Dean Baskin
@drbaskin.bsky.social
Mathematician, professor (Texas A&M). Opinions are my own.
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.
November 12, 2025 at 4:23 AM
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.
October 23, 2025 at 12:54 PM
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.
October 23, 2025 at 12:54 PM
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!)
October 21, 2025 at 6:37 PM
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
October 21, 2025 at 6:36 PM
We finished the PDE superstructure needed to get the exponential energy decay. Next up: eigenvalue counting
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.
October 18, 2025 at 12:30 AM
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
October 18, 2025 at 12:29 AM
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
October 9, 2025 at 1:27 AM
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!
October 9, 2025 at 1:27 AM
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
October 6, 2025 at 8:12 PM
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
October 6, 2025 at 8:11 PM
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.
October 3, 2025 at 4:33 PM
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!
October 3, 2025 at 4:31 PM
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.
October 1, 2025 at 4:55 PM
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!
October 1, 2025 at 4:53 PM
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.
September 30, 2025 at 2:51 PM
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.
September 30, 2025 at 2:50 PM
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.
September 27, 2025 at 1:53 AM
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.
September 27, 2025 at 1:52 AM
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.
September 20, 2025 at 2:19 AM
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.
September 20, 2025 at 2:17 AM
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.
September 20, 2025 at 2:16 AM
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.
Today was day 11: we started talking about covectors and one-forms and really tried to pin down the pairing between them and vectors. Students often struggle with this, so I spend a lot of time on it.
September 20, 2025 at 2:14 AM
Today was day 11: we started talking about covectors and one-forms and really tried to pin down the pairing between them and vectors. Students often struggle with this, so I spend a lot of time on it.