Algebra and Algebraic Geometry Seminar Spring 2019: Difference between revisions
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===Daniel Smolkin=== | ===Daniel Smolkin=== | ||
''Symbolic Powers in Rings of Positive Characteristic'' | |||
The n-th power of an ideal is easy to compute, though difficult to describe geometrically. In contrast, symbolic powers of ideals are difficult to compute while having a natural geometric description. In this talk, I will describe how to compare ordinary and symbolic powers of ideals using the techniques of positive-characteristic commutative algebra, especially in toric rings and Hibi rings. This is based on joint work with Javier Carvajal-Rojas, Janet Page, and Kevin Tucker. Graduate students are encouraged to attend! | The n-th power of an ideal is easy to compute, though difficult to describe geometrically. In contrast, symbolic powers of ideals are difficult to compute while having a natural geometric description. In this talk, I will describe how to compare ordinary and symbolic powers of ideals using the techniques of positive-characteristic commutative algebra, especially in toric rings and Hibi rings. This is based on joint work with Javier Carvajal-Rojas, Janet Page, and Kevin Tucker. Graduate students are encouraged to attend! | ||
===Juliette Bruce=== | ===Juliette Bruce=== | ||
Revision as of 23:03, 23 January 2019
The seminar meets on Fridays at 2:25 pm in room B235.
Here is the schedule for the previous semester, for the next semester, and for this semester.
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Spring 2019 Schedule
| date | speaker | title | host(s) |
|---|---|---|---|
| January 25 | Daniel Smolkin (Utah) | Symbolic Powers in Rings of Positive Characteristic | Daniel |
| February 1 | Juliette Bruce | Asymptotic Syzgies for Products of Projective Spaces | Local |
| February 8 | Isabel Vogt (MIT) | Low degree points on curves | Wanlin and Juliette |
| February 15 | Pavlo Pylyavskyy (U. Minn) | TBD | Paul Terwilliger |
| February 22 | Michael Brown | Chern-Weil theory for matrix factorizations | Local |
| March 1 | TBD | TBD | TBD |
| March 8 | Jay Kopper (UIC) | TBD | Daniel |
| March 15 | TBD | TBD | TBD |
| March 22 | No Meeting | Spring Break | TBD |
| March 29 | Chris Eur (UC Berkeley) | TBD | Daniel |
| April 5 | TBD | TBD | TBD |
| April 12 | TBD | TBD | TBD |
| April 19 | Eloísa Grifo (Michigan) | TBD | TBD |
| April 26 | TBD | TBD | TBD |
| May 3 | TBD | TBD | TBD |
Abstracts
Daniel Smolkin
Symbolic Powers in Rings of Positive Characteristic
The n-th power of an ideal is easy to compute, though difficult to describe geometrically. In contrast, symbolic powers of ideals are difficult to compute while having a natural geometric description. In this talk, I will describe how to compare ordinary and symbolic powers of ideals using the techniques of positive-characteristic commutative algebra, especially in toric rings and Hibi rings. This is based on joint work with Javier Carvajal-Rojas, Janet Page, and Kevin Tucker. Graduate students are encouraged to attend!
Juliette Bruce
Title: Asymptotic Syzygies for Products of Projective Spaces
I will discuss results describing the asymptotic syzygies of products of projective space, in the vein of the explicit methods of Ein, Erman, and Lazarsfeld’s non-vanishing results on projective space.
Isabel Vogt
Title: Low degree points on curves
In this talk we will discuss an arithmetic analogue of the gonality of a curve over a number field: the smallest positive integer e such that the points of residue degree bounded by e are infinite. By work of Faltings, Harris--Silverman and Abramovich--Harris, it is well-understood when this invariant is 1, 2, or 3; by work of Debarre--Fahlaoui these criteria do not generalize to e at least 4. We will study this invariant using the auxiliary geometry of a surface containing the curve and devote particular attention to scenarios under which we can guarantee that this invariant is actually equal to the gonality . This is joint work with Geoffrey Smith.