Nice paper! Glad to see quiver representation theory joining the fold. Def. relevant to an item on my research wish list: To provide a combinatorial encoding schema for the entrance path category associated to an arbitrary (trained) ReLU neural network arxiv.org/abs/1603.01587

Just discovered a beautiful paper elucidating general differential operators on combinatorial species with fine visuals: arxiv.org/pdf/2305.05059

Gödel's first incompleteness theorem is commonly proved by means of a diagonal argument. But, in retrospect, we can see that what Gödel was really doing was proving that Peano arithmetic is Turing-complete, and then applying an argument from computational irreducibility... (1/15)

Jonathan Gorard Lawvere core arxiv.org/abs/math/03052…

Highly recommended and inspirational! Every one of prof-g's talk is a pleasure in terms of aesthetics and content. (Pairs nicely with an ICERM talk: icerm.brown.edu/video_archive/…)

A new paper on the arXiv, my first one on clustering arxiv.org/abs/2408.06958 Together with Marius Huber and Sara Kalisnik we introduce AuToMATo, and automized version of the persistence-based clusterer ToMATo.

Can Topological Deep Learning (TDL) models compute fundamental topological invariants? 🔎🌐 Our new paper suggests that in many cases the answer is surprisingly NO. To mitigate this, we develop two new TDL architectures inspired by expressive graph networks. 1/11

There is a marvellous group theory book on Quora from Roman Andronov, copiously illustrated, giving geometric intuition into what these abstract group theoretic objects track: grouptheoryforall.quora.com

Nice.

So this is what we’ve been up to lately. Extremely excited to build the next generations of frontier models for Earth simulations. Our GFT model is the first step in that direction. More exciting updates coming soon…

1/5 Excited to announce the public code release of Aurora - a foundation model for atmospheric forecasting! 🌎⛅️ Code: github.com/microsoft/auro… Docs: microsoft.github.io/aurora Paper: arxiv.org/abs/2405.13063

Awesome new Dowker Duality article just dropped. Congrats Iris Yoon ! arxiv.org/abs/2408.13136

it's time for a thread about... scrying the future i.e., dynamical systems 1/

now, i may or may not believe in astrology (coupled oscillators); i may or may not believe in the tarot deck (eigenvectors) or fortune-telling (analytic continuation); but i can put up a good argument. and maybe i do believe after all... 6/

To read!

Still one of the best books for getting a sense of basic GR, filled with insights, wit and unique “Wheelerisms”.

Harvard's lecture notes on "Probability, Statistics, and Linear Algebra" people.math.harvard.edu/~knill/teachin…

What is the geometry of data? 🤖The geometry of weights in deep learning? 🧠The geometry of activations in neural networks? Differential geometry can describe and quantify these structures. Want to use it for your research? 🌐Discover Geomstats! github.com/geomstats/geom…

0-cochains of a network sheaf...