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31.01.2026 00:46
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This is a great thread that applies equally well to math programs.
Damn who knew the law of all places would have so many rules
She came to the B/CS no kings protest, so at least she realizes we’re also in the district
I tried them for a year and loved them so much I just subscribed for the next ten.
If you’re looking for a variety of millennial-coded crosswords that don’t mess around with cutesy clues for fascists, arrive frequently, can be played online or printed on paper, are reasonably priced, and have a great response, I strongly recommend @avcx.bsky.social
The Ivy and Bean books are great! Also Kate DiCamillo has a one-off (I think) called flora and Ulysses, which is about a girl and her friend Ulysses (who is a squirrel that obtains super powers after being sucked into a vacuum)
I read Vonnegut’s breakfast of champions when I was 14 and took the same lesson from it. I’ve only recently gotten into discworld and love its moral spine.
We started a new topic: eigenvalue counting, working towards the weyl law.
On Wednesday we discussed symmetries of the Riemann curvature tensor and introduced the ricci and scalar curvatures.
Yesterday we managed to introduce the curvature tensor. (Finally!)
We finished the PDE superstructure needed to get the exponential energy decay. Next up: eigenvalue counting
No Kings protest in College Station, TX. Texas A&M showed up. Somewhere around two thousand people showed up. #NoKings.
We are proving exponential energy decay for the damped wave equation under the geometric control condition. We have proved the resolvent estimate and are working towards the result.
After fall break we have introduced manifolds and left the comfort of flat space times behind. We are barreling toward curvature and (finally!) the Einstein equations
Today we introduced Christoffel symbols and the covariant derivative
We proved that semiclassical defect measures are concentrated on the energy surface and invariant under Hamilton flow. We will start talking about the damped wave equation soon!
Today we finally introduced semiclassical defect measures. I am hoping to start talking about the damped wave equation on Wednesday
We’re doing general coordinate changes and about to introduce the covariant derivative
I want to get to semiclassical measures so I just presented most of the rest of the calculus as a list of properties. I think we will probably use Hörmander’s trick for L2 boundedness, though.
Changing coordinates, tangent and cotangent spaces! It’s getting fun!
Today we did the composition law for general symbols. I think starting Friday we will restrict our symbol classes quite a bit to make our lives easier.
Today we differentiated tensors in inertial frames in special relativity and then spent the rest of class arguing that inertial frames cannot exist in the presence of gravity. Onward!
Working toward composition for general symbols.
Yesterday we talked about more general tensors, which included a he identification of a finite dimensional vector space with its double dual.
Today we discussed one-forms as arising (locally) from differentials of functions and the one-form/vector pairing as directional derivatives. I think we have one more day of general tensors before we finally get to the equivalence principle.
Today we proved the Borel lemma and started working toward various composition formulas for symbol classes.
This is in sharp contrast to the analytic case, where having a nonzero radius of convergence imposes a pretty significant bound on how fast the sequence of derivatives at zero can grow. In contrast, for smooth functions, you can specify them and they can grow arbitrarily quickly.
That problem: given any sequence of numbers a_k, there is a smooth (C^\infty) function with the k-th derivative of f at zero being equal to a_k.
Today was day 11. We proved the composition formula for left-quantized operators and introduced symbol classes. Next time we will prove Borel’s lemma as it relates to symbols. This theorem has essentially the same content as one of my favorite graduate analysis problems.