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4:00 pm Tuesday, February 20, 2018 AGNT: Big polynomial rings and Stillman's Conjectureby Dan Erman (UW Madison) in HBH 227- Ananyan--Hochster's recent proof of Stillman's conjecture is based on a key principle: if $f_1, \ldots, f_r$ are sufficiently general forms in a polynomial ring, then as the number of variables tends to infinity, they will behave increasingly like independent variables. We show that this principle becomes a theorem if ones passes to a limit of polynomial rings, using either the inverse limit or the ultraproduct. This yields the surprising fact that these limiting rings are themselves polynomial rings (in uncountably many variables). It also yields two new proofs of Stillman's conjecture. This is joint work with Steven Sam and Andrew Snowden.
Submitted by jb93@rice.edu |