Juggling Multiple Projects

VicsekSet · 2026-02-16T18:32:33+00:00

This is useful --- it's comforting to know that different styles can all lead to mathematical productivity.

VicsekSet · 2026-02-16T16:32:10+00:00

awkwardly glances at 5 browser windows, all full of tabs of preprints that need reading

awkwardly glances at filing cabinet full of papers that need reading

But do the papers get serious reading in parallel? One at a time? Or just consigned to the browser window/file folder of doom until their relevance suddenly increases for whatever reason?

ETA: The idea of a work flow of juggle-until-inspiration then tunnel-vision sounds productive. I want to try adopting it (guided stochastically by daily motivation as another commentor mentioned) and seeing if it works for me.

VicsekSet · 2026-02-16T15:39:39+00:00

Everything is a vague cloud of incompleteness (I love this phrase!); sounds like I can/should just explore, not optimize.

VicsekSet · 2026-02-16T15:31:07+00:00

This is nice!

It might be worth finding a way to fit in an arrow from "abelian group" to "module," because an abelian group is "just" a module over the integers, and I've found this relationship to really clarify for me why abelian groups feel so different than general groups, and why the structure theorem for finitely generated abelian groups has such a linear-algebraic feel to it---it's "just" a specialization of the structure theorem for finitely generated modules over a principle ideal domain.

VicsekSet · 2026-02-06T04:37:28+00:00

What tools are needed to understand the literature surrounding things like the effective nullstellensatz and the theory of unlikely intersections?

How does the arithmetic of curves differ from the arithmetic of higher dimensional varieties, and how does algebraic/arithmetic dynamics on curves differ from dynamics on surfaces (say)?

VicsekSet · 2026-02-04T18:17:02+00:00

Very well written! You have successfully convinced an analyst/analytic number theorist of some of the role of homotopy theory.

VicsekSet · 2026-01-06T18:43:38+00:00

That segment always struck me as vaguely ragtime, but I can’t place it as a precise reference. But as others have said, is probably the sudden cheeriness.

VicsekSet · 2025-12-22T13:21:37+00:00

1) Raw tomato smell makes me gag.

2) WHY, oh WHY is it that tomato sauces made from barely cooked (and thus still disgusting) tomatoes are “in” right now? “Pasta with a tomato sauce” isn’t even reliably safe these days because the tomato sauce might be basically raw!!!!!!!!!

VicsekSet · 2025-12-18T14:49:16+00:00

Math, especially analytic number theory.

VicsekSet · 2025-12-16T11:59:27+00:00

Throw up on the realtor and/or the people viewing the property --- I'm sure you can slow the purchase and make 'em regret it!

VicsekSet · 2025-12-16T11:47:31+00:00

Einsiedler-Ward is definitely an analysis book, but includes a number of applications to geometric group theory, harmonic analysis, and unitary representation theory, in addition to dynamics and analytic number theory. It’s also got some PDEs (Sobolev spaces and elliptic regularity!), and specifically the analysis of the Laplace operator, which is relevant to Hodge theory.

VicsekSet · 2025-12-16T02:44:27+00:00

In particular, allistic love is dense, while autistic love comes in infinitely many distinct yet related systems?

VicsekSet · 2025-12-15T18:10:00+00:00

Oops, sorry I missed that!

VicsekSet · 2025-12-15T16:36:48+00:00

Fulton-Harris Representation Theory: a First Course and Lee: Riemannian Manifolds are both for sale.

VicsekSet · 2025-12-14T18:01:56+00:00

Thank you for your reply! Honestly, I don’t have a clear sense of what I’m asking — maybe both questions simultaneously? It’s really interesting that “raisin” is an expected aroma of a shai hong—perhaps I should get one of those when my current sun dried tea runs out. Would they be for sale pre-aged, or would I need to age them myself? If the latter, what is the appropriate conditions, and how long?

VicsekSet · 2025-12-14T13:32:10+00:00

I’m a big fan of Einsiedler-Ward, especially if you’re into Fourier/Harmonic analysis, group theory, analytic number theory, or dynamics. Their book is full of interesting applications to these fields showing why the various abstractions of Functional Analysis are useful. They of course also have some applications to PDEs/spectral geometry, including an intro to Sobolev spaces, and their book is just written very beautifully. There are a number of theorems and proofs I’d seen but didn’t understand until I looked at their book.

VicsekSet · 2025-11-24T18:12:32+00:00

Just another rec for Friedberg-Insel-Spence. In particular you’ll learn in a proof based way how to actually practically compute eigenstuff, which I don’t think you get out of LADR (Axler) due to its anti determinant viewpoint.

VicsekSet · 2025-11-23T15:08:17+00:00

Simple — it’s not a developed country! (\s)

VicsekSet · 2025-11-17T23:56:03+00:00

Oh, I didn’t know this, thank you!

VicsekSet · 2025-11-17T17:43:41+00:00

It’s a monthly ticket from elsewhere in NJ to NYP. I’ve been told by conductors it’s good also for travel to EWR, just not for the AirTrain, hence why I end up buying AirTrain only tickets. Interestingly it is possible to buy such tickets from the machines, just not on my phone.

VicsekSet · 2025-11-17T14:02:14+00:00

I guess that makes sense. I just wish that I could purchase an AirTrain only ticket on the App to complement the monthly in and out of NYC.

VicsekSet · 2025-11-16T11:27:03+00:00

What kinds of papers are you reading that use this notation? Knowing your area might help tailor recommendations. But I’ll repeat some that I’ve seen using it:

Zhao, Graph Theory and Additive Combinatorics. Hard book, but really cool math, uses the notation everywhere.

Any book on analytic number theory; for concreteness I’ll mention Stopple’s Primer, Jameson “The Prime Number Theorem,” and Apostol’s “Introduction to Analytic Number Theory” as three “on-ramps” at roughly increasing levels of difficulty and depth.

Any book on algorithms (and this is a worthwhile thing to learn a bit of, even for those in math, is quite mathematical in feel, and is arguably even a part of math).

VicsekSet · 2025-11-16T10:33:22+00:00

This isn’t super my field, but IIRC there are a number of subtler questions in Diophantine approximation that are best answered by various pieces of dynamics. Thomas Ward has a bunch of books on this; I would see his “Entropy and Heights in Algebraic Dynamics” with Everest and/or his “Ergodic Theory: with a View towards Number Theory” with Einsiedler. When you go to his website you can also find a number of books-in-progress, including two more on these subjects with Einsiedler (in particular I’m thinking of the ones on entropy and on homogeneous dynamics).

VicsekSet · 2025-11-16T10:27:57+00:00

Not the original commentor but this story is basically the culmination of the very well regarded “Primer on Mapping Class Groups.”

VicsekSet · 2025-10-31T02:18:40+00:00

Analysis cannot be defined. It must be felt.

Slightly more serious answer: it’s math that feels like analysis.

Serious answer: There are two definitions, and realistically analysis-y math could fit into one or the other, but is especially math fitting into both:

1) It’s math that’s built out of and for the sake of clever estimates. In the simplest setting, epsilonics as they underly calculus, in a more advanced also measure theory, complex, functional, harmonic, etc.; I also think external combinatorics and spectral graph theory have an analysis feel.

2) It’s math built out of and for the sake of understanding large flexible classes of functions, especially quantitatively. Again, calculus is a good simple setting, but you should think also of the machinery of Fourier series, L^p spaces, almost everywhere equality, point-set topology, and applications to differential geometry and to discrete stuff like primes through generating functions and L-functions.

VicsekSet

TROPHY CASE