Yoshiko Ogata does not refer to a widely recognized figure, concept, or term based on information available up to October 2021. It’s possible that Yoshiko Ogata might be a private individual or a less prominent person in a particular field or context that hasn't gained significant public exposure.

Roger Penrose is a renowned British mathematical physicist, cosmologist, and mathematician. He was born on August 8, 1931. Penrose is best known for his contributions to the fields of general relativity and cosmology, particularly in relation to black holes, the nature of spacetime, and the mechanisms of consciousness.

Roman Jackiw is a notable physicist recognized for his contributions to theoretical physics, particularly in the areas of quantum field theory and condensed matter physics. He is known for his work on topics such as anomalies in quantum field theory, soliton solutions, and various aspects of mathematical physics.

Simone Warzel does not appear to be a widely recognized public figure or topic as of my last knowledge update in October 2023. It's possible that she may be a private individual or a relatively local or niche figure not covered extensively in major media sources.

As of my last update in October 2023, there is no widely recognized mathematical physicist named Thomas Spencer who has made significant contributions to the field in a way that is commonly referenced in academic literature or public discourse. It's possible that he could be an emerging figure or a researcher who may not yet have widespread recognition, or there may be multiple individuals with that name in different contexts.

Tomasz Robert Taylor is a Polish-born British entrepreneur and filmmaker known for his work in the film and television industry, particularly within the independent sector. He has been involved in various projects, showcasing a diverse range of storytelling approaches. Taylor's work often emphasizes creativity and innovation.

Vladimir Buslaev could refer to various individuals, but one notable figure is Vladimir Buslaev, a Russian linguist and researcher known for his contribution to the field of linguistics and language studies.

William Karush is best known for his contributions to mathematical optimization and for formulating the Karush-Kuhn-Tucker (KKT) conditions in the context of constrained optimization problems. The KKT conditions are a set of necessary conditions for a solution in nonlinear programming to be optimal, especially when dealing with inequality constraints. These conditions are fundamental in various fields, including economics, engineering, and operations research, as they provide a method for solving optimization problems.

Gaussian polar coordinates are a two-dimensional coordinate system that extends the concept of polar coordinates, typically used in the context of the standard Euclidean plane, to a Gaussian (or flat) geometry that can be useful for various applications, particularly in physics and engineering.

The Newtonian gauge is a specific choice of gauge used in the study of cosmological perturbations in the context of General Relativity. It is particularly useful in cosmology for analyzing the evolution of perturbations in the spacetime geometry during the universe's expansion. In the Newtonian gauge, the perturbed metric is expressed in a way that simplifies the analysis of scalar perturbations, which are fluctuations in the energy density of the universe, such as those arising from gravitational waves or inflationary fluctuations.

Lovelock's theorem refers to a set of results in the field of geometric analysis and theoretical physics, named after the mathematician David Lovelock. The key results of Lovelock's theorem concern the existence of certain types of gravitational theories in higher-dimensional spacetimes and focus primarily on the properties of tensors and the equations of motion that can be derived from a Lagrangian formulation.

The Schouten tensor is a mathematical object used in differential geometry and the theory of general relativity. It is a specific type of symmetric tensor derived from the Ricci curvature of a Riemannian or pseudo-Riemannian manifold.

Twistor correspondence is a mathematical framework developed by Roger Penrose in the 1960s that relates geometric structures in spacetime (in the context of general relativity) to complex geometric structures known as twistors. The correspondence aims to provide a new way of understanding the fundamental aspects of physics, particularly in the context of theories of gravitation and quantum mechanics. At its core, the twistor correspondence provides a bridge between the four-dimensional spacetime of general relativity and a higher-dimensional complex space.

The Lagrangian Grassmannian is a specific type of Grassmannian manifold that is associated with symplectic vector spaces. It can be understood as follows: 1. **Grassmannian Manifold**: In general, a Grassmannian \( G(k, n) \) is the space of all \( k \)-dimensional linear subspaces of an \( n \)-dimensional vector space. It has a rich structure and is a smooth manifold.

In mathematical physics and the theory of quantization, the statement that "quantization commutes with reduction" refers to a relationship between two processes: the reduction of symmetries in a classical system and the process of quantizing that system. To unpack this concept: 1. **Symmetry Reduction**: In classical mechanics, many systems possess symmetries described by a group of transformations (e.g., rotations, translations).

The 10th century saw various mathematicians from different cultures, primarily focusing on Islamic scholars, as this period coincided with the Islamic Golden Age. Here are some prominent mathematicians by nationality or cultural background during the 10th century: 1. **Persian**: - **Al-Khwarizmi** (circa 780-850) was earlier than the 10th century but heavily influenced later scholars. He is known for his work in algebra and algorithms.

The 11th century saw significant contributions to mathematics from various regions and cultures, though it is important to note that the mathematical landscape was quite different from today. Here are some notable mathematicians from the 11th century by nationality: 1. **Arab Mathematicians:** - **Al-Khwarizmi** (though he lived earlier, his works were influential in the 11th century): He is often referred to as the "father of algebra.

Hilda Geiringer (born Hilda P. Geiringer, 1893-1973) was an influential mathematician known for her work in applied mathematics and elasticity theory. She was notable for her contributions to the mathematical analysis of fracture mechanics and the behavior of materials under stress. Geiringer earned her Ph.D.

South Africa has a rich history of mathematics, with contributions from various mathematicians over the centuries. Below is a brief overview of notable South African mathematicians categorized by century: ### 19th Century - **George William Stoney (1826-1911)**: An influential figure, Stoney is best known for his work in physics but made contributions to mathematics as well. He proposed the concept of the electron and was involved in the early development of atomic theory.

Swiss mathematicians have made significant contributions to mathematics throughout various centuries. Here is a brief overview of notable Swiss mathematicians by century: ### 17th Century - **Jacob Bernoulli (1654–1705)**: Known for his work in probability and for the Bernoulli numbers, as well as contributions to calculus and mathematical analysis.