Algebraic Geometry Seminar
Department of Mathematics
Princeton University
Spring 2012 Lectures
Regular meeting time: Tuesdays
4:30-5:30 (Tea served at 3:30)
Place: Fine 322
| Date | Speaker | Title |
| Feb 7 |
Andrei Căldăraru University of Wisconsin SPECIAL TIME: 3:30-4:30 SPECIAL ROOM: Fine 224 |
The Hodge theorem as a derived self-intersection The Hodge theorem is one of the most important results in complex geometry. It asserts that for a complex projective variety X the topological invariants H^*(X, C) can be refined to new ones that reflect the complex structure. The traditional statement and proof of the Hodge theorem are analytic. Given the multiple applications of the Hodge theorem in algebraic geometry, for many years it has been a major challenge to eliminate this analytic aspect and to obtain a purely algebraic proof of the Hodge theorem. An algebraic formulation of the Hodge theorem has been known since Grothendieck's work in the early 1970's. However, the first purely algebraic (and very surprising) proof was obtained only in 1991 by Deligne and Illusie, using methods involving reduction to characteristic p. In my talk I shall try to explain their ideas, and how recent developments in the field of derived algebraic geometry make their proof more geometric, by allowing us to realize the Deligne-Illusie main result as a formality result for the derived self-intersection of a subvariety of a twisted space. |
| Feb 14 |
Aise Johan de Jong Columbia University |
TBA TBA |
| Feb 21 |
Ryan Kinser Northeastern University |
Geometrically characterizing representation type of
finite-dimensional algebras Given a finite-dimensional algebra A, the set of A-modules of a fixed dimension d can be viewed as a variety. This variety carries a group action whose orbits correspond to isomorphism classes of A-modules. A natural problem is to characterize various properties of an algebra A in terms of its module varieties. For example, if A is assumed to have global dimension one, then it is not difficult to show that A has finitely many indecomposable modules (up to isomorphism) if and only if all of its module varieties have a dense orbit, which is also if and only if all weight spaces of semi-invariants in the coordinate rings of its module varieties have dimension one. Our goal is to generalize these statements (with modification) to higher global dimension. After explaining the background, we present counterexamples to the naive generalizations, along with plausible modifications and cases where these modifications are correct. (Joint work with Calin Chindris, Piotr Dowbor, and Jerzy Weyman) |
| Feb 28 |
Mina Teicher Bar-Ilan University, IAS |
TBA TBA |
| Mar 6 |
TBA TBA |
TBA TBA |
| Mar 13 |
Karl Schwede Penn State University |
TBA TBA |
| Mar 20 |
Spring Recess |
|
| Mar 27 |
TBA TBA |
TBA TBA |
| Apr 3 |
TBA TBA |
TBA TBA |
| Apr 10 |
-Daniel Erman University of Michigan |
TBA TBA |
| Apr 17 |
TBA TBA |
TBA TBA |
| Apr 24 |
TBA TBA |
TBA TBA |
| May 1 |
-Bhargav Bhatt University of Michigan |
TBA TBA |
| May 8 |
Reading Period | |
Other seminars in this department
Future lectures
Preprint seminar
For more information about this seminar, contact yuliu@math.princeton.edu and/or kftucker@math.princeton.edu.