相关论文: Higher dimensional Frobenius problem: Maximal satu…

We prove that non-elementary hyperbolic groups grow exponentially more quickly than their infinite index quasiconvex subgroups. The proof uses the classical tools of automatic structures and Perron-Frobenius theory. We also extend the main…

Rational conformal field theories in 2d have partition functions built from holomorphic characters, whose classification can be addressed via the holomorphic modular bootstrap. This is facilitated by a special basis of ``quasi-characters''…

We prove rigidity results describing contextually-constrained maps defined on Grassmannians and manifolds of ordered independent line tuples in finite-dimensional vector or Hilbert spaces. One statement in the spirit of the Fundamental…

We prove that a metric measure space $(X,d,m)$ satisfying finite dimensional lower Ricci curvature bounds and whose Sobolev space $W^{1,2}$ is Hilbert is rectifiable. That is, a $RCD^*(K,N)$-space is rectifiable, and in particular for…

We present results of numerical simulations to estimate scaling exponents associated with driven surface growth in two spatial dimensions. We have simulated the restricted solid--on--solid growth model and used the time and system size…

Generalized composite fluxbrane solutions for a wide class of intersection rules are obtained. The solutions are defined on a manifold which contains a product of n Ricci-flat spaces M_1 x ... x M_n with 1-dimensional M_1. They are defined…

Motivated by questions arising in the study of the spectral theory of models of aperiodic order, we investigate sums of functions of semibounded closed subsets of the real line. We show that under suitable thickness assumptions on the sets…

We introduce a method for analyzing the convex hull of a set in non-positively curved piecewise Euclidean polygonal complexes and we apply this method to prove that, with the usual action of Fm x Zn on the metric product of the Cayley graph…

Let $f_1(n), \ldots, f_k(n)$ be polynomial functions of $n$. For fixed $n\in\mathbb{N}$, let $S_n\subseteq \mathbb{N}$ be the numerical semigroup generated by $f_1(n),\ldots,f_k(n)$. As $n$ varies, we show that many invariants of $S_n$ are…

The relation between negatively curved spaces and their boundaries is important for various rigidity problems. In \cite{biswas2024quasi}, the class of Gromov hyperbolic spaces called maximal Gromov hyperbolic spaces was introduced, and the…

The two-dimensional transient problem that is studied concerns a semi-infinite crack in an isotropic solid comprising an infinite strip and a half-plane joined together and having the same elastic constants. The crack propagates along the…

We study vectorial functions with maximal number of bent components in this paper. We first study the Walsh transform and nonlinearity of $F(x)=x^{2^e}h(\Tr_{2^{2m}/2^m}(x))$, where $e\geq0$ and $h(x)$ is a permutation over $\F_{2^m}$. If…

This paper is an exposition, with some new applications, of our results on the growth of entropy of convolutions. We explain the main result on $\mathbb{R}$, and derive, via a linearization argument, an analogous result for the action of…

Infrared fixed points of gauge theories provide intriguing targets for the modern conformal bootstrap program. In this work we provide some preliminary evidence that a family of gauged fermionic CFTs saturate bootstrap bounds and can…

Motivated by the entropic optimal transport problem in unbounded settings, we study versions of Hilbert's projective metric for spaces of integrable functions of bounded growth. These versions of Hilbert's metric originate from cones which…

Modeling of growth (or decay) curves arises in many fields such as microbiology, epidemiology, marketing, and econometrics. Parametric forms like Logistic and Gompertz are often used for modeling such monotonic patterns. While useful for…

Results on the upper and lower semicontinuity of functionals defined on spaces of convex and more general functions are established. In particular, the following result is obtained. Let $\phi(v; \cdot)$ be the density of the absolutely…

We consider a subclass of the class of group-theoretical fusion categories: To every finite group $G$ and subgroup $H$ one can associate the category of $G$-graded vector spaces with a two-sided $H$-action compatible with the grading. We…

The extended Hubbard model (EHM) describes fermions on a lattice coupled through on-site, $U$, and first-neighbor, $V$, interactions. In the context of high-$T_c$ cuprates, antiferromagnetic fluctuations may lead to an attractive channel,…

Let $G$ be a real algebraic semi-simple Lie group and $\Gamma$ be the fundamental group of a compact negatively curved manifold. In this article we study the limit cone, introduced by Benoist, and the growth indicator function, introduced…