4 citations · 9 across the 11 of their papers we have counts for
12 papers
The smallest square tileable by pairwise incomparable integer rectangles
George M. Georgiou
Croft, Falconer and Guy ({Unsolved Problems in Geometry}, Problem~C5) exhibit a tiling of the square by eight pairwise incomparable integer rectangles and remark that…
Joining Two Pairs of Planar Points by Disjoint Arcs: The Sharp Length Bound
George M. Georgiou
Problem F16 of Croft, Falconer, and Guy asks for the least worst-case length needed to join prescribed pairs of points by pairwise disjoint planar arcs, when the distance within ea…
Congruent Triangular Faces, Reflections Allowed: Universal Realization and the Minimum Face Count in Problem B22
George M. Georgiou
Problem B22 in Unsolved Problems in Geometry asks which triangles occur as the common face of a convex polyhedron, how many copies are needed, and how they may be arranged. We sett…
Five-Point Hyperbolas on Power Curves and Near Lamé-Oval Vertices
George M. Georgiou
Problem A33 of Croft--Falconer--Guy records Reznick's question about infinite plane sets for which every five-point subset determines an ellipse or, respectively, a hyperbola, and…
Reciprocal-Polar Linearization and Two Conic Constructions for the Cone Projection
George M. Georgiou
Let $$ f_R(x)=\frac{x}{1+\norm{x}/R},\qquad R>0, $$ be the radial cone projection of the plane onto the open disk $\DR=\{x:\norm{x}<R\}$. Previous work established the Self-Directr…
Straightedge-and-Compass Constructibility of the Reciprocal--th-Power Law
George M. Georgiou
Given positive lengths and and a positive integer , let be determined by We prove that a single finite unmarked-stra…
The Cone Projection : Geometric structure and the Self-Directrix Theorem
George M. Georgiou
The cone projection is a radial homeomorphism from onto the open disk of radius , obtained by an elementary cone-and-perpendicular constr…
Holographic interpolations of codimension-2 defect CFTs
George Georgiou, Dimitrios Zoakos
We provide a comprehensive overview of the current status of higher-codimension defect systems. We review the holographic description and field theoretic properties of codimension-…
Weyl Anomaly Coefficients of Holographic Defect CFTs at Weak and Strong Coupling
George Georgiou
We determine the type-A Weyl anomaly coefficient , associated with the intrinsic scalar curvature of the defect, for the class of holographically realised co-dimension two defec…
Holographic interpolations of defect CFTs
George Georgiou, Dimitrios Zoakos
We propose a new class of holographic dualities between certain, generically non supersymmetric, defect conformal field theories (dCFTs) and their gravity duals. Our construction i…
Holography of a novel codimension-2 defect CFT
George Georgiou, Georgios Linardopoulos, Dimitrios Zoakos
We propose and study a new holographic duality between a non-supersymmetric defect conformal field theory (dCFT) and its gravity dual. On the gravity side, the defect is realised b…
The massless S-matrix of integrable -models
George Georgiou
In contradistinction to the case of massive excitations, the connection between integrability and the tree-level massless scattering matrix of integrable -models is lost. Namely…