***********************************
                * Princeton Discrete Math Seminar *
                ***********************************

Speaker: Yufei Zhao (MIT)

Thursday 3rd September.

Zoom link is https://princeton.zoom.us/j/98096997979, password is needed.

Title: The joints problem for varieties

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.


		----------------------------------

Next week: TBA

Anyone wishing to be added to or removed from this mailing list should
contact Paul Seymour (pds@math.princeton.edu)