There was a meta-study published in Nature Communications (doi:10.1038/s41467-018-06292-0) about the performance of girls and boys in STEM fields. I learned about it from here.

To summarize a bit the results of the meta-study, let me quote a few sentences from its abstract:

*According to the ‘variability hypothesis’, this over-representation of males [persuing careers in STEM] is driven by gender differences in variance; greater male variability leads to greater numbers of men who exceed the performance threshold.*- Their meta study confirms the greater variability (but less average performance) of men:
*In line with previous studies we find strong evidence for lower variation among girls than boys, and of higher average grades for girls.* - But the variability hypothesis is disproven:
*However, the gender differences in both mean and variance of grades are smaller in STEM than non-STEM subjects, suggesting that greater variability is insufficient to explain male over-representation in STEM.*

I was a bit surprised by this, since I thought that such examples should be already known. Apparently not …

One reason why constructing such examples is hard, is the following result of Deligne-Sullivan from the late 70s: every compact hyperbolic manifold is virtually stably parallelizable, i.e., every compact hyperbolic manifold admits a finite-sheeted covering whose tangent bundle becomes trivial after taking the direct sum with a trivial bundle.

Note that being stably parallelizable implies that all Stiefel-Whitney classes vanish, which is much stronger than being spin (which just needs the first two Stiefel-Whitney classes to vanish). So especially, every compact hyperbolic manifold is virtually spinnable.

]]>Let me start with a picture of the speaker of the SPP, Bernhard Hanke, explaining at the beginning of the conference the next steps leading to the second funding period of the SPP. (I unfortunately forgot to take a picture of Carsten Balleier from the DFG saying a few words at the beginning.)

Next a few pictures from some of the plenary talks.

A picture from a coffee break at the Schloßgarten Cafe.

The next is a picture of Grigori Avramidi quoting how Thurston explained to Sullivan what a horocycle is (you can read this story in the December 2015 issue of the Notices of the AMS – the Thurston memorial issue – on page 1329, link-to-pdf).

And last, two pictures from the Conference Dinner.

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Though probably for many too long to read in detail, reading just the introductions is already interesting.

]]>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 (link) that \(O(n\log(n))\)-time is conditionally (i.e., if a certain conjecture in network coding is true) the best possible.

Update (May 7th): the results in the last linked preprint (link) are extremely strong and hence one should, at least for the time being, take it with a grain of salt (further information: link).

]]>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

The other one is the **Ars legendi-Fakultätenpreis Mathematik** (webpage), which will be awarded to **Robert Rockenfeller** (homepage). Actually, since I’m quite interested in the art of teaching mathematics, I invited him next summer to Regensburg to our department colloquium to talk about what he did which earned him this prize; and I would actually recommend others to do the same – at least last year I was positively astonished by the talk (and what he did teaching-wise) by last-years laureate.

John Roe passed away last year. His personal webpage is still online for those who want to get a glimpse at all he was interested in.

Here are a few pictures from the meeting. In the first one you see Christopher Wulff giving his talk on solving some of John’s conjectures, the second one is Rufus Willett’s talk about *Being a student of John Roe*, and on the third one you see Qin Wang projecting a quote of John (you have to zoom in a bit to read it). (Unfortunately, I forgot to take a picture of Nigel Higson giving an overview of John’s mathematical work.)

But the most interesting talk for me was by Sara Zelenberg about *Mathematics for sustainability* – the book with which John was occupied at the end (Sara is one his co-authors of this book).

Let me finish this post by showing two pictures. The first one is the group picture of this special session, which was taken in front of a projection of an old conference picture (Paul Baum’s 60th). The second one is another picture from that conference (with naming provided by Nigel Higson).

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… 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 to her field can be found at the following blog: link; and another one here: link.

]]>The Australian Academy of Sciences states:

Professor Williamson is a world leader in the field of geometric representation theory. Among his many breakthrough contributions are his proof, together with Ben Elias, of Soergel's conjecture—resulting in a proof of the Kazhdan-Lusztig positivity conjecture from 1979; his entirely unexpected discovery of counter-examples to the Lusztig and James conjectures; and his new algebraic proof of the Jantzen conjectures.]]>