I've been asked to serve as a founding (co)editor-in-chief of a new mathematics journal. There is some freedom in setting journal policy, etc.
What are some things that you want to see when it comes to dealing with journals? What do you hate about the process?
Share widely!
If this tweet gets > 500 ♥️s, I will compile the entire set of Computational Algebraic Topology lecture notes (8 Chapters, 106 pages) into a single hyperref-ed PDF and share the link here.
Pass it along.
I am teaching an 8-week course at Oxford on the fundamentals of topological data analysis (including persistent homology, cellular sheaves, & discrete Morse theory).
All Notes:
All Videos:
Course thread! (0/8)
In lieu of my soundcloud, here's the promised pdf containing all the lecture notes for the Computational Algebraic Topology course:
Curious about topological data analysis, persistent homology, cellular sheaves or discrete Morse theory? Check them out!
If this tweet gets > 500 ♥️s, I will compile the entire set of Computational Algebraic Topology lecture notes (8 Chapters, 106 pages) into a single hyperref-ed PDF and share the link here.
Pass it along.
Topological Data Analysis as you've never seen it before:
@robertghrist
is bringing my lecture notes () to life in a new animated video series ()!
Here are the videos which have been released so far... enjoy! And tell your friends.
Last week, I co-organised a workshop at the lovely
@NewtonInstitute
in Cambridge. We tried to do a few things differently; some of these worked well, others didn't.
Here are two principles that worked well.
1/6
Like many of you, I've recently had to make my peace with asynchronous lectures. This term, I'm teaching Computational Algebraic Topology
@OxUniMaths
--- this course covers the foundations of topological data analysis and is meant for senior undergraduates.
(1/4)
Annual reminder that I am teaching this topological data analysis course again this term
@OxUniMaths
, and *all of the materials are already online* so you can follow along at your pace :)
I am teaching an 8-week course at Oxford on the fundamentals of topological data analysis (including persistent homology, cellular sheaves, & discrete Morse theory).
All Notes:
All Videos:
Course thread! (0/8)
Outstanding bit of notation that I've just seen in a graduate student's thesis writeup:
B_r(x) for open ball of radius r around x, and B_r[x] for closed ball.
Don't know if he got it from somewhere, but I'm kicking myself for not thinking of this for my own papers...
The two stages of math problem solving, or why math is so depressing:
1. This problem is so hard, I don't even know where to start. I must be stupid.
2. The solution was so obvious I can't believe I spent so much time without seeing it. I must be stupid.
Many mathematicians, whether they confess it publicly or not, have a "Tombstone Theorem" --- the result you'd want on your tombstone if you were to pass away today.
Here's mine.
(0/8)
I'm fascinated by this amazing phase transition that occurs around year 2 or 3 of graduate school.
All meetings before this magic moment involve me explaining things to my grad students, and all meetings after that involve them explaining things to me.
Here are twelve pages on
#PersistentHomology
, which is the focus of Week 6 in the Computational Algebraic Topology course. I'm giving all my secrets away :)
Course webpage if you want to see older notes to chase backreferences!
Also:
1) You don't like the explanation you read
2) With much effort you figure out a clear explanation
3) It is basically identical to the original explanation you disliked, but somehow it makes sense to you now
How learning math works:
1) You don’t like the explanation you read.
2) With much effort you figure out a clear explanation.
3) The explanation you came up with is obvious to experts but nobody ever mentions it.
ProTip: if you want to learn everything there is to know about derived categories, just draw this sigil on your mirror at midnight and chant “RHom Verdier” three times.
I usually avoid writing papers that either (1) have lots of co-authors, or (2) contain no genuinely new ideas, or (3) require me to read *many* of existing papers.
This new paper violates all three rules...
1/7
Many years ago, I saw a much-beloved Mathoverflow question by
@wtgowers
on "Common False Beliefs in Mathematics":
Last week I realized that I held a false belief. I don't know if it's common, but it is downright INFURIATING.
(1/7)
Introducing 🔥GeoTorch🔥, my student Mario L Casado's cool new library for optimization on interesting Riemannian manifolds. It handles Stiefel varieties, Grassmannians, and Lie groups! If you're thirsty for deep learning on SO(n), check it out :)
1/ Here are two stories about my graduate school experience at Rutgers, both about a man who has played a much larger role in my career than he realised.
I've seen so much terrible academic advice on this website over the last few days (thanks to this wretched default "For you" tab) that I have decided to start offering my own.
1. Don't waste time studying the p-adics, their p-value is always larger than 0.05
The notes for Week 3 of Computational Algebraic Topology contain one weird homology trick, recently discovered by a PhD student (tenured profs hate it!)
Very cool new paper by Jabob Leygonie and Greg Henselman-Petrusek on the following inverse problem: given a barcode, find a filtered simplicial complex whose persistent homology realizes that barcode.
The course starts on Monday --- in Week 1 we will cover simplicial complexes, geometric realizations, simplicial maps, and how to associate filtrations to finite datasets. The journey begins here:
Notes:
Videos:
Week 4 of Computational Algebraic Topology is here! These lecture notes serve as an appetizer for both category theory and homological algebra en route to describing powerful tools for working with simplicial homology!
Lecture 3 of computational algebraic topology is up! Here we meet Euler characteristics, chain complexes and homology. If you make it to the end, there's ONE WEIRD PICTURE THAT EXPLAINS EVERYTHING. OTHER IMAGES HATE IT.
Homologists of the world, unite! You have nothing to lose but your chains.
The final week of Computational Algebraic Topology involves discrete Morse theory, a wonderful tool for homology-preserving reduction of large chain complexes.
Notes:
I usually avoid writing papers that either (1) have lots of co-authors, or (2) contain no genuinely new ideas, or (3) require me to read *many* of existing papers.
This new paper violates all three rules...
1/7
After a great collaboration to join efforts ... here it is: our Xmas present for TDA practitioners🥳
It was a big pleassure to work with Dashti Ali,
@Aras121
,
@viditnanda
,
@eduph_tw
and Manu Soriano-Trigueros
I have to read like 300 postdoc applications this morning. Just wanted convey a big thank-you to the wonderful person who opened their research statement with
"My research interests fall into a few main categories, most of which are Abelian."
Baby
#2
is due any day now, and I am too wired to do the intelligent thing (i.e., sleep).
So please join me, the wonderful
@osumray
, and
@haharrington
on a journey through some fun machine learning & representation theory.
1/11
It is an edict of the Archangel Gabriel that directed graphs shall be called "quivers" before one can do any representation theory on them. Here's a short thread to celebrate a new preprint () with
@annaseigal
and
@haharrington
.
(1/7)
Here are twelve pages on
#PersistentHomology
, which is the focus of Week 6 in the Computational Algebraic Topology course. I'm giving all my secrets away :)
Course webpage if you want to see older notes to chase backreferences!
I should be proving theorems, but I can't stop thinking about a hypothetical restaurant which exclusively serves appetizers in large portions and is called "Hors d'oeuvres of Magnitude".
Ever tried to sneak sheaves, derived categories and local cohomology into
@PNASNews
? Not easy, but with help from outstanding co-authors it can be done.
Thanks to
@haharrington
, Jared Tanner, and most of all, to Bernadette Stolz!
Special Announcement: the Bourbakistas and von Neumenn have logged on to tell us that ordinary multiplication of positive integers doesn't actually commute.
Recently had the amazing experience of being completely disarmed by an anonymous referee report. After this paragraph, even if the referee had recommended that I "replace all the words with new ones," I would have done so with a smile on my face.
The iconic image of the supermassive black hole at the center of Messier 87, has received its first official makeover, thanks to a new machine-learning technique known as PRIMO! 🧵⬇️
A new picture-filled thread for a new paper!
This is joint work with Ulrike Tillmann and our awesome student Marc Fersztand. To my mind, it is the first point of contact between topological data analysis and geometric invariant theory.
1/12
Mathematicians on the academic job market this year: please reply with a description of (or link to) your work!
If there are enough responses, I will leave this tweet pinned for the next few months and hopefully more people will get to hear about you.
Good luck 👍
I'm co-organising a 6 month program
@NewtonInstitute
on all things equivariant & geometric in early 2024!
If you are interested in attending some or all of this — esp. Workshop 2 — please drop me a line, and tell all your friends :)
[1/20] Complexes of groups are concrete objects living at the intersection of many abstract fields of mathematics: algebraic topology, algebraic+differential geometry, and even higher categories.
But their most natural home is in geometric group theory...
I've never understood this weird stereotype of the British being a pessimistic people. You can't walk 15 minutes along any path in Oxford without stumbling across a bloody sundial. If that's not a sign of unrelenting optimism, I don't know what is.
Homotopy theory has a formidable (and richly deserved!) reputation: too abstract, hard to compute... But large parts can be made concrete, and help simplify computation of weaker topological invariants (eg cohomology). Homotopy is the focus of Week 2 of the TDA course!
(1/3)
Week 7 of computational algebraic topology is all about sheaves! Check out the notes (if you dare)
You will meet sheaf cohomology, etale spaces, sections... And I think the title picture is
@robertghrist
's best one yet
Care to participate in another experiment? I've never done a thread on twitter before, and I really want to *show* you one of my favorite mathematical objects. Sounds like a two-for-one; let's go! 1/13
@littmath
"Jake, the senator has repeatedly mentioned that he wants the states to have more powers. I agree, but we need to go further. The best system of governance is one where each community locally decides what is best for it.
In fact, let L be such a local system..."
A brief thread about this shiny new paper with colleague Harald Oberhauser and our wonderful PhD student Uzu Lim. Here we obtain precise bounds on the number of points required for estimating tangent spaces of smooth manifolds with high confidence.
(1/5)
One of the great things about living in the UK is the ability to see some spectacular views during the winter afternoons. Here is the stunning vista from my office at 3pm yesterday:
Just received a referee request by a journal I've never heard of for a paper well outside my area of expertise; when I click on the link to decline, it says I must create an account, log in, and then decline. What circle of hell is this?