Professor A.J. de Jong, Columbia university, Department of Mathematics.

Basic setup: we will work backwards through the recent proof of the direct summand conjecture by Yves Andre. We will follow the proof as reworked in Bhargav's preprint.

Links:

- The original exposition by Andre is here Yves Andre's paper.
- Bhargav's preprint: Bhargav's paper.
- Hochster's home page: Hochster's page.
- Bhargav's home page: Bhargav's page.

Organizational:

- If you are my graduate student, then please talk to me about attending this seminar.
- Please email me if you want to be on the associated mailing list.
- The talks will be 2x45 minutes with a short break.
- Time and place:
**Fridays, 10:30 -- 12:00 in Room 407** - First meeting: Friday, January 27.

List of lectures: TBA

- Friday, January 27. Speaker: Johan de Jong. Statement and discussion of the direct summand conjecture, proof in characteristic zero, proof in characteristic p. Some discussion of the derived direct summand conjecture.
- Friday, February 3. Speaker: Johan de Jong. Overview of the proof as in the paper by Bhargav.
- Friday, February 10. Speaker: David Hansen. Introducing perfectoid spaces and almost mathematics.
- Friday, February 17. Speaker: Dmitrii Pirozhkov. Almost purity.
- Friday, February 24. Speaker: Shizhang Li. The almost faithfully flat thingamabob of Yves Andre.
- Friday, March 3. Speaker: Johan de Jong. Formal schemes, hensel schemes, a thesis problem, and sheafy adic spaces; or, how not to give a seminar talk.
- Friday, March 10. No talk.
- Friday, March 17. Spring break.
- Friday, March 24. No talk.
- Friday, March 31. Speaker: Shizhang Li, Pro-almost-zero or almost-pro-zero, that is the question
- Friday, April 5. Speaker: Michael Harris, Counting points on compact Shimura varieties, and the trace formula