New survey on Durov’s approach to the field with one element

As Thomas points out in a comment, Javier Fresan has posted a survey on the thesis of Durov. Although Durov’s thesis is fairly readable, it is almost 600 pages long, so Fresan’s survey is a very welcome addition to the F1 literature.

For more on the field with one element, see F_un Mathematics. Durov’s work has also been discussed earlier at the n-category cafe and the Secret Blogging Seminar.

Events in the coming year

Over the past few weeks I have been updating the Events page, and there is now a long list of interesting conferences, workshops and summer schools taking place in the coming year. I wish there was a more sensible way of finding and listing events, like a “conference section” on the arXiv, following the subject classification used for preprints. The current way of doing things, with random mathematicians posting random lists of events on various webpages seems very inefficient for everyone involved. Anyway, if you share some of my interests then you are likely to find something useful in the updated list. Note that if you are young there is often funding available from the conference organisers if you apply early.

Some highlights:

• A workshop in Leiden in October, under the somewhat obscure name Frobenius lifts. One of the main topics covered is so called Lambda-algebraic geometry, which is a new kind of geometry related to the field with one element. See this preprint of Borger for more exciting details!
• A one-year research programme in Barcelona on arithmetic geometry, with a number of workshops.
• An Advanced School on Homological and Geometrical Methods in Representation Theory, in Italy in January/February.

See the full list for much more…

Deligne on cohomology of algebraic varieties

A week ago, Deligne gave a talk at the Newton Institute on cohomology of algebraic varieties, and this is now available to watch here in a number of formats. The talk is a very nice and accessible introduction to the classical cohomology theories in algebraic geometry, and gives some hint of the rich arithmetic structures they carry, such as Galois actions and Hodge structures. He also touches at things like periods and derived categories, while all the time staying at a fairly elementary level.