Multiplying integers

The classical algorithm, that everyone knows from elementary school, for multiplying two n-digit integers runs in \(O(n^2)\)-time. Recently, there was a preprint posted on HAL (link) in which the authors provide an algorithm which runs in \(O(n\log(n))\)-time. A nice article about this discovery may be found at the QuantaMagazine: link. Further, it was also recently proven in another preprint … Continue reading "Multiplying integers"

Two quite different prizes

In the last few weeks were two quite different prizes awarded, on which I want to report. In March 14th, 2019, the L’Oréal-UNESCO For Women in Science International Awards (homepage, UNESCO webpage, wikipedia) were presented to five women. One of the five laureates is Claire Voisin (wikipedia) who is “rewarded for her outstanding work in algebraic geometry. Her pioneering … Continue reading "Two quite different prizes"

2019 Abel Prize

Karen Uhlenbeck (Wikipedia) is the 2019 Abel Prize Laureate (Wikipedia, Homepage) … for her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics. There is a nice article about it over at Quanta Magazine (link). A mathematical introduction … Continue reading "2019 Abel Prize"

2019 Christopher Heyde Medal

Three days ago the Australian Academy of Sciences announced the recipients of its 2019 Honorific Awards (Twitter, Webpage). Among them is Professor Geordie Williamson FAA FRS (Wikipedia), Mathematician at the University of Sydney (Homepage), who receives the Christopher Heyde Medal. The Australian Academy of Sciences states: Professor Williamson is a world leader in the field of … Continue reading "2019 Christopher Heyde Medal"

Global existence for non-linear wave equations

Non-linear wave equations (in 3+1 dimensions) are ubiquitous in physics, playing a vital role in many subfields of it. There are many methods available to show short-time existence of solutions for such equations, but global-in-time existence is a much more subtle problem. In the 1980s Klainermann introduced a so-called null condition on the nonlinearities of … Continue reading "Global existence for non-linear wave equations"

Wolf Prize in Mathematics 2019

The Wolf Prize in one of the most prestigious prizes in mathematics (Wikipedia entry). This year’s laureates are Prof. Gregory Lawler (Wikipedia, Homepage) and Prof. Jean Francois le Gall (Wikipedia, Homepage). The corresponding press release of the EMS may be found here.

The Whitehead manifold and positive scalar curvature

Recall that the Whitehead manifold is a contractible 3-manifold which is not homeomorphic to Euclidean 3-space (Wikipedia entry). It was proven by Chang-Weinberger-Yu (link) that the Whitehead manifold can not admit a complete metric of uniformly positive scalar curvature. Last year their result was strengthened by Jian Wang in arXiv:1805.03544 to the statement that the Whitehead manifold can … Continue reading "The Whitehead manifold and positive scalar curvature"

Sir Michael Atiyah 1929 – 2019

Sir Michael Atiyah died three days ago on January 11th, 2019 (news of The Royal Society). A nice obituary (together with one for Jean Bourgain) may be found on this blog: link. Here is another obituary by the New York Times.