The Milnor conjecture, proposed by John Milnor in the 1950s, is a statement in the field of algebraic topology, particularly concerning the nature of the relationship between the topology of smooth manifolds and algebraic invariants known as characteristic classes. The conjecture specifically relates to the Milnor's "h-cobordism" theorem and the properties of the "stable" smooth structures on high-dimensional manifolds.
Esakia duality is a correspondence between two categories: the category of certain topological spaces (specifically, spatial modal algebras) and the category of certain algebraic structures known as frame homomorphisms. This duality is named after the mathematician Z. Esakia, who developed the theory in the context of modal logic and topological semantics.
Ind-completion is a concept from the field of category theory, specifically related to the completion of a category with respect to a certain type of structure or property. In mathematical contexts, "ind-completion" often refers to a way of completing a category by formally adding certain limits or colimits.
The Gromov boundary is a concept in geometric topology, particularly in the study of metric spaces, especially those that are geodesic and hyperbolic. It is used to analyze the asymptotic behavior of spaces and to understand their large-scale geometry. More formally, the Gromov boundary can be defined for a proper geodesic metric space. A metric space is considered proper if every closed ball in the space is compact.
The Švarc–Milnor lemma is a result in differential geometry and algebraic topology, particularly concerning the relationship between the topology of a space and the geometry of its covering spaces. It is named after mathematicians David Švarc and John Milnor.
Sequence breaking is a term used primarily in the context of video games, particularly in speedrunning and exploration within metroidvania-style games. It refers to the act of bypassing or circumventing certain parts of a game's intended progression sequence. This can be achieved through various means, such as glitches, exploits, or creative use of game mechanics.
A **metric space** is a mathematical structure that consists of a set equipped with a function that defines a distance between any two elements in the set. More formally, a metric space is defined as a pair \( (X, d) \), where: 1. **Set**: \( X \) is a non-empty set.
Irina Novikova is a physicist known for her work in the field of quantum optics and photonics. She has made significant contributions to areas such as electromagnetically induced transparency (EIT), quantum memory, and the interaction of light with matter. Her research often involves exploring how light can be controlled and manipulated at the quantum level, which has important implications for quantum information science and technology.
Lev Pitaevskii is a notable Russian physicist known for his significant contributions to the fields of statistical mechanics and condensed matter physics. He is particularly recognized for his work on quantum fluids, including Bose-Einstein condensates, and for co-developing the Gross-Pitaevskii equation, which describes the behavior of such systems.
Michael Tendler is not a widely recognized public figure, so there is limited information available about a person by that name. It's possible that he is a private individual or someone who may have emerged in news or popular culture after my last update in October 2023.
Sergey Bagayev is a scientist known for his work in the fields of mathematics and computer science. While specific details about his contributions may vary, he is typically recognized for his research and publications in areas such as algorithms, computational theory, and potentially other interdisciplinary applications involving mathematics and technology.
Soudan 2 is a neutrino detector located at the Soudan Underground Laboratory in Minnesota, USA. It was originally constructed as a continuation of the work in the field of particle physics aimed at detecting neutrinos, which are extremely light and elusive subatomic particles. Soudan 2 began full operations in the late 1980s and was designed to study neutrinos produced by cosmic rays and by the Sun.
Norio Kaifu, or KAI-FU, is a well-known figure in the field of artificial intelligence and machine learning. He has held prominent positions in major technology companies, including Apple, Microsoft, and Google, where he has contributed to the development of various AI technologies. Kaifu is also recognized as an entrepreneur and author, often discussing the implications of AI on society, economy, and technology.
Margaret Oakley Dayhoff (1925–2017) was an influential American biochemist and a pioneer in the field of bioinformatics and computational biology. She is best known for her foundational work in developing methods for comparing protein sequences, as well as for creating the first comprehensive protein sequence database. Dayhoff played a crucial role in advancing computational techniques that helped analyze biological data, which made significant contributions to our understanding of molecular biology and genetics.
Dimitra Markovitsi does not appear to be a widely recognized public figure or entity as of my last knowledge update in October 2023. It's possible that she could be a private individual, a lesser-known professional, or someone who has gained recognition after that date.
Jaume Mora could refer to various things depending on the context, but it is not a widely recognized term or figure that I am aware of based on my last knowledge update in October 2023. It might refer to a person, a place, or perhaps a brand or concept that emerged after my last update.
"Surfaces" can refer to different concepts depending on the context. Here are a few interpretations: 1. **Mathematics and Geometry**: In mathematics, particularly in geometry, a surface is a two-dimensional shape that can exist in three-dimensional space. Examples include spheres, planes, and more complex shapes like toruses or paraboloids. Surfaces can be described mathematically using equations.
As of my last knowledge update in October 2023, there is no widely recognized product, service, or concept specifically known as "Circumgon." It may be a term, brand, or a concept that emerged after that time or could potentially be a misspelling or a lesser-known term.
The term "Triple Helix" refers to a model of innovation that emphasizes the collaboration between three key sectors: academia, industry, and government. This concept is used to explain how these three entities can interact and collaborate to foster economic growth, technological advancement, and social innovation. 1. **Academia**: Represents research institutions and universities that generate knowledge, conduct research, and develop new technologies.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact