相关论文: Canonical Lattices and Integer Relations Associate…
In earlier work, using the light cone picture, a world sheet field theory that sums planar phi^3 graphs was constructed and developed. Since this theory is both non-local and not explicitly Lorentz invariant, it is desirable to have a…
We present a graph-theoretic model for dynamical systems $(X,\sigma)$ given by a surjective local homeomorphism $\sigma$ on a totally disconnected compact metrizable space $X$. In order to make the dynamics appear explicitly in the graph,…
Relational mechanics is a gauge theory of classical mechanics whose laws do not govern the motion of individual particles but the evolution of the distances between particles. Its formulation gives a satisfactory answer to Leibniz's and…
We construct a compactification of the moduli of toric pairs by using ideas from mirror symmetry. The secondary fan $\Sigma(Q)$ is used in [Ale02] to parametrize degenerations of toric pairs. It is also used in [CLS11] to control the…
Fix a K3 lattice $\Lambda$ of rank two and $L\in\Lambda$ a big and nef divisor that is positive enough. We prove that the generic $\Lambda$-polarised K3 surface has an integral nodal rational curve in the linear system $|L|$, in particular…
We review recent results concerning finite size corrections to the Ising model free energy on lattices with non-trivial topology and curvature. From conformal field theory considerations two distinct universal terms are expected, a…
We show that under certain conditions the flyping operation on rational tangles, which produces topologically isotopic tangles, may also produce tangles which are not Legendrian isotopic when viewed in the standard contact structure on…
Lattice-based Cryptography is considered to have the characteristics of classical computers and quantum attack resistance. We will design various graphic lattices and matrix lattices based on knowledge of graph theory and topological…
On an arbitrary toric variety, we introduce the logarithmic double complex, which is essentially the same as the algebraic de Rham complex in the nonsingular case, but which behaves much better in the singular case. Over the field of…
We study cocompact lattices with dense projections in a product $G_1 \times G_2$ of locally compact groups and show, under the assumption that each $G_i$ is a closed subgroup of the automorphism group $Aut(T_i)$ of a regular tree satisfying…
Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research direction requiring non-perturbative methods. Recent…
We consider a notion of rationalizability, where the rationalizing relation may depend on the set of feasible alternatives. More precisely, we say that a choice function is locally rationalizable if it is rationalized by a family of…
We formulate a general abstract criterion for verifying the local-to-global principle for a rigidly-compactly generated tensor triangulated category. Our approach is based upon an inductive construction using dimension functions. Using our…
We introduce the notion of $\mathcal{C}$-system of filters, generalizing the standard definitions of both extenders and towers of normal ideals. This provides a framework to develop the theory of extenders and towers in a more general and…
The striking boundary dependency (the Arctic Circle phenomenon) exhibited in the ice model on the square lattice extends to other planar set-ups. We present these findings for the triangular and the Kagome lattices. Critical connectivity…
In the theory of coalgebras $C$ over a ring $R$, the rational functor relates the category of modules over the algebra $C^*$ (with convolution product) with the category of comodules over $C$. It is based on the pairing of the algebra $C^*$…
We study the connection between Rational Conformal Field Theory (RCFT), $N=2$ massive supersymmetric field theory, and solvable Interaction Round the Face (IRF) lattice models. Specifically, one identifies the fusion rings with the chiral…
We relate the version of rational Symplectic Field Theory for exact Lagrangian cobordisms introduced in [5] with linearized Legendrian contact homology. More precisely, if $L\subset X$ is an exact Lagrangian submanifold of an exact…
We prove the following result: Let K be a lattice, let D be a distributive lattice with zero, and let $\phi$: Con K $\to$ D be a {∨, 0}-homomorphism, where Conc K denotes the {∨, 0}-semilattice of all finitely generated…
Magnetic fields play a critical role in the propagation of charged cosmic rays. Particular field configurations supported by different astrophysical objects may be observable in cosmic ray maps. We consider a simple configuration, a…