A simplicial sphere is a type of topological space that arises in the field of algebraic topology and combinatorial geometry. More specifically, it is a simplicial complex that is homeomorphic to a sphere. ### Definition A **simplicial complex** is a set of simplices that satisfies certain conditions, such as closure under taking faces and the intersection property.

Partially solved games are games for which some knowledge about optimal strategies exists, but the game has not been completely solved. This means that while certain positions or states of the game may have been analyzed to the point of determining the best moves or strategies, not every possible position has been explored exhaustively.

"Col" is a minimalist strategy game designed by the company HyperCube, where players navigate a series of interconnected paths while trying to capture points on a grid-like board. The gameplay focuses on strategic movement and positioning while competing against other players or AI. The mechanics often involve simple rules that lead to complex strategies, making it accessible yet challenging. The game is known for its clean aesthetics and thoughtful design, appealing to fans of tactical board games and puzzle-solving.

Igor Pak is a mathematician and professor known for his work in various fields, including combinatorics, mathematical biology, and mathematical education. He is associated with the University of California, Los Angeles (UCLA) and has made contributions to mathematical research and teaching. In addition to his academic work, Pak is known for creating engaging resources for mathematics education and promoting problem-solving skills among students.

Jeff Kahn is a figure known in various contexts, but without additional specification, it's difficult to pinpoint exactly which Jeff Kahn you're referring to, as there may be multiple individuals by that name across different fields such as entertainment, business, or academia. One notable Jeff Kahn is a writer and producer known for his work in television and film, contributing to shows like "The Simpsons" and "Drew Carey's Show.

Lucio Lombardo-Radice was an Italian psychologist and researcher, best known for his work in the field of psychopathology and cognitive psychology. He gained recognition for his studies on the human mind's processes and their implications for understanding mental health and disorders. Lombardo-Radice contributed to the development of various theories and methodologies that aimed to deepen the understanding of psychological phenomena, particularly in relation to perception, memory, and cognitive function.

The term "parameter" can have different meanings depending on the context in which it is used. Here are a few common interpretations: 1. **Mathematics and Statistics**: In mathematical functions, a parameter is a variable that is not of primary interest but can be used to define a family of functions. For example, in the equation of a line, the slope and intercept are parameters that affect the line's position and orientation.

Symbolic dynamics is a branch of mathematics that studies dynamical systems through the use of symbols and sequences. It focuses on representing complex dynamical behaviors and trajectories in a simplified way using finite or countable sets of symbols. The primary idea in symbolic dynamics is to encode the states of a dynamical system as sequences of symbols. For example, one can take a continuous or discrete dynamical system and map its trajectories onto a finite alphabet (like {0, 1} for binary sequences).

Witt vectors are a construction in mathematics, specifically in the context of algebra and number theory, that generalizes the idea of p-adic integers and provides a way to study vector spaces over finite fields and rings. They were introduced by Ernst Witt in the 1940s and are used primarily in the areas of algebraic geometry, modular forms, and more broadly in the study of arithmetic.

Cayley's mousetrap is a combinatorial structure related to graph theory and enumerates certain types of objects, particularly rooted trees. Named after the British mathematician Arthur Cayley, the term is often used in connection with the enumeration of trees in combinatorial analysis. In a broader sense, Cayley's mousetrap refers to a technique or method in combinatorial enumeration that enables mathematicians to count specific arrangements or structures systematically.

T-theory is a concept in theoretical physics, particularly in the context of string theory and quantum gravity. It is associated with the idea of a particular duality in string theory known as T-duality. T-duality refers to a symmetry between different types of string theories that allows one to relate a string theory with a compactified dimension of a certain size to another string theory with the same dimension compactified at a smaller size.

In graph theory, an **edge cover** of a graph is a set of edges such that every vertex of the graph is incident to at least one edge in the set. In other words, an edge cover is a collection of edges that "covers" all vertices in the graph.

Planarity testing is a computational problem in graph theory that involves determining whether a given graph can be drawn on a plane without any of its edges crossing. A graph is said to be planar if it can be represented in such a way that no two edges intersect except at their endpoints (i.e., at the vertices). The significance of planar graphs lies in various applications across computer science, geography, and network design, among other fields.

An **interval exchange transformation** (IET) is a mathematical concept used in the field of dynamical systems and ergodic theory. It involves a way of rearranging segments of an interval (typically the unit interval \([0, 1]\)) by applying a transformation that is defined by splitting the interval into several subintervals of specific lengths, then permuting those subintervals according to a specific rule.

Surgery theory is a branch of geometric topology, which focuses on the study of manifolds and their properties by performing a kind of operation called surgery. The central idea of surgery theory is to manipulate manifold structures in a controlled way to produce new manifolds from existing ones. This can involve various operations, such as adding or removing handles, which change the topology of manifolds in a systematic manner.

A CW complex (pronounced "C-W complex") is a type of topological space that is particularly useful in algebraic topology. The term "CW" stands for "cellular" and "weak," referring to the construction method used to create such complexes. A CW complex is constructed using "cells," which are basic building blocks, typically in the shape of disks of different dimensions.

In category theory, a "cosmos" is a concept that extends the idea of a category to a more general framework, allowing for the study of "categories of categories" and related structures. Specifically, a cosmos is a category that is enriched over some universe of sets or types, which allows for a more flexible approach to discussing categories and their properties.

The concept of a Giraud subcategory arises in the context of category theory, particularly in the study of suitable subcategories of a given category. Giraud subcategories are named after the mathematician Jean Giraud, and they are important in the study of sheaf theory and topos theory. A Giraud subcategory is typically defined as a full subcategory of a topos (or a category with certain desirable properties) that retains the essential features of "nice" categories.