Related papers: The transition constant for arithmetic hyperbolic …

Let $X$ be a nonempty real variety that is invariant under the action of a reflection group $G$. We conjecture that if $X$ is defined in terms of the first $k$ basic invariants of $G$ (ordered by degree), then $X$ meets a $k$-dimensional…

Let $n$ be a positive integer and $G$ be a transitive permutation subgroup of $S_n$. Given a number field $K$ with $[K:\mathbb{Q}]=n$, we let $\widetilde{K}$ be its Galois closure over $\mathbb{Q}$ and refer to…

In complex dynamics, the boundaries of higher dimensional hyperbolic components in holomorphic families of polynomials or rational maps are mysterious objects, whose topological and analytic properties are fundamental problems. In this…

Assuming Lehmer's conjecture, we estimate the degree of the trace field $K(M_{p/q})$ of a hyperbolic Dehn-filling $M_{p/q}$ of a 1-cusped hyperbolic 3-manifold $M$ by $$ \dfrac{1}{C}(\max\;\{|p|,|q|\})\leq \text{deg }K(M_{p/q}) \leq…

Group-based reinforcement can induce discontinuous transitions from inactive to active phases in higher-order contagion models. However, these results are typically obtained on static interaction structures or within mean-field…

We obtain some new upper bounds on the maximum number $f(n)$ of edges in $n$-vertex graphs without containing cycles of length four. This leads to an asymptotically optimal bound on $f(n)$ for a broad range of integers $n$ as well as a…

We study theoretically and numerically the conditions required for the appearance of a superradiance transition in graphene. The electron properties of graphene are described in the single $p_z$-orbital tight-binding approximation, in which…

Degree bounds for algebra generators of invariant rings are a topic of longstanding interest in invariant theory. We study the analogous question for field generators for the field of rational invariants of a representation of a finite…

We develop a rotational hyperbolic theory for surface homeomorphisms. We use the equivalence relation on ergodic measures that have nontrivial rotational behaviour defined in [arXiv:2312.06249] to define a rotational counterpart of…

According to recent arguments by the author, the conformal field theory (CFT) describing the scaling limit of the integer quantum Hall plateau transition is a deformed level-4 Wess-Zumino-Novikov-Witten model with Riemannian target space…

In a recent work [R. Shojaei et al, Physical Review E 100, 022303 (2019)] the Authors calculate numerically the critical temperature $T_c$ of the balanced-imbalanced phase transition in a fully connected graph. According to their findings,…

Let H = (H,V) be a hypergraph with edge set H and vertex set V. Then hypergraph H is invertible iff there exists a permutation pi of V such that for all E belongs to H(edges) intersection of(pi(E) and E)=0. H is invertibility critical if H…

We introduce the notions of geometric height and graded (geometric) relative hyperbolicity in this paper. We use these to characterize quasiconvexity in hyperbolic groups, relative quasiconvexity in relatively hyperbolic groups, and convex…

We introduce the projective Hermite constant for positive definite binary hermitian forms associated with an imaginary quadratic number field $K$. It is a lower bound for the classical Hermite constant, and these two constants coincide when…

This paper gives lower bounds on the spectral radius of vertex-transitive graphs, based on the number of ``prime cycles'' at a vertex. The bounds are obtained by constructing circuits in the graph that resemble ``cactus trees'', and…

Let V denote a set of N vertices. To construct a "hypergraph process", create a new hyperedge at each event time of a Poisson process; the cardinality K of this hyperedge is random, with arbitrary probability generating function r(x),…

We introduce the notion of finite stature of a family $\{H_i\}$ of subgroups of a group $G$. We investigate the separability of subgroups of a group $G$ that splits as a graph of hyperbolic special groups with quasiconvex edge groups. We…

In this paper we give a upper bound of 40 on Rubik's cube group. The previously known upper bound has been 42 since 1995. In order to prove our claim we use computational methods. The program used is GAP computer algebra. Further more we…

In this note we use Yaman's dynamical characterization of relative hyperbolicity to prove a theorem of Bowditch about relatively hyperbolic pairs $(G,\mathcal{H})$ with $G$ hyperbolic. Our proof additionally gives a description of the…

The $H$--$T$ phase diagram of UTe$_2$ for magnetic field along the hard $b$ axis contains an unresolved internal boundary near $\mu_0H \sim 14$--15~T, previously inferred from ac susceptibility and transport experiments but lacking…