Daniel Litt ✓
@littmath · Toronto, Ontario · joined 12 Aug 2010
Assistant professor (of mathematics) at the University of Toronto, visiting Harvard Fall 2026. Forever confused. Algebraic geometry, number theory, etc. He/him.
62 930Followers
932Following
32 770Posts total
519.4KViews on collected posts
Postingan terbaru
Mencari postingan baru…
@littmath it's all an excuse to think about Alice and Bob. who are they, where do they run, why do they keep picking balls from urns as the world around them fades away?
570 views · 10 likes
· 1 reposts · 0 replies
Open on X →
Apologies for the long self-indulgent post; hopefully it's a bit useful to see how, other than one-shotting things, the models can be used to do mathematics, and how at least some professionals are thinking about this.
7.1K views · 107 likes
· 2 reposts · 2 replies
Open on X →
So there's a mathematical question I've been thinking about on and off for about 10 years. For the first 5 or so years I made very little progress, but learned a bit about the general area (while working on other things). In the last 5 years I've made some modest progress with
47.7K views · 683 likes
· 30 reposts · 28 replies
Open on X →
SITUATION DETECTED: andrew wiles IPOs for a trillion dollars
29.8K views · 480 likes
· 10 reposts · 10 replies
Open on X →
I don't know about the chess analogy or the views of people with money, but I do think there's pretty broad agreement that furthering human knowledge is an inherently good thing.
20.8K views · 234 likes
· 11 reposts · 16 replies
Open on X →
The problem with is that maths has, at least for the last 100 years or so, justified its existence (i.e. funding) through the idea that furthering human knowledge is an inherently good thing. And I just don't think the people with money believe that anymore...
40.4K views · 76 likes
· 4 reposts · 14 replies
Open on X →
This is right. People are (understandably) concerned about negative second-order effects of these solutions, especially to problems that have been central to a field for some time and guided past work.
But, don't you believe in mathematics? There will always be more to learn.
23.7K views · 261 likes
· 17 reposts · 12 replies
Open on X →
"math is dead because a computer solved a problem"
Every serious mathematician knows that a solution to a famous problem immediately generates dozens or hundreds more problems ... that's how it's always worked https://t.co/meVr73pUTC
31.5K views · 92 likes
· 4 reposts · 6 replies
Open on X →
@littmath Most liked post about non-abelian cohomology 🏅
Congrats on finishing!
10.4K views · 33 likes
· 1 reposts · 1 replies
Open on X →
You can read the paper here: https://t.co/QFtNNK5Aql
3.6K views · 47 likes
· 1 reposts · 1 replies
Open on X →
This project has been in the works for some time. One fun aspect of it is that this paper is the first one I've written in part after AI tools exceeded some invisible threshold of usefulness for math research tasks. I'll talk a bit about this some other time! https://t.co/DaABZOy
3.9K views · 36 likes
· 2 reposts · 2 replies
Open on X →
This is really an excuse to develop non-abelian analogues of the structures on cohomology Katz exploits; for example, a non-abelian analogue of the Hodge index theorem. https://t.co/8P8t0tsDPx
2.5K views · 42 likes
· 2 reposts · 1 replies
Open on X →
There is an associated (non-linear!) differential equation--see e.g. below--controlling this action. We prove an analogue of Katz's theorem for these equations: the arithmetic of this differential equation controls the action of \pi_1(S,s) on representations of \pi_1(X_s). https:
2.6K views · 28 likes
· 1 reposts · 5 replies
Open on X →
The players are as follows. Let f: X-->S be a smooth projective morphism of complex varieties, and fix s in S. The topological object we will study is the natural (outer) action of \pi_1(S,s) on \pi_1(X_s), and the induced action of \pi_1(S,s) on representations of \pi_1(X_s).
2.6K views · 24 likes
· 1 reposts · 1 replies
Open on X →
This paper with Josh instead studies connections between topology and arithmetic mediated not by cohomology, but by what we (and others) refer to as "non-abelian cohomology" -- spaces parametrizing representations of the fundamental group of a variety.
2.7K views · 30 likes
· 1 reposts · 1 replies
Open on X →
Katz's proof relies on the structures on and compatibilities between different kinds of cohomology theories of algebraic varieties; for example, the Hodge index theorem, and various compatibilities between de Rham cohomology in positive characteristic and characteristic zero.
2.8K views · 25 likes
· 1 reposts · 1 replies
Open on X →
These are the ODEs satisfied by so-called "period integrals": loosely speaking, functions obtained by integrating polynomially varying families of algebraic functions.
2.9K views · 31 likes
· 1 reposts · 1 replies
Open on X →
In general the p-curvature conjecture is open, but it is known (due to work of Katz) for certain ODEs, called Picard-Fuchs equations or Gauss-Manin connections, which come from the cohomology of algebraic varieties. https://t.co/wyFADOnFhd
3.2K views · 37 likes
· 1 reposts · 2 replies
Open on X →
The starting point for this paper is a different connection between arithmetic, geometry, and topology--the Grothendieck-Katz p-curvature conjecture. It predicts that the algebraicity of solutions to a linear ODE is controlled by the arithmetic of the ODE.
3.4K views · 44 likes
· 1 reposts · 1 replies
Open on X →
This control is mediated in most cases by an invariant of a variety called its cohomology, which has both topological and arithmetic incarnations. Loosely speaking, a large part of the theory of motives is about compatibilities between these incarnations.
3.5K views · 42 likes
· 1 reposts · 2 replies
Open on X →
For example, the Weil conjectures (proved by Dwork, Grothendieck, and Deligne) show that the Betti numbers of a (smooth projective) variety defined by polynomials with integer coefficients are controlled by the number of solutions to those polynomials over finite fields.
3.7K views · 50 likes
· 1 reposts · 1 replies
Open on X →
One of the basic themes of 20th century mathematics is that the topology of the set of complex solutions to a system of polynomial equations is controlled by the arithmetic of the polynomials.
5.8K views · 85 likes
· 1 reposts · 2 replies
Open on X →
The basic objects of study here are algebraic varieties--shapes defined as the set of solutions to a system of polynomial equations--and polynomial maps between them. https://t.co/Zf97ynVrdC
10.3K views · 85 likes
· 3 reposts · 3 replies
Open on X →
New paper with Josh Lam, about which I'm really excited! I want to try to briefly explain what the point is in this thread. https://t.co/c98Inw9Mgu
253.8K views · 537 likes
· 35 reposts · 19 replies
Open on X →
Dibandingkan akun berukuran sama
8 postingan dari 90 hari terakhir, dibandingkan dengan rentang 10K–100K pengikut. tampil luas, tetapi sedikit penonton yang merespons.
Median tayangan26 770akun ini886median untuk 10K–100K
Jangkauan, %42.54%akun ini3.22%median untuk 10K–100K
Interaksi, %1.41%akun ini1.99%median untuk 10K–100K
| Metrik | Akun ini | Median untuk 10K–100K | Rasio |
|---|---|---|---|
| Median tayangan per postingan | 26 770 | 886 | 30.2× |
| Jangkauan (tayangan ÷ pengikut) | 42.54% | 3.22% | 13.2× |
| Tingkat interaksi | 1.41% | 1.99% | 0.71× |
Akun lain pada rentang ini → Bandingkan dengan akun lain → Bagaimana tolok ukur ini disusun →
Growth & engagement
How the posts we collected actually performed: views and reaction rate post by post, what the audience did with them, and where the follower count goes.
Views per post
2.6K14 Jan
2.6K
2.5K
3.9K
3.6K
10.4K15 Jan
31.5K2 Sep
23.7K
40.4K3 Sep
20.8K
29.8K4 Sep
47.7K5 Sep
7.1K
570
Last 14 collected posts, oldest on the left. The scale is logarithmic: one post can outrun the rest a hundred times over.
Engagement rate per post
1.01%14 Jan
1.32%
1.77%
1.03%
1.35%
0.34%15 Jan
0.33%2 Sep
1.23%
0.24%3 Sep
1.26%
1.68%4 Sep
1.56%5 Sep
1.57%
1.93%
Reactions — likes, reposts, replies and quotes — divided by views. Median for 10K–100K accounts is 1.99%.
What the audience does
Likes80.3%3 119 in total
Reposts3.4%133 in total
Replies3.4%132 in total
Quotes0.4%16 in total
Bookmarks12.5%486 in total
Share of every reaction we collected for this account. Replies mean argument, reposts mean endorsement, bookmarks mean the post was worth keeping.
The follower curve appears once this account has two daily snapshots — we take one a day, and this one is on its first.
Akun serupa
♥️خــͥــᷠــͣــͣــͪــᷜـــــانـــــی🇵🇰
@iamkhaani
125.9K followers
· 661.3K posts
Chris Waddle
@chriswaddle93
125.8K followers
· 4.2K posts
DCP North-West Delhi
@DCP_NorthWest
125.8K followers
· 12.5K posts
Omaha Productions ✓
@OmahaProd
125.8K followers
· 5.6K posts
Matthew Syed ✓
@matthewsyed
125.8K followers
· 18.1K posts
Taiwan News ✓
@TaiwanNewsEN
125.8K followers
· 62.2K posts
Morning Show with Boomer & Gio
@WFANmornings
125.7K followers
· 20.4K posts
Thevoguewriters ✓
@thevoguewriters
125.7K followers
· 6K posts