Time: 2:00-3:30 p.m (Note the special time) Place: Jeffery Hall 319
Speaker: Mike Roth (Queen's University)
Title: The fundamental group of the complement of a nodal plane curve
Abstract: We will finish the proof that the fundamental group of the complement of a plane nodal curve is abelian.
Time: 3:30 p.m. Place: Jeffery Hall 319
Speaker: Mike Roth (Queen's University)
Title: Zak’s theorems on tangencies IV
Abstract: We will finish the proof of Hartshorne’s conjecture on linear normality, and introduce the problem of computing the fundamental group of the complement of a nodal curve in the plane.
Time: 3:30 p.m. Place: Jeffery Hall 319
Speaker: Mike Roth (Queen's University)
Title: Zak's theorems on tangencies III
Abstract: We will prove Hartshorne’s conjecture on linear normality of subvarieties of small dimension, in the form of the restatement in terms of secant varieties.
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.
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.
Time: 3:30 p.m. Place: Jeffery Hall 319
Speaker: Mike Roth
Title: Zak’s theorems on tangencies I
Abstract: We will prove some results due to F. Zak on the linear spaces tangent to a smooth variety, the Gauss map of an embedded variety, and a related questions.
Time: 3:30 p.m. Place: Jeffery Hall 319
Speaker: Mike Roth
Title: Applications of the connectedness theorem to Secant varieties
Abstract: We will begin by recalling what happened the previous semester, and then continue giving applications of the connectedness theorem, this time to the dimensions of secant varieties.
Time: 3:30 p.m. Place: Jeffery Hall 319
Speaker: Mike Roth
Title: First applications of the connectedness theorem
Abstract: We will deduce some consequence of the connectedness theorem, giving applications to fundamental questions about embeddings of varieties.
