### Breakthrough Prize for higher-dimensional geometry

The award ceremony is certainly not what mathematicians are used to, and there are certainly many things that one can say for and against such monstrous awards and the ambience around. In any case, if you‘d like to see the ceremony, the math part starts at 1:22:30. The breakthrough prize for 2018 was given to … Continue reading "Breakthrough Prize for higher-dimensional geometry"

### What’s new on the ArXiv: Quasi-isometric groups with no common model geometry

Do quasi-isometries between groups always arise from actions on a common model space? Previous counterexamples invoked central extensions of lattices, e.g., of surface groups. A new construction of infinitely many classes is now using amalgams of surface groups. Stark, Woodhouse: Quasi-isometric groups with no common model geometry, https://arxiv.org/pdf/1711.05026.pdf If a group $$\Gamma$$ acts geometrically (i.e., … Continue reading "What’s new on the ArXiv: Quasi-isometric groups with no common model geometry"

### S-matrices and the big unification

A week ago, the long-awaited preprint Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet by Arkani-Hamed, Bai, He, and Yan, appeared on the ArXiv. Michael Rios and David Chester in two videos try to explain the essence of the new work and, for example, the compatibility with Garrett Lise’s E8 theory. … Continue reading "S-matrices and the big unification"

### What’s hot at math overflow 22/2017

Concepts in topology successfully transferred to graph theory and combinatorics with non-trivial applications?

### What‘s new on the ArXiv: 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 "What‘s new on the ArXiv: A deformation of instanton homology for webs"

### What’s hot at mathoverflow 21/2017

Concepts in topology successfully transferred to graph theory and combinatorics with non-trivial applications?

### Slides and Pictures from the Kickoff Meeting

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

### 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 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:

### 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?