相关论文: Canonical Lattices and Integer Relations Associate…
Motivated by the structural analogies between point lattices and linear error-correcting codes, and by the mature theory on locally testable codes, we initiate a systematic study of local testing for membership in lattices. Testing…
We present a family of rank symmetric diamond-colored distributive lattices that are naturally related to the Fibonacci sequence and certain of its generalizations. These lattices re-interpret and unify descriptions of some un- or…
We affirm a conjecture of Sacks [1972] by showing that every countable distributive lattice is isomorphic to an initial segment of the hyperdegrees, $\mathcal{D}_{h}$. In fact, we prove that every sublattice of any hyperarithmetic lattice…
We apply a Mayer-Vietoris sequence argument to identify the Atiyah-Segal equivariant complex K-theory rings of certain toric varieties with rings of integral piecewise Laurent polynomials on the associated fans. We provide necessary and…
Phonons are usually introduced by choosing a local displacement field. This paper keeps that local description, but identifies the global geometric object represented by it. The aim is not to change the local acoustic equations, but to…
For a finite real reflection group $W$ with Coxeter element $\gamma$ we give a uniform proof that the closed interval, $[I, \gamma]$ forms a lattice in the partial order on $W$ induced by reflection length. The proof involves the…
We propose our account of the meaning of local symmetries. We argue that the general covariance principle and gauge principle both are principles of democratic epistemic access to the law of physics, leading to ontological insights about…
We introduce the notion of Lorentzian fans, which form a special class of tropical fans that are particularly well-suited for proving Alexandrov-Fenchel type inequalities. To demonstrate the utility of Lorentzian fans, we prove a practical…
While there is a well developed theory of locally solid topologies, many important convergences in vector lattice theory are not topological. Yet they share many properties with locally solid topologies. Building upon the theory of…
Relational lattice is a formal mathematical model for Relational algebra. It reduces the set of six classic relational algebra operators to two: natural join and inner union. We continue to investigate Relational lattice properties with…
Equipartition theory, beginning with the classical ham sandwich theorem, seeks the fair division of finite point sets in $\mathbb{R}^d$ by the full-dimensional regions determined by a prescribed geometric dissection of $\mathbb{R}^d$. Here…
Let $p$ be a prime, and let $\mathrm{X}$ be a smooth $p$-adic formal scheme over $\mathrm{Spf} \mathcal{O}_K$ where $K/\mathbf{Q}_p$ is a finite extension. We show that reflexive sheaves on the stack $\mathrm{X}^{\mathrm{Syn}}$ are…
We show that lattice isomorphisms between lattices of slowly oscillating functions on chain-connected proper metric spaces induce coarsely equivalent homeomorphisms. This result leads to a Banach-Stone-like theorem for these lattices.…
We introduce and explore a natural rank for totally disconnected locally compact groups called the bounded conjugacy rank. This rank is shown to be a lattice invariant for lattices in sigma compact totally disconnected locally compact…
Let $\Gamma$ be a weakly irreducible higher rank lattice. In this paper, we will prove various rigidity results for the $\Gamma$-action following a philosophy of the Zimmer program. We provide new rigidity results including local and global…
Local cohomology functors are constructed for the category of cohomological functors on an essentially small triangulated category T equipped with an action of a commutative noetherian ring. This is used to establish a local-global…
Coherence with respect to Kelly-Mac Lane graphs is proved for categories that correspond to the multiplicative fragment without constant propositions of classical linear first-order predicate logic without or with mix. To obtain this…
We establish a general normal subgroup theorem for commensurators of lattices in locally compact groups. While the statement is completely elementary, its proof, which rests on the original strategy of Margulis in the case of higher rank…
We study canonical filtrations of finite-dimensional associative algebras and Lie algebras. These filtrations are defined via optimal destabilizing one-parameter subgroups in the sense of geometric invariant theory (GIT), and appear to be a…
We introduce the notion of a polyptych lattice, which encodes a collection of lattices related by piecewise linear bijections. We initiate a study of the new theory of convex geometry and polytopes associated to polyptych lattices. In…