electrodynamics, have…
Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define…
Tight triangulations are exotic, but highly regular objects in combinatorial topology. A triangulation is tight if all its piecewise linear embeddings into a Euclidean space are as convex as allowed by the topology of the underlying…
A topological condition is given, characterizing which closed manifolds in dimensions < 8 (and conjecturally in general) admit symplectic structures. The condition is the existence of a certain fibration-like structure called a hyperpencil.…
It is well known that the Lagrangian and Hamiltonian descriptions of field theories are equivalent at the discrete time level when variational integrators are used. Besides the symplectic Hamiltonian structure, many physical systems exhibit…
We study superpositions and direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces,…
Dipole-conserving fluids serve as examples of kinematically constrained systems that can be understood on the basis of symmetry. They are known to display various exotic features including glassylike dynamics, subdiffusive transport, and…
The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such…
Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modelling random evolutions of human organ shapes. The notion of geodesic paths between shapes is central to shape analysis and has a…
For an integrable hierarchy which possesses a bihamiltonian structure with semisimple hydrodynamic limit, we prove that the linear reciprocal transformation with respect to any of its symmetry transforms it to another bihamiltonian…
We prove that steady state bifurcations in finite-dimensional dynamical systems that are symmetric with respect to a monoid representation generically occur along an absolutely indecomposable subrepresentation. This is stated as a…
In order to look for a well-behaved counterpart to Dolbeault cohomology in D-complex geometry, we study the de Rham cohomology of an almost D-complex manifold and its subgroups made up of the classes admitting invariant, respectively…