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SUMMARY:Giulio Caviglia (Purdue University)
DTSTART:20201117T130000Z
DTEND:20201117T140000Z
DTSTAMP:20260423T021007Z
UID:VCAS/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/37/">Th
 e Eisenbud-Green-Harris Conjecture</a>\nby Giulio Caviglia (Purdue Univers
 ity) as part of IIT Bombay Virtual Commutative Algebra Seminar\n\n\nAbstra
 ct\nThe $f$-vector of a simplicial complex is a finite sequence of integer
 s defined by the number of $i$-dimensional faces of the complex. All possi
 ble such vectors are completely characterized thanks to a classical theore
 m by Kruskal and Katona. This result\, when rephrased in terms of Hilbert 
 functions of certain quotients of polynomial rings by monomial ideals\, ex
 tends the celebrated theorem of Macaulay on lexicographic ideals.\nThe Eis
 enbud-Green-Harris conjecture is a further generalization of both the Krus
 kal-Katona theorem and the well-known Cayley–Bacharach theorem for plane
  curves. I will survey the known results on this conjecture including a re
 cent joint work with Alessandro De Stefani.\n
LOCATION:https://researchseminars.org/talk/VCAS/37/
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