### What in the world is topological quantum matter?

Always wondered what the work of the 2016 Nobel prize laureates might have to do with topology? This recent video from Fan Zhang may give a first idea:

SPP 2026 - Geometry at Infinity

Why is the definition of higher homotopy groups the “right one”? Why is there no symplectic version of spectral geometry? Pullback and homology Is this generalization of Borsuk-Ulam true? Roots of unity Vandermonde matrix is totally positive Why are free objects “free”? Does there exist any non-contractible manifold with fixed point property?

Today, there was the Séminaire Bourbaki, which takes place every four months in Paris. The list of the talks can be found here. Interesting from the point of view „Geometry at Infinity“ was especially the talk of Olivier Guichard regarding work of Kapovich-Leeb-Porti and Labourie on convex-cocompact groups in higher rank symmetric spaces: Another talk … Continue reading "Séminare Bourbaki: Convex-cocompactness in higher rank"

Zimmer’s conjecture aims to extend Margulis’ superrigidity theorem to a nonlinear setting. Except for actions on the circle there has not been much progress in the last 35 years. A new preprint of Brown-Fisher-Hurtado and its predecessor are now settling the conjecture for finite index subgroups of \(SL(n,{\mathbb Z})\) and cocompact lattices in \(SL(n,{\mathbb R})\). … Continue reading "What’s new on the ArXiv: Zimmer’s conjecture for actions of SL(m,Z)"

Is there a geometric interpretation for Reidemeister torsion?

Vladimir Voevodsky – one of the most influential mathematicians of the last decades – deceased yesterday at the age of only 51 years.

Open subsets of Euclidean space in dimension 5 and higher admitting exotic smooth structures

This week there was the workshop “Non-positively curved groups and spaces” in Regensburg.

This week there was the common meeting of the Austrian and German mathematical societies at the University of Salzburg and besides many interesting math talks there was also a session about the future of knowledge management.

3D Billiards problem inside a torus

## Recent Comments