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What are the latest breakthroughs? These posts summarize current mathematical research. They cover significant and influential results announced in talks, preprints and publications. These results are often preliminary, and their correctness may be as yet uncertain.
Modular invariant q-deformed numbers: first steps
AUTHOR: V. Ovsienko. The goal of this short review is to explain the main ideas of the emerging new theory. of “quantum rational’,’ based on modular, or PSL(2,]-invariance,
and that of “quantum irrationals”.
Milman and Neeman Post Proof of Triple and Quadruple Bubble Conjectures in $R^n$ and $S^n$
AUTHOR : F. Morgan : EDITORS : J. Hass, R. Ghrist : ART : R. Ghrist In 1884 Hermann Schwarz proved that
Artificial Intelligence in Knot Theory
AUTHOR : C. Adams : EDITOR/ART : R. Ghrist : To move mathematics forward, researchers are constantly seeking new relationships between various areas of
Computability and Undecidability for Euler Fluids
AUTHOR/EDITOR/ART : R. Ghrist : This is a review of recent work by R. Cardona, E. Miranda, D. Peralta-Salas, and F. Presas,
Floating bodies of equilibrium in 2D, the tire track problem, and electrons in a parabolic magnetic field
AUTHOR : S. Tabachnikov : EDITOR/ART : R. Ghrist : This review is for the preprint: F. Wegner, From elastica to floating
The Birkhoff-Poritsky conjecture for centrally-symmetric billiard tables
AUTHOR : S. Tabachnikov : EDITOR/ART : R. Ghrist : This review concerns the following preprint: M. Bialy and A. Mironov, The