Sheaf Theory retweeted
This is why no one in the Netherlands gets hired anymore, and it's only the country with the 2nd highest employment rate in the world
As a Dutch person let me tell you it's way worse than it seems.
The AVERAGE stress related absence is 250+ days. The AVERAGE burnout related absence is 300+ days.
While on sick-leave, you can return to work for just 4 weeks and the 2 year period **resets**.
Your employer is forced to assist you in this. They have to pay for doctors, experts, and so on. If they don't, you get an extra year's wages.
While on sick-leave, you can work a second job. As long as this is outside business hours of the first job, or the work is different, your first employer still pays you 70%.
Here's another cool one: you can go on holiday during sick-leave. The employer can force you to use your vacation days for that, but then they have to pay you 100% of your wages rather than 70% during that period.
Simple solution: you just work with contractors right? No, because a contractor can just claim employee status after getting sick. Many such cases.
All of this is obviously broken. If you say this you're met with half-baked "worker's rights" arguments, as you can see in this comment section.
Sheaf Theory retweeted
Big, big, big, big props for quasiriemann and no Siegel zeroes (with many other beauties in there), I’m kicking myself for talking all over about it being within reach but not actually having pushed.
There are some sad stories related to their users getting scooped / conflicts of interest (kakeya maximal comes to mind), and obviously we had some of the problems (without commenting on precise rumours).
We should put that aside for today though. It’s obviously the most significant moment in mathematical history.
Sheaf Theory retweeted
Why can a heat pump deliver more heat than the work supplied while no engine converts every bit of heat into work?
Engines, heat pumps and refrigerators share the same energy balance but measure success differently.
- Engine: absorbs Qₕ, produces W → η = W / Qₕ.
- Heat pump: work W delivers Qₕ → ε = Qₕ / W (often >1).
- Refrigerator: work W extracts Q_c → ε = Q_c / W.
This math runs car engines, efficient heating and food cooling. Energy conservation is universal; the goal sets the figure of merit.
Sheaf Theory retweeted
"Masters Math Lectures and Assignments" by Richard G. Klotz is a free collection of university mathematics lecture notes and problem sets.
The website has material on Calculus I–III, Vector Analysis, Differential Equations, Linear Algebra, Analysis, Abstract Algebra, Complex Analysis, Differential Geometry, Calculus on Manifolds, and Real Analysis. Each course has lecture notes and assignments available as downloadable PDFs.
The notes explain both the theory and the methods used to solve common problems, including derivatives, integrals, differential equations, linear systems, vector spaces, and other topics.
This is a useful resource for university students, for those starting a degree in mathematics, engineering, physics, or computer science, and for anyone who needs to review or study undergraduate mathematics.
univmathnotes.com
Sheaf Theory retweeted
"Algebra, Topology, Differential Calculus, and Optimization Theory for Computer Science and Machine Learning" is an excellent free university-level textbook on the mathematical foundations of computer science and machine learning.
Across more than 1,000 pages, it covers groups, rings, fields, vector spaces, bases, linear maps, matrices, direct sums, determinants, Gaussian elimination, LU and Cholesky decomposition, echelon forms, iterative methods for solving linear systems, differential calculus, topology, convexity, optimization, and many other topics.
It is a rigorous, broad, and modern reference with a clear focus on the mathematics behind AI, machine learning, and computer science.
cis.upenn.edu/~jean/math-dee…
Sheaf Theory retweeted
A Black Hole Can Be Dragged Through Spacetime
A Black Hole does not have to sit still.
Einstein’s equations allow a stranger possibility... a Black Hole that accelerates.
This is the C-metric, an exact solution of General Relativity describing an accelerating Black Hole.
The Black Hole accelerates because the geometry of Spacetime says it must.
The C-metric is one of those exact solutions that reminds us how wild General Relativity really is. Gravity is not just attraction, and Spacetime is not just a stage.
Sometimes the stage itself contains the force.
#Astrophysics #GeneralRelativity #Einstein #CMetric #BlackHole #CosmicStrings #Spacetime #Cosmology #Mathematics #Physics
Sheaf Theory retweeted
Intricate hydrodynamic patterns emerge when fluids interact with curved manifold geometries.
The upper panel demonstrates the exterior calculus formulation of continuum mechanics on manifolds through a three-dimensional radial manifold shape, a curved surface patch with tangent vectors, and coordinate representations of the tangent and cotangent spaces.
The lower panel shows computed hydrodynamic flow responses on complex manifold shapes, with applied forces inducing vortices and saddle points in the flow.
It is used to simulate fluid behavior on curved surfaces in studies of soft materials and biological interfaces.
