The Erdős–Gyárfás conjecture is a statement in the field of graph theory that pertains to the coloring of graphs. Specifically, it suggests that for any graph \( G \) that does not contain a complete bipartite subgraph \( K_{p,q} \) (i.e.

The Virasoro conjecture is a fundamental result in the field of string theory and two-dimensional conformal field theory (CFT). It relates to the algebra of Virasoro operators, which are central to the study of CFTs, particularly in the context of two-dimensional quantum gravity and string theory. In essence, the conjecture asserts that there exists a certain relation between the partition functions of two-dimensional conformal field theories and the geometry of the underlying space.

The Section Conjecture is a significant hypothesis in the field of arithmetic geometry, particularly concerning the relationship between algebraic varieties and their associated functions or sections. It was formulated by mathematicians in the context of the study of abelian varieties and their rational points. More specifically, the conjecture relates to the *Neron models* of abelian varieties over a number field and their sections.

Resolution of singularities is a mathematical process in algebraic geometry that aims to transform a variety (which can have singular points) into a smoother variety (which has no singularities) by replacing the singular points with more complex structures, often in a controlled way. This process is crucial for understanding geometric properties of algebraic varieties and for performing various calculations in algebraic geometry.

The Littlewood conjecture is a statement in number theory proposed by John Edensor Littlewood in 1925. It concerns the distribution of fractional parts of sequences of the form \( n \alpha \), where \( n \) is a positive integer and \( \alpha \) is an irrational number.

The "List of unsolved problems in mathematics" refers to a collection of problems that remain unsolved despite being significant and well-studied in the field of mathematics. Many of these problems have withstood the test of time, eluding resolution by mathematicians for decades or even centuries.

The Fujita conjecture is a statement in the field of algebraic geometry, particularly concerning the minimal model program and the properties of algebraic varieties. Proposed by Takao Fujita in the 1980s, the conjecture pertains to the relationship between the ample divisor classes and the structure of the variety. Specifically, the Fujita conjecture relates to the growth of the dimension of the space of global sections of powers of an ample divisor.

The Fröberg conjecture, proposed by Anders Fröberg in 1981, is a conjecture in the field of algebraic geometry and commutative algebra. It deals with the study of the Betti numbers of a certain class of algebraic varieties, specifically focusing on the resolutions of certain graded modules.

The Pierce–Birkhoff conjecture is a conjecture in the field of lattice theory, specifically concerning finite distributive lattices and their Maximal Chains. It was proposed by the mathematicians Benjamin Pierce and George Birkhoff. The conjecture essentially deals with the nature of certain kinds of chains (series of elements) within these lattices and posits conditions under which certain structural properties hold.

The Inscribed Square Problem refers to a geometric problem of finding the largest square that can be inscribed within a given shape, usually a convex polygon or a specific type of curve. The goal is to determine the dimensions and position of the square such that it fits entirely within the boundaries of the shape while maximizing its area.

Heesch's problem is a question in the field of geometry, specifically in relation to tiling and the properties of shapes. It asks whether a given shape can be extended into a larger shape by adding additional copies of itself, while maintaining a specific tiling condition—specifically, that the tiles fit together without gaps or overlaps.

The Bombieri–Lang conjecture is a concept in number theory that relates to the distribution of rational points on certain types of algebraic varieties. Specifically, it deals with the behavior of rational points on algebraic varieties defined over number fields and has implications for understanding the ranks of abelian varieties and the distribution of solutions to Diophantine equations. The conjecture can be stated in a few steps for certain types of varieties, particularly for curves and higher-dimensional varieties.

The Reconstruction Conjecture is a concept in the field of graph theory, specifically related to the properties of graphs. It posits that a simple graph (i.e., a graph without loops or multiple edges) can be uniquely determined (reconstructed) from the collection of its vertex-deleted subgraphs.

Transient Lunar Phenomena (TLP) refers to short-lived light or color changes observed on the surface of the Moon. These phenomena are typically temporary and can last from a few minutes to several hours. TLP can manifest in various forms, including bright spots, color variations, or changes in the visibility of certain lunar features.

A strangelet is a hypothetical type of exotic matter that is composed of strange quarks. In particle physics, quarks are elementary particles and fundamental constituents of matter. There are six flavors of quarks: up, down, charm, strange, top, and bottom. Normally, matter is made up of up and down quarks (e.g., protons and neutrons).

Stephen Webb is an astrophysicist and researcher primarily known for his work in the field of cosmology and the study of the universe's structure and evolution. He notably contributed to the field of astrobiology and the search for extraterrestrial intelligence (SETI). Webb is also recognized for his literary work, particularly his book "If the Universe Is Teeming with Aliens... WHERE IS EVERYBODY?

The Abundance Conjecture is a concept within the field of number theory, focusing on the behavior of certain algebraic integers. Specifically, it deals with the distribution of prime numbers and the density of subsets of integers with specific properties. While the conjecture has been discussed in various contexts, it is often associated with the idea that among the integers, there exists a rich abundance of those that exhibit certain arithmetic properties, such as being prime or having a specific number of divisors.

VVV-WIT-07 is a variable star that was identified through the VVV (Vista Variables in the Via Lactea) survey. It belongs to the class of stars known as "WIT" stars, which are characterized by their variability. Specifically, VVV-WIT-07 is notable for its unusual behavior or characteristics, which have drawn the attention of astronomers. The VVV survey is aimed at studying the Milky Way's structure and stellar populations through infrared observations.

Unidentified Infrared Emission (UIR) refers to a series of broad and relatively weak emission features observed in the infrared spectrum, particularly in the context of astronomical observations. These features are typically detected in the infrared spectrum of various astronomical objects, including star-forming regions, planetary nebulae, and the interstellar medium.

SCP-06F6 is a fictional entity from the SCP Foundation, a collaborative writing project that features a collection of horror-themed stories surrounding anomalous objects, entities, or phenomena. Each SCP entry is assigned a unique number and typically includes a description, containment procedures, and documentation about the SCP.