Tuesdays 4-6, Evans 748
| date | speaker | title | abstract | |
|---|---|---|---|---|
| 08/29 | Hannah Kerner Larson | The embedding theorem in Hurwitz-Brill-Noether theory | Abstract: Brill--Noether theory studies the maps of general curves to projective spaces. The embedding theorem of Eisenbud and Harris states that a general degree d map C to P^r is an embedding when r is at least 3. Hurwitz--Brill--Noether theory starts with a curve C already equipped with a fixed map C to P^1 (which often forces C to be special) and then studies the maps of C to other projective spaces. In this setting, the appropriate analogue of the invariants d and r is a finer invariant called the splitting type. Our embedding theorem determines the splitting types \vec{e} such that a general map of splitting type \vec{e} is an embedding. This is joint work with Kaelin Cook--Powel, Dave Jensen, Eric Larson, and Isabel Vogt./ | 9/5 | David Eisenbud | Socle Summands in Syzygies | I'll discuss two open problems about infinite resolutions, explain the ``Burch index'', and prove that, if a local Artinian ring has Burch index at least 2, then the 7th syzygy of every module has a summand isomorphic to the residue field. This is joint work with Hai Long Dao. |
| 9/12 | Xianglong Ni | Weyman's generic free resolutions of length three | One approach to studying the structure of finite free resolutions is to construct and analyze universal examples. Unfortunately, Bruns proved that these examples typically do not exist---but they do if one weakens the standard notion of universality to allow for non-unique specialization. Weyman constructed such "generic" examples for length three resolutions, with a careful handling of this non-uniqueness. Moreover, this apparent defect of the construction actually endows the generic example with additional symmetry, from which a surprising connection to the ADE classification arises. I'll explain how this extra symmetry can be leveraged to better understand Weyman's generic example, and some of its applications to linkage and the structure theory of perfect ideals. | |
| 9/19 | Bernd Ulrich | Linkage I | The first of a series of talks explaining the elements of this geometric theory that began with the classification of curves in $P^3$. The series will continue with an exposition of still-unpublished work giving new invariants of linkage in higher dimensions. | |
| 9/26 | No seminar: DE out of town | |||
| 10/3 | Daigo Ito | Derived Categories in Algebraic Geometry (tentative) | ||
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| 10/17 | No seminar: DE out of town | title | ||
| 10/24 | Mohamed Barakat | Doctrine-specific ur-algorithms | Various constructions of categories have a universal property expressing the freeness/initiality of the construction within a specific categorical doctrine. Expressed in an algorithmic framework, it turns out that this universal property is in a certain sense a doctrine-specific “ur-algorithm” from which various known categorical constructions/algorithms (including spectral sequences of bicomplexes) can be derived in a purely computational way. This can be viewed as a categorical version of the Curry-Howard correspondence to extract programs from proofs. | |
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| 12/5--last seminar of the semester | speaker | title | ||
Tuesdays 3:10-4:30, Evans 939
| date | speaker | title |
|---|---|---|
| 01/24 | Lauren Cranton Heller | Short virtual resolutions |
| 01/31 | no seminar | |
| 02/07 | no seminar | |
| 02/14 | David Eisenbud | Differential graded algebra resolutions |
| 02/21 | Jay Yang | Virtual resolutions of monomial ideals and virtual shellability |
| 02/28 | David Swinarski | Singular curves in Mukai's model of \(\bar M_7\) |
| 03/07 | Anurag Singh | When are the natural embeddings of classical invariant rings pure? |
| 03/14 | Anthony Várilly-Alvarado | Using algebraic geometry to probe the Earth's mantle |
| 03/21 | Xianglong Ni | Schubert varieties and the structure of codimension three perfect ideals |
| 03/28 | spring break | |
| 04/04 | Madeleine Weinstein | Metric algebraic geometry |
| 04/11 | Eric Larson | Interpolation for Brill-Noether curves |
| 04/18 | Eric Larson | The Minimal Resolution Conjecture for points on general Brill--Noether curves |
| 04/25 | Owen Barrett | Semistable reduction for curves over valuation rings |
| 05/02 | Yukari Ito | G-Hilbert scheme and the McKay correspondence |
| 08/31 | David Eisenbud | Summands in high syzygies |
| 09/07 | Lauren Cranton Heller | Multigraded regularity and betti numbers |
| 09/14 | Xianglong Ni | Linkage in codimension three |
| 10/11 | Franny Dean | Log concavity of sequences and a Hodge theory on matroids |
| 10/24 | Robin Hartshorne | History of the complete intersection problem |
| 11/01 | Luis Giraldo | An algebraic geometric approach to study polynomial vector fields in \(\mathbb C^2\) |
| 11/08 | Frank-Olaf Schreyer | Extensions of paracanonical curves of genus 6 |