The hottest Topology Substack posts right now

And their main takeaways
Category
Top Science Topics

Tips for new community members

Quantum Formalism • 39 implied HN points • 09 Mar 22
🚌 Education Mathematics Physics Geometry Topology Group Theory
  1. Start with the 'Foundation Module' YouTube playlist for basics on finite-dimensional Hilbert spaces and quantum mechanics postulates
  2. Consider auditing crash courses on topics like Topology & Differential Geometry for Lie Groups and Group Theory for advanced knowledge
  3. Exploring topics like smooth manifolds and Group Theory can be valuable not just in quantum computation but also in applied fields like ML and Cryptography

Linear Algebra Is Not Enough!

Quantum Formalism • 59 implied HN points • 01 Jun 20
🔬 Science Mathematics Quantum Mechanics Functional Analysis Topology Group Theory
  1. Linear Algebra is foundational in quantum mechanics but may not be enough if dealing with infinite-dimensional Hilbert spaces.
  2. To fully understand quantum mechanics, one needs to delve into Functional Analysis along with other mathematical branches like Topology, Measure Theory, and Group Theory.
  3. The newsletter focuses on explaining the mathematical formalism of quantum mechanics through easily understandable posts on relevant topics.

Lecture 3 Replay

Quantum Formalism • 19 implied HN points • 02 Aug 21
🚌 Education Quantum physics Topology
  1. The lecture was split into 3 parts for easy replay: Opening Discussion & Post Crash Course Program, Introduction to Metric Spaces (PART A), and Introduction to the Metric Topology (PART B).
  2. Viewers can watch the replay on YouTube after networking issues during the live session.
  3. The registration page for the next live session on the Topology Crash Course is available at the provided link.

Influential Mathematicians: Maurice René Fréchet

Quantum Formalism • 19 implied HN points • 23 Jul 20
🔬 Science Mathematics Quantum Mechanics Statistics Topology Functional Analysis
  1. Maurice René Fréchet, a disciple of Jacques Hadamard, made significant contributions to mathematics through his work on metric spaces and abstract spaces, laying the groundwork for modern mathematical formalism, including quantum mechanics.
  2. Fréchet's research on functional analysis has influenced the development of the quantum formalism, allowing for the creation of abstract concepts crucial in understanding quantum mechanics.
  3. The Riesz–Fréchet representation theorem plays a key role in making mathematical sense of Dirac's bra-ket notation used in quantum mechanics, showcasing the impact of Fréchet's work in this field.

Lecture 5 Replay

Quantum Formalism • 0 implied HN points • 12 Sep 21
🚌 Education Quantum physics Topology
  1. The replay of lecture 5 is available on YouTube, split into 3 parts for convenient viewing and discussing path-connectedness, open covers, and compactness.
  2. Registration is open for lecture 6 on topology, focusing on the manifold section.
  3. You are encouraged to join the Discord community server as part of the Quantum Formalists group for further discussions and engagement.
Get a weekly roundup of the best Substack posts, by hacker news affinity:

Lecture 5 Invitation

Quantum Formalism • 0 implied HN points • 06 Sep 21
🚌 Education Topology
  1. The upcoming lecture will focus on a topology crash course before moving on to topological manifolds.
  2. Registration is available for the lecture happening this Friday at 5 pm BST.
  3. You're encouraged to join the Discord community server for further engagement.

Lecture 4 Replay

Quantum Formalism • 0 implied HN points • 16 Aug 21
🚌 Education Quantum physics Topology
  1. The replay of lecture 4 is available on YouTube split into 3 parts for easy viewing.
  2. Registration for lecture 5 is open, leading into the much-anticipated manifold section.
  3. Lecture 4 covers topics such as Topological Bases, Product Topology, Topological Invariants, and Connectedness.

Tessellating the Globe

Bram’s Thoughts • 0 implied HN points • 18 Jan 24
🔬 Science Geometry Topology
  1. The world jigsaw puzzle design has imperfections when trying to tessellate it without visible seams.
  2. Two geometries proposed to fix the issue involve dividing the globe into hemispheres and deforming them into squares or into triangles corresponding to a tetrahedron's faces.
  3. Alignment of these geometries with the equator and land bodies is an interesting challenge.

Lecture 2 Replay

Quantum Formalism • 0 implied HN points • 16 Jul 21
🚌 Education Quantum physics Topology
  1. The lecture replay covers a topology crash course.
  2. The session was split into 3 parts: Intro & Industry Fellowship Announcement, Main Lecture, and Extra About Measure Theory.
  3. The speaker promised a future crash course on Measure Theory & Functional Analysis to refine the definition of sigma-algebra in constructing one from finite topologies.

Replay + Invitation to Lecture 2

Quantum Formalism • 0 implied HN points • 05 Jul 21
🚌 Education Quantum physics Topology
  1. Lecture one is now available on YouTube, split into Welcome & Agenda, PART A (Course Introduction & Comments), and PART B (the actual Topology lecture).
  2. The next lecture on Topology is scheduled for Friday, July 16, with registration open. Joining the Discord community is recommended to connect with others and set up study groups.
  3. There was a gap before the next lecture to allow time for understanding topological concepts and solving challenges. This was decided based on a poll to give participants more time for preparation.

Discord Server Invitation + Background Poll

Quantum Formalism • 0 implied HN points • 30 Jun 21
🚌 Education Topology Crash course Survey
  1. Join the Quantum Formalism Discord server for a topology crash course.
  2. The crash course will cover core concepts like topological spaces, closed sets, subspace topology, neighborhoods, and Hausdorff spaces.
  3. The course will include elements of Differential Geometry in the manifold section and participants are asked to fill out a short survey to help adjust the level of abstraction.

Lecture #1 Reschedule

Quantum Formalism • 0 implied HN points • 15 Jun 21
🚌 Education Physics Topology
  1. The first lecture on Topology Crash Course has been rescheduled due to a funeral service on June 25
  2. Alternative dates offered are June 24, June 29, and July 2, all at 5pm BST
  3. Participants are reminded to review basic set-theoretic and real analysis concepts mentioned during the last Q&A session

Lie Theory Prerequisite

Quantum Formalism • 0 implied HN points • 28 Apr 21
🔬 Science Quantum Mathematics Topology Deep Learning
  1. The post provides a crash course motivation and schedule for Lie Theory, encouraging viewers to watch preparatory material on YouTube and offering usage cases outside of mathematics for motivation.
  2. Highlighted articles and studies demonstrate real-world applications of Lie Theory in areas like quantum computation, deep learning, and unitary operators in quantum mechanics.
  3. The presenter provides access to slides and recommended study materials on GitHub, emphasizing the importance of preparation before the upcoming course session on Lie Theory.

Latest Community updates

Quantum Formalism • 0 implied HN points • 12 Apr 21
🚌 Education Mathematics Physics Topology Geometry
  1. The Lie Theory prerequisite mini-series will focus on point-set topology, metric spaces, and basics of differentiable manifolds.
  2. Reviewing basics of set theory, including intersections, unions, Cartesian products, and maps between sets, is recommended for the upcoming lectures.
  3. While the Lie Theory module may not be sufficient to understand Eric Weinstein's 'Geometric Unity' paper, it provides a foundational knowledge base that can ease the understanding of complex topics in differential geometry and topology.

Certificate of Attendance versus Certificate of Completion + Quantum Webinar

Quantum Formalism • 0 implied HN points • 04 Nov 21
🚌 Education Topology Certificates Crash course
  1. Two certificates are being issued for the crash course: Certificate of Attendance for those who attended the entire course, and Certificate of Completion for those who comprehend the basics discussed.
  2. The crash course covers topics like topological and smooth manifolds.
  3. A Quantum Webinar by Dr. Ryuji Takagi from Nanyang Technological University in Singapore is scheduled, presenting their recent ArXiv paper 'Fundamental limits of quantum error mitigation'.

Lecture 6 Registration

Quantum Formalism • 0 implied HN points • 29 Sep 21
🚌 Education Lecture Topology
  1. Lecture 6 registration for the topology crash course is now open at the provided crowdcast link.
  2. The lecture will feature a cartoon joke at the end, involving a flat earth theorist and a mathematician (topologist).
  3. Joining the Discord community server is highly encouraged for more engagement and interaction.