Author: Thilo Kuessner

A deformation of instanton homology for webs

The four color theorem from graph theory is certainly the most famous problem for which so far only a brute force computational proof exists. A new preprint of Kronheimer-Mrowka supports an approach towards this theorem via homology theories. Kronheimer. Mrowka: A deformation of instanton homology for webs, https://arxiv.org/pdf/1710.05002.pdf The four color theorem says that every … Continue reading "A deformation of instanton homology for webs"

Gauß in Regensburg

The German Mathematical Society (DMV) offers twice a year the „Gauß Lecture“, an overview lecture with a well-known mathematician. The lecture is intended to show current developments in mathematics and addresses the interested public. At this link is the chronicle of previous lectures. The last of this years lectures has been given by Cédric Villani at … Continue reading "Gauß in Regensburg"

What’s hot at mathoverflow 20/17

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?  

Séminare Bourbaki: Convex-cocompactness in higher rank

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 for actions of SL(m,Z)

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 "Zimmer’s conjecture for actions of SL(m,Z)"