David Beers @davidbeersmath.bsky.social · 10/06/2026Last week I got a departmental teaching award. Yay teaching! 030
David Beers @davidbeersmath.bsky.social · 05/01/2026Two of my students showed up to my final last quarter with matching "I ❤️ Complex Analysis" shirts. That counts as a win in my book 010
David Beers @davidbeersmath.bsky.social · 19/11/2025Dying to know what Kate's Crazy Conjectures are 010
Reposted by David BeersRamón Nartallo-Kaluarachchi @rnartallo.bsky.social · 29/08/2025This month's @londmathsoc.bsky.social newsletter contains a feature by one of the world's greates living scientists (me) and also work by Roger Penrose. I hope you enjoy :) www.lms.ac.uk/sites/defaul...lms.ac.uk 041
Reposted by David BeersHaochen Yang @benjaminojr.bsky.social · 04/06/2025New interdisciplinary math+bio paper! Mouse liver assembloids model periportal architecture and biliary fibrosis. In vitro assembloids modelling the mouse liver periportal region were built to study processes causing scarring (cholestatic injury/biliary fibrosis) and the shape change this causes. 162
Reposted by David BeersRamón Nartallo-Kaluarachchi @rnartallo.bsky.social · 04/06/2025Speaking at NetSci2025 about our recent Learning on Graphs paper. We build up a theoretical and applied approach to use Hodge theory on graphs to study stochastic systems! arxiv.org/pdf/2409.07479 #NetSci2025 051
David Beers @davidbeersmath.bsky.social · 27/05/2025Whether the converse of the above tweet is true, we know not. Finally, were able to tell a similar story about local identifiability of Čech persistence, except it involves hypergraphs instead of graphs, and a rigidity theory that is, to our knowledge, new. 10/10 010
David Beers @davidbeersmath.bsky.social · 27/05/2025Using a modern rigidity theory result of Gortler, Theran, and Thurston, we also proved that if G is globally rigid, then P is identifiable. G being globally rigid means you cannot teleport points in P without preserving edge lengths in G, unless you teleport via isometry. 9/10 110
David Beers @davidbeersmath.bsky.social · 27/05/2025As it turns out, it is difficult to figure out when a graph is rigid in general- indeed rigidity theory is an active subject in real algebraic geometry. This suggests that it is hard to figure out which point clouds are locally identifiable. 8/10 110
David Beers @davidbeersmath.bsky.social · 27/05/2025G being rigid means we can't wiggle the points in P without changing the edge lengths of G, unless we wiggle the points in P via isometry. 7/10 100
David Beers @davidbeersmath.bsky.social · 27/05/2025Here is how to find out if P is locally identifiable (under Vietoris-Rips PH). Make a graph G with vertex set P and any edge whose inclusion in the V-R filtration coincides with a change in topology. Any generic P is locally identifiable exactly when G is rigid. 6/10 110
David Beers @davidbeersmath.bsky.social · 27/05/2025Its natural to ask which point clouds are best described by PH. These are the point clouds P such that if Q has the same PH, then P and Q are isometric. Such a P is called identifiable. If P is isometric to any NEARBY Q with the same PH then P is called LOCALLY identifiable 5/10 110
David Beers @davidbeersmath.bsky.social · 27/05/2025We can quantify how big a level set is by computing its dimension. If D is a family of barcodes (one for each homological degree) with k distinct endpoint values, we showed the following inequalities hold (see picture) 4/10 110
David Beers @davidbeersmath.bsky.social · 27/05/2025What we are interested in this paper is how descriptive this mapping is. One way to ask this is to ask how big the level sets are. Big level sets mean many point clouds have the same barcodes, so PH is not very descriptive at barcodes with big level sets. 3/10 110
David Beers @davidbeersmath.bsky.social · 27/05/2025As many of my faithful followers will be aware, using either Čech or Vietoris-Rips persistent homology (PH) we get a barcode in each homological degree from any point cloud. So we have a mapping PH: Point clouds with n points in d dimensions -> Barcodes 2/10 110
David Beers @davidbeersmath.bsky.social · 27/05/2025I posted about this paper this a while ago on another website, but figured I'd post it here now that I have a few followers. (Joint with @haharrington.bsky.social, Jacob Leygonie, @uzulim.bsky.social, and Louis Theran). arxiv.org/abs/2411.08201 1/10 184
Reposted by David BeersRamón Nartallo-Kaluarachchi @rnartallo.bsky.social · 15/05/2025Last week, I gave the Networks seminar here at Oxford on: 'Nonequilibrium steady-states: from diffusion to digraphs', talking about some of my recent work on discrete approximations of nonequilibrium diffusions. It is available online: www.youtube.com/watch?v=ezep... :)youtube.comRamon Nartallo-Kaluarachchi: Non-equilibrium steady-states, from diffusion to digraphsYouTube video by Fresh from the ArXiv 052
