Francis Brown discussed in today’s lecture several applications of the theory of motivic periods. I was personally struck by that on integral points on curves via Kim’s extension of Chabauty’s method.
You can read more in Francis’s recent preprint in the ArXiv.
Here are two sets of notes on A. Levin’s talk last week: “Modular arrangements”
In his short kick-off talk Monday, Don Zagier suggested the following papers as an introduction to some of the general themes of the trimester.
(with M. Kontsevich) Periods.
In Mathematics Unlimited–2001 and Beyond (B. Engquist and W. Schmid, eds.), Springer, Berlin-Heidelberg-New York (2001), 771-808
Japanese translation: In Suugaku no saisentan–21 seiki e no chousen, Vol. 1, Springer, Tokyo (2002), 74-125
Arithmetic and topology of differential equations
Proceedings of the 2016 ECM, 57 pages (Hirzebruch Lecture).
Both papers (as well as all of Don’s papers) can be found on his
Vasily gave concrete details on various calculations (get an exceptional collection, count rational curves, get a connection, take its Fourier transform, get a Picard-Fuchs equation, intersect the vanishing cycles from its four simple singularities using modular forms et voila! you’re back at the start) for V5, the minimal Fano threefold of anticanonical degree 40.
To paraphrase Don Zagier: bedside reading.
A remark on minimal Fano threefolds (to be used in conjunction with
Classification problems and mirror duality)
Here are different ways you can keep up to date on what is going on with the trimester program at HIM.
- Visit the blog periodically
- Subscribe as an e-mail follower of this blog (see the box on the menu on right of this page)
- Check the trimester page at HIM (linked on the menu on the right of the page)
- Check the program’s google calendar (also linked on the menu on the right of the page)
- If you’d like to get e-mail reminders of talks send me an e-mail
- Ditto if you’d like to share the program’s google calendar
[From Herbert Gangl, who will soon figure out how to post to this blog himself]
Here is a link to an (unedited) version of Francis Brown’s talk today, in case you missed it. Alas, due to a misunderstanding the first few minutes are missing, but otherwise it should be complete.
Spencer Bloch outlined today some of the options for activities in our trimester at HIM.
- Groupe de travail
- What is…?
- Winter school
These would work as follows.
- Groupe de travail: Highly technical, intended for people working in the field.
- What is…?: Introductory lecture on the very specific topic of the title, intended for everyone
- Winter school: Introductory lectures on a given subject, intended particularly for students
- Lecture: General mathematics lecture on a topic germane to the trimester’s themes
- Workshop: One of the three week-long focused activities of the trimester with several talks each day.
All speakers are strongly encouraged to submit relevant material (notes, slides, pre-print, etc.), something beyond the talk’s abstract.