Ariel D. Procaccia is a prominent researcher in the fields of computer science and artificial intelligence, particularly known for his work on algorithmic game theory, computational social choice, and auction design. He has made significant contributions to understanding how algorithms can be used to solve complex problems in social settings, such as voting and resource allocation. Procaccia has published extensively on topics such as fairness in algorithms, the mechanisms of decision-making processes, and the mathematical foundations of social choice theory.

"Games by designer" typically refers to a categorization of games based on their individual creators or designers. This approach allows players and enthusiasts to explore the works of specific game designers, showcasing their unique styles, themes, and gameplay mechanics.

Puzzle designers are creators who conceptualize, design, and develop puzzles for various formats, including games, escape rooms, online platforms, and printed materials. Their work involves crafting engaging and challenging puzzles that often require logical reasoning, problem-solving skills, and creativity to solve. Puzzle designers may work in various fields, including: 1. **Board Games and Video Games**: They create puzzles that are integral to gameplay and narrative progression.

Video game designers are professionals who create the concepts, mechanics, and overall vision for video games. Their role encompasses a variety of tasks, and they work collaboratively within a team that may include programmers, artists, sound designers, and writers. Here are some key aspects of what video game designers do: 1. **Game Concept Development**: Designers brainstorm and develop ideas for games, including themes, genres, and target audiences. They may create initial game prototypes or concepts that outline the gameplay experience.

A list of game designers typically includes individuals known for their significant contributions to the video game industry. Here are some notable game designers: 1. **Shigeru Miyamoto** - Creator of iconic series such as Mario, The Legend of Zelda, and Donkey Kong. 2. **Hideo Kojima** - Known for the Metal Gear series, particularly Metal Gear Solid, and Death Stranding.

Geometric graphs are a type of graph in which the vertices correspond to points in some geometric space, and the edges represent some geometric relationships between these points. The arrangement of the vertices in the plane (or in higher dimensions) usually relates to distances, angles, or other geometric properties. Key aspects of geometric graphs include: 1. **Vertex Representation**: The vertices are typically represented by points in a Euclidean space (commonly the 2D or 3D plane).

Visibility Graph Analysis (VGA) is a method used primarily in the fields of spatial analysis, urban planning, landscape architecture, and other areas to assess spatial relationships and visibility within a given environment. It transforms physical spaces into a mathematical representation to analyze how different locations can be "seen" from one another, thus helping to understand visibility, accessibility, and spatial integration.

The Pompeiu problem is a classical question in geometry named after the Romanian mathematician Dimitrie Pompeiu. It involves the relationship between geometric shapes and their properties in relation to points within these shapes.

Inversive distance is a mathematical concept used primarily in the fields of geometry and complex analysis. It is often employed in the context of circles or spherical geometry and is defined in relation to circles. The inversive distance between two circles is defined as the reciprocal of the distance between their respective centers, adjusted for the radii of the circles.

A Steiner chain is a geometric concept that refers to a particular arrangement of circles. Specifically, it is a sequence of circles that are tangent to each other and to some fixed line or point, along with the circles being arranged such that they share a common tangent at the points of tangency.

The Assouad dimension is a concept from geometric measure theory and fractal geometry that provides a way to measure the "size" or "complexity" of a set in terms of its dimensionality. It is particularly useful in analyzing the structure of sets that may exhibit fractal behavior.

Classical Wiener space, often referred to in the context of stochastic analysis and probability theory, is a mathematical construct used to represent the space of continuous functions that describe paths of Brownian motion. It provides a rigorous framework for the analysis of stochastic processes, particularly in the study of Gaussian processes.

A Delone set, also known as a uniformly discrete or relatively dense set, is a concept from mathematics, particularly in the study of point sets in Euclidean spaces and in the area of mathematical physics, crystallography, and non-periodic structures.

Doubling space is a concept often used in various fields, including mathematics, computer science, and physics, and it can refer to different ideas depending on the context. 1. **Mathematics and Geometry**: In the context of mathematical spaces, doubling often refers to the property of metric spaces where ball sizes can be controlled by the number of smaller balls that can cover the larger ones.

Flat convergence generally refers to a concept in optimization and machine learning, particularly in the context of training neural networks. It describes a situation where the loss landscape of a model has regions where the loss does not change much, even with significant changes in the model parameters. In other words, a "flat" region in the loss landscape indicates that there are many parameter configurations that yield similar performance (loss values), as opposed to "sharp" regions where small changes in parameters lead to large changes in loss.

In mathematics, particularly in the field of differential geometry and topology, a Fréchet surface is not a standard term primarily encountered in classical texts; it might refer to concepts related to Fréchet spaces or Fréchet manifolds, which are more common notions in functional analysis and manifold theory. However, if one were to discuss a "Fréchet surface," it may imply a surface that is modeled or analyzed within the context of Fréchet spaces.

The Gilbert–Pollack conjecture is a hypothesis in the field of combinatorial optimization, specifically regarding the packing of sets in geometric spaces. It posits a relationship between the size of a set and its ability to be packed tightly with respect to certain constraints. Formally, the conjecture deals with the arrangement and packing of spheres in Euclidean space, particularly in three dimensions. It suggests that for any collection of spheres in three-dimensional space, there exists an optimal packing density that cannot be exceeded.

The Hopf-Rinow theorem is a fundamental result in differential geometry and the study of Riemannian manifolds. It connects concepts of completeness, compactness, and geodesics in the context of Riemannian geometry. The theorem states the following: 1. **For a complete Riemannian manifold**: If \( M \) is a complete Riemannian manifold, then it is compact if and only if it is geodesically complete.

The Kirszbraun theorem, also known as Kirszbraun's extension theorem, is a result in the field of metric geometry and functional analysis. It addresses the extension of Lipschitz continuous functions.

Laakso space is a type of metric space that is notable in the study of geometric topology and analysis. It is defined to provide an example of a space that has certain interesting properties, particularly concerning the concepts of dimension and embedding. One of the intriguing characteristics of Laakso space is that it is a non-trivial space which exhibits a unique kind of fractal structure.