Ben Grant

from now on I'm just going to truncate the taylor series for sin at the first term. sin(x) = 0 for all x. this approximation

- is efficient to compute
- has bounded error
- has excellent analytic properties
- has very high accuracy for small values, which occur frequently in applications

the award or an HM, but because it feels like this reviewer didn’t take my application seriously at all, and I worry that I’m not the only person this happened to. End of rant, thanks for reading.

algebraic combinatorics— this reviewer was leaving comments about my desire to do research in “set theory,” about “supercompactness,” and about “the combinatorics of the first singular cardinal.” I did not mention any of these whatsoever.

I am mostly just disappointed, not because I didn’t receive

were almost directly copied but with additional typos that I didn’t make (???), but by far the most annoying part to me is that other bullet points were about things that I just *did not talk about at all* in my application. For context, the focus of my proposal was in representation theory and

detailed reviews that demonstrated they, at a minimum, read and thought about my statement and proposal. The third reviewer, on the other hand, left as their comments a relatively incoherent mix of bullet-point-style remarks. Some of these points were directly copied pieces of my statements, some

Very mild rant. GRFP reviews from last year’s application cycle came out a couple days ago. I applied last year but did not receive the award or an honorable mention (oh well, this happens, not the part that’s frustrating). Two of the three reviewers assigned to my application left very positive,

question, but it seems (to me) like a very natural point of view nonetheless.

the “regular functions” on A^n into an object R_n (i.e., taking R_n=Hom(A^n,A)) should give you the “algebraic” dual of the “geometric” A^n. Then duals of mappings f:A^n—>A^m are just their images f^*:R_m—>R_n under Hom(-,A).

I am not sure if this gives a reasonable answer to the original duality

This is perhaps naive and not-so-well-thought-out, but it seems to me like the question here might be interesting to look at from an algebraic geometry perspective. Morphisms A^n—>A appearing in an algebraic structure might be understood as “regular functions” on A^n as an “affine space.” Collecting

Ah, I see that someone else already beat me to this

understanding) one of the starting points of gauge theory

Correct me if I’m mistaken (I don’t know much physics), but I think what you’re talking about is that there are lots of different connections on the (trivial) fiber bundle R^3xR->R. Different connections give different ways of identifying points in different fibers. This is (to my very limited

Ah okay, I believe this works! I think (sort of like Brendan’s argument) this gives an embedding of the poset of functions [0,1) → ℝ ordered pointwise into the poset of all O(f) (given by (α ↦ r_α) ↦ O(the function you described))

I like this a lot!

Not sure about the partial order you get for arbitrary functions ℝ → ℝ, though. Certainly there are 2^c of these functions, but maybe it’s possible the poset of O(f) is strictly smaller?

There are only c functions ℕ → ℝ, and this set surjects onto the partial order you’re interested in, so it has cardinality c. If you’re interested in continuous or smooth functions ℝ → ℝ, there are also only c of these (by continuity, they’re determined by what values they take on ℚ)

Daniel Labardini Fragoso: Derksen-Weyman-Zelevinsky mutations of infinite-dimensional modules I: Foundations https://arxiv.org/abs/2508.21757 https://arxiv.org/pdf/2508.21757 https://arxiv.org/html/2508.21757

Decompositions of augmentation varieties via weaves and rulings The braid variety of a positive braid and the augmentation variety of a Legendrian link both admit decompositions coming from weaves and rulings, respectively. We prove that these decompositions agree under an isomorphism between the braid variety and the augmentation variety. We also prove that both decompositions coincide with a Deodhar decomposition and another decomposition coming from the microlocal theory of sheaves. Our proof relies on a detailed comparison between weaves and Morse complex sequences. Among other things, we show that the cluster variables of the maximal cluster torus of the augmentation variety can be computed from the Legendrian via Morse complex sequences.

arxiv.org/abs/2508.20226
/Decompositions of augmentation varieties via weaves and rulings/
Johan Asplund, Orsola Capovilla-Searle, James Hughes, Caitlin Leverson, Wenyuan Li, Angela Wu

A screenshot of some of the lyrics to “$0” by Cameron Winter on Spotify: God is real God is real I’m not kidding God is actually real I’m not kidding this time I think God is actually for real God is real God is actually real God is real I wouldn’t joke about this I’m not kidding this time

Man the lyricism here is something (excellent, beautiful song). I wouldn’t joke about this, I’m not kidding this time

Burn OpenAI to the ground.

SUBgroups Online peer groups for first-year math graduate students.

Registration for the SUBgroups program for first-year math grad students is now open!

Find out more and register here: gradsubgroups.org

Please share with any first-year math grad students you know who are looking for some regular peer support!

If I had a dollar for every time, I would have uncountably many dollars

“Recollements” do exactly this, I think

HBO Max and Disney Plus are my favorite tropical semiring

A picture of me holding a half-full cup of iced coffee from Caribou Coffee

Layover in Denver on my way to a workshop in Oregon this week, excited to do some math and see some friends

They’ve put it all right back into sports.

Roger Casals, Pavel Galashin, Mikhail Gorsky, Linhui Shen, Melissa Sherman-Bennett, Jos\'e Simental
Comparing cluster algebras on braid varieties
https://arxiv.org/abs/2508.03816

Totally and completely unrelated: if anyone can help me prove that a certain set is analytic but not Borel, let me know. I’ve tried finding a continuous reduction to it from the set of ill-founded trees in omega^<omega, but have not had any luck so far.

The one I have in mind is right at the sweet spot between logic and combinatorics, too, which is a place I always enjoy being

Good feeling when you come up with a research question that (1) you have no idea how to tackle and (2) the answer is going to be interesting, no matter what it is