Description
Date/Time: 17 November 2020, 6:30pm IST/ 1:00pm GMT/ 8:00am EDT (joining
time: 6:15 pm IST - 6:30 pm IST)
Speaker: Giulio Caviglia, Purdue University, USA
Google meet link: meet.google.com/gyc-baih-xas
Title: The Eisenbud-Green-Harris Conjecture
Abstract: The $f$-vector of a simplicial complex is a finite sequence of
integers defined by the number of $i$-dimensional faces of the complex.
All possible such vectors are completely characterized thanks to a
classical theorem by Kruskal and Katona. This result, when rephrased in
terms of Hilbert functions of certain quotients of polynomial rings by
monomial ideals, extends the celebrated theorem of Macaulay on
lexicographic ideals.
The Eisenbud-Green-Harris conjecture is a further generalization of both
the Kruskal-Katona theorem and the well-known Cayley–Bacharach theorem for
plane curves. I will survey the known results on this conjecture including
a recent joint work with Alessandro De Stefani.