Related papers: Oded Schramm: From Circle Packing to SLE

Oded Schramm (1961-2008) influenced greatly the development of percolation theory beyond the usual ${\mathbb{Z}}^d$ setting; in particular, the case of nonamenable lattices. Here, we review some of his work in this field.

This article provides an introduction to Schramm(stochastic)-Loewner evolution (SLE) and to its connection with conformal field theory, from the point of view of its application to two-dimensional critical behaviour. The emphasis is on the…

We introduce a new class of fractal circle packings in the plane, generalizing the polyhedral packings defined by Kontorovich and Nakamura. The existence and uniqueness of these packings are guaranteed by infinite versions of the…

A brief report on recent work on the sphere-packing problem.

This article presents a whirlwind tour of some results surrounding the Koebe-Andre'ev-Thurston Theorem, Bill Thurston's seminal circle packing theorem that appears in Chapter 13 of The Geometry and Topology of Three-Manifolds. It will…

This article is meant to serve as a guide to recent developments in the study of the scaling limit of critical models. These new developments were made possible through the definition of the Stochastic Loewner Evolution (SLE) by Oded…

Presented here are over one hundred conjectures ranging from easy to difficult, from many mathematical fields. I also summarize briefly methods and tools that have led to this collection.

Spurred by the new examples found by Kornel Szlach\'anyi of a form of lax monoidal category, the author felt the time ripe to publish a reworking of Eilenberg-Kelly's original paper on closed categories appropriate to the laxer context. The…

We review some of the results that have been derived in the last years on conformal invariance, scaling limits and properties of some two-dimensional random curves. In particular, we describe the intuitive ideas that lead to the definition…

Based on the seminal work by John T. Sheridan [1] we discuss the usefulness and validity of simple diffraction theories frequently used to determine and characterize optical holographic gratings. Experimental investigations obtained in…

This is a survey on the theory of skew-cyclic codes based on skew-polynomial rings of automorphism type. Skew-polynomial rings have been introduced and discussed by Ore (1933). Evaluation of skew polynomials and sets of (right) roots were…

We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.

A variant of the Circle Packing Theorem states that the combinatorial class of any convex polyhedron contains elements midscribed to the unit sphere centered at the origin, and that these representatives are unique up to M\"obius…

In this note, we show how to relate the Schramm-Loewner Evolution processes (SLE) to highest-weight representations of the Virasoro Algebra. The conformal restriction properties of SLE that have been recently studied in the paper…

This is the first of a series of papers on sheaf theory on smooth and topological stacks and its applications. The main result of the present paper is the characterization of the twisted (by a closed integral three-form) de Rham complex on…

This article surveys many aspects of the theory of quandles which algebraically encode the Reidemeister moves. In addition to knot theory, quandles have found applications in other areas which are only mentioned in passing here. The main…

Starting with the classical circle geometry of Sophus Lie, we give a survey about some of the developments in the area of chain geometries during the last three decades.

Nearly 15 years ago, a set of qualitative spatial relations between oriented straight line segments (dipoles) was suggested by Schlieder. This work received substantial interest amongst the qualitative spatial reasoning community. However,…

Two-view structure from motion (SfM) is the cornerstone of 3D reconstruction and visual SLAM (vSLAM). Many existing end-to-end learning-based methods usually formulate it as a brute regression problem. However, the inadequate utilization of…

We develop a link between degree estimates for rational sphere maps and compressed sensing. We provide several new ideas and many examples, both old and new, that amplify connections with linear programming. We close with a list of ten open…