Difference between revisions of "Algebra and Algebraic Geometry Seminar Spring 2019"

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(Spring 2019 Schedule)
(Abstracts)
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== Abstracts ==
 
== Abstracts ==
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===Daniel Smolkin===
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"Symbolic Powers in Rings of Positive Characteristic"
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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!
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===Juliette Bruce===
 
===Juliette Bruce===

Revision as of 18:03, 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.

Algebra and Algebraic Geometry Mailing List

  • Please join the AGS Mailing List to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).


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.