Oh yeah, before I forget! My tex notes for this semester are finally up-to-date. Thread with links and some quick previews (1/?)
Floer Homology

(Pictures entirely due to the wonderful Akram Alishahi!) ImageImageImageImage

(Pictures adapted from originals by Philip Engel!) ImageImageImageImage
Algebraic Number Theory

Paul Pollack is also posting YT videos of these lectures here:
youtube.com/playlist?list=… ImageImageImageImage
Homological Algebra (a personal fave!!!!)

Most diagrams here (and, well, everything else lol) sourced from Brian Boe's lectures, along with a few from Weibel ImageImageImage
But yeah, hopefully these are enjoyable or useful to others! I update them periodically throughout the semester.

Also, I definitely make zero claims to originality LOL, they're basically just glorified (sometimes reworded) transcriptions.

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More from @dzackgarza

7 Jan
For anyone interested in such things, I think I've found a nice workflow for sanely reading + annotating papers on a tablet:

- Run Zotero in the bg on your PC, and use the "Save to Zotero" Chrome extension on PDFs

- In Zotero, use Zotfile's "Push to Tablet" feature..
...with its settings pointing to a Dropbox folder.

- Use Dropsync to automate folder syncing to the tablet

- Put a link to that folder on your home screen, then set Xodo as the default PDF app

- Read, annotate with a stylus

- Next time you're on your PC, "Get From Tablet"
And it just updates the existing PDF attachment with the annotated one. It seems like you can just push/pull files en masse too, so the 2 manual steps aren't awful.

Also, Xodo is great, it distinguishes pen/touch: touch for scroll/zoom, pen for selecting text to highlight
Read 4 tweets
7 Jan
Biggest goal for the new year: consistently tracking things! I feel so much better when I throw things into my todo list and stick to them.

I'm working on better tracking long-term goals now, since these end up needing slightly more than lists 😅
I need to make time a meaningful concept until vaccines are out, so I'm trying out daily/weekly/monthly goals. Just some light "# of Pomodoros doing X" kinds of things, like practicing scales, re-synthesizing old notes, or reading new math books.
Incidentally, I think this is one aspect of student life that we don't talk abut enough! Seeing how other people accomplish goals and stay productive can be really inspiring imo. Tons of people share their methods in the fitness world, way less so in academia.
Read 5 tweets
5 Jan
Oh yeah, and forgot to post about these yesterday:

1) I've started including some (sane!) source code for my tex notes Image

2) Some significant updates to last year's notes on moduli spaces! Fixed a lot of broken/missing diagrams, and moved it to the most recent template to defs/theorems/exercises are highlighted. ImageImageImage
I made a lot of the gnarly diagrams and equations actually readable, and added some very exciting Inkscape+Tikz diagrams lol ImageImageImage
Read 4 tweets
1 Jun 20
Follow-up thread with the other half of the solution to this problem: computing the homology of this glued ("adjunction") space!

This will mostly be an excuse to talk about one of my favorite theorems from introductory algebraic topology: the Mayer Vietoris sequence.

(Full disclosure, there is a *much* easier way to do this problem, namely finding a nice space homotopy equivalent to X.)

Recall that our adjunction space X was described as "2 spheres glued along their equators by a degree 2 map".

Read 27 tweets
26 May 20
A small thread about (part of) the solution to this problem! (1/n) Image
For now, let's just think about computing the fundamental group, π_1(X). First things first: what exactly are we working with?

For Topology questions, often a good start is to ask yourself "What's the picture?"
Here's a depiction: we're starting with two 2-spheres (in equations, just subsets of Euclidean space of the form (x-a)^2 + (y-b)^2 = r^2), here A and B.

Both have an "equator", i.e. a distinguished embedded copy of a circle S^1, say all of the points with y coordinate 0.
(3/n) Image
Read 17 tweets
28 Oct 19
1/ Finally had some time to review my conference notes, so here's a thread on the talks!

The actual abstracts are here: math.virginia.edu/2019/09/mid-at…
2/ The first talk was about how certain H-spaces (a generalization of topological groups) -- those with no "v_n torsion" -- can be expressed as product of certain irreducible H-spaces Y_k that 1) also have no v_n torsion, and 2) are somewhat understood.
3/ This parallels how spaces can be characterized (up to homotopy equivalence) as "twisted products" of Eilenberg-MacLane spaces (the "atoms" of homotopy theory) using Postnikov towers.
Read 36 tweets

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