## what is #angs@t?

Welcome to #angs@t (pronounced ‘angst’), the group-blog accompanying the master-course ‘seminar noncommutative geometry’ given at Antwerp University (Belgium).

Clearly, ‘angs’ is short for Antwerp Noncommutative Geometry Seminar, and the addendum @t indicates that all tweets about the seminar should include the hashtag #angs. Such tweets will appear in the sidebar on the main page.

## practical info

The IRL-part of the seminar begins every friday around 13h in room G 0.16 (campus Middelheim) and ends sometime after 16h when exhaustion strikes lecturer and/or public. Normally lectures are given in Dutch unless the assembled public demands otherwise, in which case we effortless switch to pidgin English.

The virtual-part of the seminar happens here and on twitter, and will be entirely in English. Here, we will collaboratively try to write course-notes, using the EditFlow plugin. Anyone interested to contribute can send an email to lieven.lebruyn at ua.ac.be. If you have a twitter-account, please tweet about the seminar using the hashtag #angs.

# the plan

We will try to sketch an approach to the next biggest conjecture in number theory (after the Riemann hypothesis), the ABC-conjecture, using geometry over the field with one element $\mathbb{F}_1$ and noncommutative geometry.

Here’s a crude outline of the topics/papers we will cover (anticipate major changes):

- Smirnov’s approach to the ABC-conjecture via geometry over $\mathbb{F}_1$ as outlined in his paper ‘Hurwitz inequalities for number fields‘, St. Petersburg Math. J. 4 (1993) 357-375.
- The bestiary of proposals for a geometry over $\mathbb{F}_1$ as catalogued in the paper Mapping $\mathbb{F}_1$-land:An overview of geometries over the field with one element by Lopez Pena and Lorscheid.
- The promising approach by James Borger using $\lambda$-rings as described in his paper Lambda-rings and the field with one element.
- Connection with noncommutative geometry based on the papers On the arithmetic of the BC-system by Connes and Consani and Cyclotomy and endomotives by Marcolli.