Congrats to my colleagues at Uni Vienna for their work on relativity for non-smooth space-time, and for this public outreach article!

www.quantamagazine.org/a-new-geomet...

Happy international women in math day! To commemorate, let us remember Sofya Kovalevskaya

en.m.wikipedia.org/wiki/Sofya_K...

She was the first woman, in modern times, who obtained a doctorate in maths. Despite the system being rigged against women, her contributions were fundamental and unique.

Mathematik als Schlüssel: Vom Transport zum Pixel
TUForMath Vortrag von Julio Backhoff (Universität Wien)

10.04.2025 um 18:00 Uhr
Freihaus TU Wien, Wiedner Hauptstraße 8-10, Hörsaal 8

Bild c_Dall-E

www.tuwien.at/tuformath/ne...

(Final Part)We can essentially cover the circles with triangles as in the previous part. So now the total length of the yellow segments divided by “R” is equal to the total length of blue divided by “r”. Making the angle between consecutive reds become arbitrarily small, we conclude the argument!

(Part 3) Now let’s look at two circles with the same center. Their radii are “R” and “r”. By our previous remark, in the new picture the ratio of the length of the yellow segment over “R”, is equal to the length of the blue segment over “r”. The angle between the red segments can be anything.

(Part 2) First we remind ourselves of the pretty fact, that two triangles sharing the same angles must be “similar”. For instance, in the picture this means that “a” divided by “b” is equal to “A” devided by “B”.

(Part 1) Happy Pi day everybody! Indeed today is 3.14.

You might remember that Pi is defined as the ratio between the circumference of a circle and its diameter. But in principle this ratio could depend on the circle chosen, right?… Well, let us remember why the choice of the circle doesn’t matter!

(Final) By the way if we replace the role of the ”100% return” by "x times 100% return", so for instance 50% corresponds to x=1/2, then with N large we get e raised to the power x in the computations. This is the celebrated exponential function (of x), which we so feared during the pandemic!

(Continued) Or hypothetically we could divide the year in "N parts", and get returns of (100/N)% per part. By investing 1 and reinvesting and reinvesting etc, we would make (1+1/N) multiplied with itself N times! If N is large the number obtained this way is precisely the Euler number e.

(Continued) A lucky investment of 1 Euro could yield, say, a 100% return in a year. After a year I will have 2 Euros (original 1 plus 1 profit). Or, hypothetically, I could earn (100/2)% per semester, so if I invest and reinvest, I will have made (1+1/2) times (1+1/2), which is 2.25.

Merry e-day. Here "e" stands for Euler's number e, which is approximately 2.71. Hence 27th of January, though one could also celebrate February 1st!

The number e appears everywhere in nature's laws, the sciences, engineering, and in economics and finance. I'll explain that next ...

How short can a scientific paper be? Check this funny blog post. (Too late for me btw: the zero words paper already exists!)

"The Heidelberg Laureate Forum is a conference where young researchers in maths / informatics spend a week interacting with the laureates of the disciplines: winners of the Abel Prize,Turing Award, ACM Prize in Computing, Fields Medal, Abacus Medal and Nevanlinna Prize." Applications still open!

Today we had a beautiful colloquium talk by Hugo Duminil-Copin. Watch this video about him, commemorating his Fields Medal (aka Nobel prize in Maths) in 2022.

youtu.be/5dXulZVstbY?...

P = NP? It’s a question that computational complexity theorists have been asking for over 50 years. Oracles have helped them better understand what they’re working with.
www.quantamagazine.org/why-computer...

(Part 3) Changing the numeraire, as we did when passing from Part 1 to Part 2, is difficult for our intuition. Wouldn’t you say that the picture in Part 2 is more favourable for an investor in currencies? At a high level, this is what we studied with my colleagues in this work. (End of thread)

(Part 2) But we could also use Dollar as a reference. This picture is completely equivalent to the one in Part 1. The reference currency in these examples is what’s called „numeraire“. It is used as a unit of measure for economic and financial quantities, and it doesn’t need to be a currency!

(Part 1) Let’s explain the concept of numeraire with an example. We have two assets, Asset D = 1 Dollar, and Asset E = 1 Euro. Today they’re worth the same. In a year the relative values of euro & dollar changes in two ways, with equal probability. The picture shows this, using Euro as reference.

Excellent beginning of the year. Our article "Geometric martingale Benamou-Brenier transport and geometric Bass martingales" (with Gregoire Loeper and Jan Obloj) has been accepted for publication at Proceedings of AMS!
arxiv.org/abs/2406.04016