# Yufei Zhao “The joints problem for varieties”

August 13, 2020
19.00 MSK (UTC +3)

# Yufei Zhao "The joints problem for varieties"

Yufei Zhao from MIT will give the talk "The joints problem for varieties" on the labs' Big Seminar.

The talk will be held in zoom
Meeting ID: 279-059-822
Password: first 6 decimal places of $\pi$ after the decimal point

You can also write to Alexander Polyanskii (alexander.polyanskii@yandex.ru) or to Maksim Zhukovskii (zhukmax@gmail.com) if you want to be added to mailing list.

Abstract:

We generalize the Guth-Katz joints theorem from lines to varieties. A special case of our result says that N planes (2-flats) in 6 dimensions (over any field) have $O(N^{3/2})$ joints, where a joint is a point contained in a triple of these planes not all lying in some hyperplane. Our most general result gives upper bounds, tight up to constant factors, for joints with multiplicities for several sets of varieties of arbitrary dimensions (known as Carbery's conjecture). Our main innovation is a new way to extend the polynomial method to higher dimensional objects.

Joint work with Jonathan Tidor and Hung-Hsun Hans Yu.

Slides

## Watch the video:

Everyone is invited to attend. The language of the lecture is English. The event is aimed at master and graduate students, as well as researchers in the field of combinatorics.