Related papers: High-Girth Steiner Triple Systems
The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most…
We study characterizations of ergodicity, weak mixing and strong mixing of W*-dynamical systems in terms of joinings and subsystems of such systems. Ergodic joinings and Ornstein's criterion for strong mixing are also discussed in this…
The conjectures of Manin and Peyre are confirmed for a certain threefold.
We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and…
We prove Simon's conjecture for 3-manifolds.
It is conjectured that every cusped hyperbolic 3-manifold admits a geometric triangulation, i.e. it is decomposed into positive volume ideal hyperbolic tetrahedra. Here, we show that sufficiently highly twisted knots admit a geometric…
In this paper, we consider compatible Hom-Lie triple systems. Compatible Hom-Lie triple systems are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra. We also define a cohomology theory for compatible…
We introduce the theory of div point sets, which aims to provide a framework to study the combinatoric nature of any set of points in general position on an Euclidean plane. We then show that proving the unsatisfiability of some first-order…
We prove the GGS conjecture (1993), due to Gerstenhaber, Giaquinto, and Schack, which gives a particularly simple explicit quantization of classical r-matrices for Lie algebras gl(n) in terms of an element R satisfying the quantum…
This article presents a variety of algebraic proofs of Steiner's $1$-Cycle Theorem. It also demonstrates that, under an exponential upper-bound on the iterates, the only $1$-cycles in the (accelerated) $3x-1$ dynamical system are $(1)$ and…
Possible reasons for the uniqueness of the positive geometric law in the context of stability of random extremes are explored here culminating in a conjecture characterizing the geometric law. Our reasoning comes closer in justifying the…
Inspired by the Erd\H{o}s' problem in Ramsey theory, we propose a dynamical version of the problem and answer it positively for circle maps.
Despite the many applications of rate-independent systems, their regularity theory is still largely unexplored. Usually, only weak solution with potentially very low regularity are considered, which requires non-smooth techniques. In this…
This paper wishes to foster communication between mathematicians and physicists working in mirror symmetry and orbifold Gromov-Witten theory. We provide a reader friendly review of the physics computation in [arXiv:hep-th/0607100] that…
It has long been conjectured that generic dynamical systems has finite periodic orbits, ever since the time of Poincar\'e. In this article, a perturbation method is proposed for the $C^r$ closing of periodic orbits. This method is…
We show that infinitely many three-term arithmetic progressions $N, N+d, N+2d$ of powerful numbers exist with $d = 2\sqrt{N} + 1$. We further conjecture that infinitely many of these progressions consist of three consecutive terms in the…
We prove the Aharoni Berger Conjecture
We prove an existence result for twisted K\"ahler-Einstein metrics, assuming an appropriate twisted K-stability condition. An improvement over earlier results is that certain non-negative twisting forms are allowed.
We prove the existence of $n$-periodic orbits for almost all $n\in\mathbb{N}$ in the R\"ossler system with attracting periodic orbit, for two sets of parameters. The proofs are computer-assisted.
By using the Three-lines theorem for a certain analytic function defined in terms of the trace and a duality argument method, we prove Audenaert-Kittaneh's conjecture related to $p$-Schatten classes. This generalizes the main result…