I am now at the biennial Spanish number-theory conference, which, this time around, is taking place in Sevilla. It is my first time in the south of Spain. On the way here, I was in Avignon for the first day of the theatre festival.
The following are just brief impressions; they should not be taken for serious criticism. I found every spectacle I attended very worthwhile.
So now everybody knows why I was posting more and more rarely. I recently posted a proof of the ternary Goldbach conjecture: it was split into two articles – a new one on major arcs, and a new and improved version of the article on minor arcs I wrote last year.
Of course, I’m expected to write a summary of the main ideas here – not just emphasizing the new points, as I do when giving a talk to an audience of specialists, but giving an overall picture of the proof and all its parts, old and new. Let me do that.
I know that the audience here is very mixed – if you don’t have the background to follow a paragraph, just keep on reading.
I have had my hands full for quite a while. I intend to get back to blogging now — starting with a few short notes.
First, as some of you may know, I recently posted and submitted a survey paper on one of my main areas of research, viz., growth in groups:
In retrospect, it was a very good thing that I was required to write it (by the conditions on this). It has allowed me to summarize a great deal of what I have been doing in the last few years, as well as to explain other people’s work (to the best of my ability). Participants in the field come from many different areas – I hope I have managed to render ideas from different sources accessible in a fairly transparent way and in one single place.
As many of you also know, and as some others will be saddened to learn from the dedication in the survey paper above, one of my main coauthors, Ákos Seress, passed away a few weeks ago at the age of 54. I look back fondly to our many conversations on permutation groups and to our friendship. He will be missed.
As most readers of this blog know, I am spending a month in Madrid, lecturing on growth in groups and otherwise enjoying myself.
Yesterday, a group of us went to Segovia:
View from the alcázar
The city is notable for (a) its aqueduct, which the Romans must have built at least in part to show off; (b) its fortress, or alcázar. Before the Arab conquest of Spain, there must have been no impressive fortresses, pillows or pins.
On Thursday evening, I was ten minutes late to a reading of the poetry of Tomas Tranströmer. I was not the only one late; going first into the elevator, I noticed that the person going with me was Vargas Llosa.
“Me siento menos mal de llegar diez minutos tarde,” said I.
“Es que la manifestacion esta bloqueando la calle hasta [Madrid toponym]…”, explained Vargas Llosa.
I was trumped, though, the following day, when I retold my interesting conversation at the local maths department. Another person had once stepped on Cortazar’s shoes.
“Me estas pisando los pies”, dijo Cortazar.
I am a little disappointed that he had exactly two.
Correction: The person involved in the second anecdote reports that Cortazar’s exact words were: “Estas caminando sobre mis zapatos”. Much more poetical!
Abro una pagina del diccionario de la Real Academia y encuentro: carolo, cárolus, caromomia carón, carona, caroncharse, caroncho, caronchoso, caronjo, caroñoso (ojo: no carroñoso), caroquero, caroreño, carosiera, carosiero, carosis, carota. In other words, no recognizable word entre las mas caseras carolino and caroteno. And all I wanted to know was whether catala was a real word…
Back in July, I spent some time in Goettingen. As most readers of this blog, it is an old university town with plenty of history – Gauss, Riemann, Hilbert and their friends
all worked and lived there. There was a rather nice workshop on the circle method, and we all had coffee somewhere between the display cases of a nifty collection of mathematical instruments from the pre-digital era.
How to take an inverse Fourier transform in the nineteenth century.