Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Curves Seminar

Curves Seminar - Mike Roth (Queen's University)

Wednesday, February 28th, 2018

Time: 3:30 p.m.  Place: Jeffery Hall 319

Speaker: Mike Roth (Queen's University)

Title: Zak’s theorems on tangencies II

Abstract: We will prove a result due to F. Zak on the secant variety to a smooth variety (under a certain codimension condition). This result proves a conjecture of Hartshorne on linear normality of subvarieties of small codimension.

Curves Seminar - Daniel Erman (Wisconsin-Madison)

Wednesday, February 7th, 2018

Time: 3:30 p.m.  Place: Jeffery Hall 319

Speaker: Daniel Erman (Wisconsin-Madison)

Title: Big polynomial rings and Stillman’s conjecture

Abstract: Ananyan–Hochster's recent proof of Stillman's conjecture is based on a key principle: if f_1,.., 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.