R. H. Bing, or Robert Lee Bing, was an influential American mathematician known for his work in topology, a branch of mathematics focused on the properties of space that are preserved under continuous transformations. He made significant contributions to the field, including the introduction of concepts such as Bing's decomposition, which pertains to the study of non-compact surfaces and their structures.

Ronald Brown is a prominent mathematician known for his contributions to the fields of algebraic topology and category theory. He has worked extensively on concepts related to higher-dimensional algebra, particularly in the context of homotopy theory and topological spaces. One of his notable contributions is the development of the theory of "cubical sets" and "cubes," which are useful in studying the topology of spaces.

Thomas Goodwillie is a mathematician known for his work in the fields of topology and homotopy theory. He is particularly noted for his contributions to the theory of iterated loop spaces and for the development of the Goodwillie calculus, which is a framework for studying the relationships between polynomial functors in the category of topological spaces.

W. B. R. Lickorish, commonly known as Bill Lickorish, is a mathematician known for his contributions to the field of topology, particularly in knot theory and 3-manifolds. He has authored numerous research papers and is recognized for his work on the properties of knots and links, as well as on other areas of geometry and topology. His work has had a significant impact on the understanding of the mathematical properties of complex spaces.

Yakov Eliashberg is a prominent Russian-American mathematician, known for his contributions to the fields of symplectic geometry and topology. Born on December 17, 1946, Eliashberg has made significant advancements in the understanding of symplectic manifolds and was a key figure in the development of the theory surrounding Weinstein neighborhoods and the h-principle. His work has had a substantial impact on both geometry and mathematical physics.

Zoltán Szabó is a Hungarian mathematician known for his contributions to various areas of mathematics, particularly in the fields of topology and algebra. However, details about his specific contributions or works may not be widely known or available, as there may be multiple individuals with that name in the mathematics community.

Cohomological descent is a concept in algebraic geometry and algebraic topology, which is particularly associated with the study of sheaves and cohomology. It captures the idea of how properties of sheaves (or more generally, objects in a category) can be characterized in terms of local data, often related to covering spaces or open covers.

Horrocks construction refers to a specific architectural and engineering technique used in the design of certain types of structures, particularly those requiring stability and durability. It is named after the engineer or architect associated with the development or popularization of this method.

The Burkhardt quartic is a specific type of algebraic surface defined by a polynomial equation of degree four in projective space. It is named after the mathematician Arthur Burkhardt, who studied the properties of such surfaces.

The Peterson–Stein formula is a result in the field of representation theory, particularly relating to the characters of semisimple Lie algebras. It provides a way to compute the values of certain characters of these algebras using simpler components. Specifically, the formula gives an expression for the characters of irreducible representations of a semisimple Lie algebra in terms of the characters of its subalgebras and the structure constants of the algebra.

The Szilassi polyhedron is an interesting mathematical object that is classified as a toroidal polyhedron. It is notable for being a non-convex, 14-faced polyhedron that has a unique property: each of its faces is a heptagon (7-sided polygon).

The Barth–Nieto quintic is a specific type of algebraic variety that is notable in the study of complex geometry and algebraic geometry. It is defined as a smooth quintic hypersurface in \(\mathbb{P}^4\) (the complex projective space of dimension 4) given by a particular polynomial.

The Igusa quartic is a specific type of algebraic surface that arises in the study of complex multiplication and the theory of modular forms, particularly in the context of elliptic curves and abelian varieties. It is named after the Japanese mathematician Jun-ichi Igusa, who introduced it in the 1960s.

In mathematics, particularly in algebraic geometry and differential geometry, a **moduli space** is a geometric space that parametrizes a family of algebraic structures, such as curves, vector bundles, or more generally, geometrical objects. The idea is to organize the objects of a particular type into a space, where each point in this space corresponds to a distinct structure (often up to some kind of equivalence).

A **semialgebraic space** is a concept primarily arising in the field of real algebraic geometry and relates to the study of sets defined by polynomial inequalities.

Semidefinite programming (SDP) is a subfield of convex optimization that deals with the minimization of a linear objective function subject to semidefinite constraints.

In mathematics, particularly in set theory and algebra, the concept of a quotient by an equivalence relation is an important one. When you have a set \( S \) and an equivalence relation \( \sim \) defined on that set, you can partition the set into disjoint subsets, known as equivalence classes.

In mathematics, particularly in the field of algebraic geometry, a **Scheme** is a fundamental concept that generalizes the notion of algebraic varieties. Introduced by Alexander Grothendieck in the 1960s, schemes provide a framework for working with solutions to polynomial equations, accommodating both classical geometric objects and more abstract algebraic structures.

A CR manifold (Cauchy-Riemann manifold) is a differential manifold equipped with a special kind of geometric structure that generalizes the concept of complex structures to a more general setting. Specifically, a CR manifold has a certain kind of foliation by complex subspaces that leads to the definition of CR structures. To define a CR manifold, consider the following components: 1. **Smooth Manifold**: Start with a smooth manifold \( M \) of real dimension \( 2n \).