Huge congrats!!!!!!

6/ All of this is backed by extensive certified computations, a beautiful blend of theory and code. If you're into geometric topology, or the interface of maths and physics, this is worth a read!!

5/ As an application, they compute indices for large surgeries, confirming conjectures and revealing new structural patterns.The results suggest a well-defined extension of the index to closed manifolds.

4/ Building on a reinterpretation of the index as a generating function over Q-normal surfaces, the authors develop a gluing formula for relative indices.

3/ The 3D index is a q-series inspired by physics, associated to ideal triangulations of cusped 3-manifolds. It encodes rich geometric and physical information, and it is conjecturally a topological invariant.

2/ The paper proves the Gang–Yonekura formula, describing how the 3D index transforms under Dehn filling a cusp in a 3-manifold.

Congrats!!! @monsoon0.bsky.social

My fault!!! Hopefully out soon

Thanks!!

We hope that the topological information we generated here will aid and inspire new functional and evolutionary analysis of proteins!

We think that this only scratches the surfaces of what topology can teach us on proteins. We mapped the topology of the currently known protein universe and made it available online.

Topological features also identify locations of mutations that are disease-causing and structurally damaging, and capture differences between homologous enzymes in thermophile and mesophile organisms.

We analyze topologically the whole of AlphaFold2, and show how topological features capture global features of the protein universe, such as domain architecture, binding sites and thermodynamics.