William Floyd is a mathematician known for his contributions to computer science, particularly in the areas of algorithms and combinatorial optimization. He is perhaps best known for the Floyd-Warshall algorithm, which is an efficient method for finding shortest paths in a weighted graph with positive or negative edge weights (but no negative cycles). This algorithm is widely used in various applications, including network routing and urban traffic planning.

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.

The Atiyah-Bott formula is a significant result in the field of geometry and topology, particularly in the context of mathematical physics and the theory of characteristic classes. Specifically, it provides a formula for the integral of a certain cohomology class over the moduli space of complex structures on a manifold. At its core, the Atiyah-Bott formula gives a way to compute the Euler characteristic of the space of sections of a certain vector bundle.

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.

In category theory and algebraic topology, the concept of *fibration* is a generalization of the notion of a fiber bundle. When we speak of a fibration of simplicial sets, we are referring to a specific type of fibration within the context of simplicial sets, which serve as a combinatorial model for topological spaces. ### Simplicial Sets A **simplicial set** is a combinatorial structure that encodes information about topological spaces.

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 Vietoris–Béguin mapping theorem, often simply referred to as the Vietoris theorem, is a result in algebraic topology that pertains to the relationship between homology groups of topological spaces and continuous functions between them. The theorem provides conditions under which the homology of a space can be computed from the homology of a subspace and the mapping properties of a continuous function defined on it.

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.

The Segre cubic refers to a specific type of algebraic variety in projective space, and it is often denoted as \( S \). Specifically, it is a hypersurface of degree 3 in the projective space \( \mathbb{P}^4 \).

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.