Syzygies of Algebraic Varieties
Workshop For Graduate Students, Postdocs, and Young Researchers
Nov 20 - 22, 2015
at the University of Illinois at Chicago (UIC)
Support provided by NSF RTG grant DMS-1246844.
Overview: This workshop, aimed at graduate students and young postdocs, will expose participants to some current research topics on Syzygies of Algebraic Varieties. The workshop will have lecture series by the experts listed below on topics close to their own research, including a mix of lectures and problem sessions. Over the course of the weekend, we hope to present a number of open questions with sufficient background to be worked on both during and after the workshop.
Jinhyung Park (KIAS) [
Sijong Kwak (KAIST) [
Understanding of the defining equations and syzygies via inner projections and generic initial ideals
- References: http://arxiv.org/find/math/1/au:+Kwak_S/0/1/0/all/0/1
- Abstract: I will introduce algebraic and geometric methods using inner projections to understand defining equations and their relations of projective schemes. In addition, by using the theory of generic initial ideals with respect to the graded reverse lexicographic order, we can further understand the behavior of the graded Betti numbers. In this lecture, I introduce basic constructions including double point divisors and known results on the generic initial ideals, and apply them to equations and syzygies.
Steven Sam (University of Wisconsin)
Using representation theory to calculate syzygies
- Lecture notes: http://www.math.wisc.edu/~svs/talks/2015/uic-notes.pdf
- Abstract: In this mini-course, we will cover some of the material from Jerzy Weyman's book "Cohomology of Vector Bundles and Syzygies" and will give an overview of how one can use techniques from representation theory to calculate syzygies of certain varieties like determinantal varieties.
Lawrence Ein (UIC) [
Gonality and Syzygies of Algebraic Varieties
- References: https://www.dropbox.com/s/sxdiukh1vo267rj/EinReferences.pdf?dl=0
- Abstract: I plan to sketch the proof of my joint work with R. Lazarsfeld on the gonality conjecture on the syzygies of algebraic curves of large degree. I will also discuss recent joint work with R. Lazarsfeld and B. Ullery on a generalization of gonality to higher dimensional varieties and show how these invariants can be used as a measure of the irrationality of an algebraic variety. If time allows, I will also briefly describe asymptotic syzygies of higher dimensional algebraic varieties.
Funding: The deadline to apply for funding has passed. For questions about funding or about the workshop in general, please email Kevin Tucker at firstname.lastname@example.org.
- Introductory Lecture 5:30-6:30pm by Jinhyung Park in SEO 636
- Workshop Dinner 7:30pm-9:30pm at House of Fortune in Chinatown (2407 S Wentworth Avenue)
- Coffee and Refreshments 8:30-9:30am in SEO 300
- Minicourse One 9:30am-12:30pm by Sijong Kwak in SEO 636
- Lunch (provided) 12:30-2:00pm in SEO 300
- Minicourse Two 2:00-5:00pm by Steven Sam in SEO 636
- Coffee and Refreshments 8:30-9:30am in SEO 300
- Concluding Lecture 9:30-11:00am by Lawrence Ein in SEO 636
Getting to UIC: The workshop will be held in the UIC Math Department, which is located in the Science and Engineering offices building (SEO, 851 S Morgan St, Chicago, IL 60607). Signs with instructions on where to go will be throughout in the building, but you can also come to Kevin Tucker's office (SEO 417) looking for more information as well.
- By car: UIC is easily accessible by car, and is located just off of either the 90/94 or 290 interstates. If you are coming into UIC, it's best to park at the Halsted Parking Structure at the NE corner of the Taylor and Halsted intersection. You will have take a ticket for the parking garage; if we know in advance you will be parking there, you can bring your ticket in to the workshop and we can validate it to cover the cost. Note that in/out priveledges are not included in the validation. Also note that the parking at the Crown Plaza is far more expensive, and should be avoided if possible. It is recommended that you plan to park your car in the Halsted Parking Structure for the weekend instead.
- By train/bus: UIC is also close to Chicago's Union Station with conveinient Amtrak trains / Megabus routes to many locations in the region. A cab to UIC from Union Station should cost under $10. The Greyhound station is also very close by, and an easy walk to UIC.
- By air: Chicago has two major airports, O'Hare (ORD) and Midway (MDW), and it is easy to get to UIC from either one (many travel sites will let you look for both simultaneously using the airport code CHI).
If you are flying into O'Hare, you can take a Blue Line train (costing $5) into the city (towards the loop or Forest Park) which stops right next to the UIC campus (at the UIC/Halsted station) and in walking distance (half a mile) to the Crown Plaza hotel. For reference, a taxi from O'Hare to downtown will cost around $45 before tip (and can be paid with a credit card).
If you are flying into Midway, you can take an Orange Line train (costing $2.50) into the city (towards the loop), which will take you within walking distance of the Crown Plaza hotel (about a quarter of a mile from the Washington/Wells station) or allow you to transfer to the Blue Line (at the Harold Washington Library station) which stops right next to the UIC campus (at the UIC/Halsted station). Another good option is to take the Orange Line into the loop (e.g. Harold Washington Library station) and then take a short cab ride to UIC or the Crown Plaza (at most $10). For reference, a taxi from Midway to downtown will cost around $25 before tip (and can be paid with credit card).