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"
Concepts in topology successfully transferred to graph theory and combinatorics with non-trivial applications?
Listening to 33 math talks within 2 times 6 hours is certainly a unique experience. If you missed the event, you may enjoy the slides of the talks: All Slides for Download
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"
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:
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?