KAIST Thematic Program on Syzygies & Secants

Place

Department of Mathemtaical Sciences, KAIST, Daejeon, South Korea

Period

September - November, 2024

Event of the last week of November: Mini-Workshop 3
November 25 (Monday)
Natural Science Building (E6) Room 1410 (Edu4.0)

14:00 - 15:00 Steven Dale Cutkosky  (University of Missouri, Columbia)
Title: Asymptotic behavior of Hilbert functions of divisorial filtrations

15:30 - 16:30 Wenbo Niu (University of Arkansas)
Title: Distinguished subvarieties of base locus of linear systems

17:00 - 18:00 Hema Srinivasan (University of Missouri, Columbia)
Title: Kunz-Waldi semigroups and their generalizations

Zoom: https://kaist.zoom.us/j/86705848798?pwd=VMLqWAuLnsXiQMDF4GaMt6mUdthnOb.1

Meeting ID: 867 0584 8798
Password: syzygies

Lecture Series

• Frank-Olaf Schreyer (Saarland University)

Title: An experimental and computational approach to algebraic geometry

Abstract: The lecture series gives a view on computational methods and their some applications to existence and classfication problems. In the first lectures I will introduce Groebner basis and their basic applications in commutative algebra such as computing kernel and images of morphism between finitely presented modules over polynomial rings. As a theoretical application of Groebner basis I will give Petri's analysis of the equations of a canonical curve. The second topic will be Computer aided existence and unirationality proofs of algebraic varieties and their moduli spaces. In case of curves liaison theory is needed, which will be developed. For existence proofs random searches over finite fields is a technique that has not been exploited very much. I will illustrate this technique in a number of examples, in particular for the construction of certain surfaces. Classification of non-minimal surfaces uses adjunction theory. We will discuss this from a computational point of view.

Place: Natural Science Building (E6) Room 1410 (Edu4.0)

Schedule: 10:30 AM - 11:30 AM

• September: 5(Thu), 10(Tue), 12(Thu), 19(Thu)

• October: 1(Tue), 15(Tue), 17(Thu), 22(Tue), 24(Thu), 29(Tue)
  * 10 times totally

• Lawrence Ein (University of Illinois at Chicago)

Place: Natural Science Building (E6) Room 1401

• Lecture 1: October 24 (Thursday) 14:00 - 15:00, 
  Title: The Green-Lazarsfeld theorem on projective normality
  Abstract: We'll present a proof of the theorem of Green and Lazarsfeld on projective normality using the bend and break trick of  Mori (an argument due to Mukai and Sakai).

• Lecture 2: October 28 (Monday) 14:30 - 15:30
  Title: Kemeny's proof of Voisin's theorem on the syzygies of a generic canonical curve
  Abstract: We'll present the beautiful proof of Kemeny on Voisin's theorem using a  rank 2 bundle on a K3 surface.

• Lecture 3: October 30 (Wednesday) 14:30 - 15:30
  Title: Asymptotic syzygies
  Abstract: We'll present the results of Ein-Lazarsfeld and Park on asymptotic syzygies of a higher dimensional variety.

Colloquium

• Frank-Olaf Schreyer (Saarland University)

Title: Classification of 3-linear varieties of small codimension

Schedule: Oct 17 (Thu) 16:15-17:15

Mini-Workshops

• Workshop 1 on Oct 10(Thu)
  Place: Natural Science Building (E6) Room 1401

• 10:30 - 11:30 Daniele Agostini (University of Tübingen)
  Title: Ulrich sheaves on secants of curves

• • 14:00 - 15:00 Kangjin Han (DGIST)
    Title: On the ideals of $k$-secants of some Veronese embeddings

  • 15:30 - 16:30 Michael Kemeny (University of Wisconsin - Madison)
    Title: Projections of syzygies

• Workshop 2 on Oct 16 (Wed)
  Place: Natural Science Building (E6) Room 1410 (Edu4.0)

  • 11:00 - 12:00 Justin Lacini (Princeton University)
    Title: Syzygies of adjoint linear series on projective varieties 

  • 14:00 - 15:00 Hyunsuk Moon (KIAS)
    Title: Rank 3 generators of Segre-Veronese Embedding

  • 15:30 - 16:30 Claudiu Raicu (University of Notre Dame)
    Title: Stable sheaf cohomology on flag varieties 

  • 17:00 - 18:00 John Sheridan (Princeton University)
    Title: Torelli theorems for certain Steiner bundles on projective space

• Workshop 3 on Nov 25 (Mon)
  Place: Natural Science Building (E6) Room 1410 (Edu4.0)

  • 14:00 - 15:00 Steven Dale Cutkosky  (University of Missouri, Columbia)
    Title: Asymptotic behavior of Hilbert functions of divisorial filtrations

  • 15:30 - 16:30 Wenbo Niu (University of Arkansas)
    Title: Distinguished subvarieties of base locus of linear systems

  • 17:00 - 18:00 Hema Srinivasan (University of Missouri, Columbia)
    Title: Kunz-Waldi semigroups and their generalizations

Seminars

• Online Lectures

• Sep 13(Fri) 10:30 - 11:30 Steven V Sam (University of California, San Diego)
  Title: From total positivity to pure free resolutions 

• Oct 23 (Wed) 16:30 - 17:30 Marian Aprodu (University of Bucharest & IMAR)
  Title: Resonance and vector bundles

• Oct 30 (Wed) 10:00 - 11:00 Eric Larson (Brown University)
  Title: Normal bundles of rational curves in Grassmannians 

• Korean Participants

• Sep 20(Fri) 11:30 - 12:30 Yeongrak Kim (Pusan National University)
  Title: Resonance, Syzygies, and Rank-3 Ulrich bundles on V_5

• Oct 2(Wed) 16:30 - 17:30 Jaewoo Jung (IBS-CCG)
  Title: Syzygies of Stanley-Reisner ideals

• Oct 4(Fri) 10:30 - 11:30 Junho Choe (KIAS)
  Title: Quadratic equations of tangent varieties and 4-way tensors of linear forms 

• Oct 7(Mon) 16:30 - 17:30 Doyoung Choi (KAIST)
  Title: Degree of the 3-secant variety

• Oct 18(Fri) 10:30 - 11:30 Yonghwa Cho (Gyeongsang National University)
  Title: The structure of algebraic surfaces with maximal number of nodes

Participants

• Marian Aprodu (University of Bucharest & IMAR)
  participation: online

• Daniel Erman (University of Hawaii)
  participation: online

• Gavril Farkas (Humboldt University of Berlin)
  participation: online

• Eric Larson (Brown University)
  participation: online

• Steven V Sam (University of California, San Diego)
  participation: online

• Daniele Agostini (University of Tübingen)
  participation: Sep 30(Mon) - Oct 11(Fri)

• Michael Kemeny (University of Wisconsin - Madison)
  participation: Oct 6(Sun) - Oct 13(Sun)

• Claudiu Raicu (University of Notre Dame)
  participation: Oct 12(Sat) - Oct 26(Sat)

• Justin Lacini (Princeton University)
  participation: Oct 13(Sun) - Oct 20(Sun)

• John Sheridan (Princeton University)
  participation: Oct 13(Sun) - Oct 20(Sun)

• Lawrence Ein (University of Illinois at Chicago)
  participation: Oct 22(Tue) - Nov 2(Sat)

• Steven Dale Cutkosky (University of Missouri, Columbia)
  participation: Nov 18(Mon) - Nov 27(Wed)

• Hema Srinivasan (University of Missouri, Columbia)
  participation: Nov 18(Mon) - Nov 27(Wed)

• Wenbo Niu (University of Arkansas)
  participation: Nov 24(Sun) - Nov 30(Sat)

• Euisung Park (Korea University)

• Wanseok Lee (Pukyong National University)

• Kangjin Han (DGIST)

• Yeongrak Kim (Pusan National University)

• Hyunsuk Moon (KIAS)

• Junho Choe (KIAS)

• Jong In Han (KAIST)

• Doyoung Choi (KAIST)

• Jaewoo Jung  (IBS-CCG)

• Yonghwa Cho (Gyeongsang National University)

• Jeaman Ahn (Kongju National University)

Organizers

• Sijong Kwak (KAIST)

• Jinhyung Park (KAIST)

• Frank-Olaf Schreyer (Saarland University)