Student Commutative Algebra Seminar, Spring 2014.

• Thursday, January 23,
  Today's seminar is replaced by the Colloquium in room 412.
  Speaker: Claudiu Raciu, Princeton University
  Title: "Syzygies of line bundles on Segre-Veronese varieties"
  Abstract: Syzygies are important classical invariants attached to algebraic varieties. They can be defined iteratively starting from the defining equations of a variety and continuing with the relations between these equations, the relations between the relations etc. In the special case of the Segre-Veronese embeddings of products of projective spaces, the structure of syzygies is particularly rich, due to the presence of a large group of symmetries. Their study can be approached through a variety of techniques, placing them at the confluence of algebraic geometry, commutative algebra, representation theory and combinatorics. I will discuss some recent results on the structure of the syzygies of line bundles on Segre-Veronese varieties, and explain how their vanishing controls the asymptotic vanishing behavior (in the sense of Ein and Lazarsfeld) of syzygies of arbitrary algebraic varieties.
  
  
• Thursday, February 6, 2014, 4:15 -- 5:15 PM, room 312 LeConte
  Speaker: Cameron Atkins
  Title: "The long exact sequence of Tor associated to a short exact sequence of modules"
  
  
• Wednesday, February 12, 2014, 3:30 -- 4:30 PM, room 412 LeConte
  Speaker: Nathan Ilten, University of California-Berkeley
  Title: "Linear Spaces of Singular Matrices."
  
  
• Thursday, February 13, 2014, No seminar.
  
  
• Thursday, February 20, 2014
  Today's seminar is replaced by
  Speaker: Michael Griffin, Emory University
  Title: "A framework of Rogers-Ramanujan identities and their arithmetic properties."
  Time and place: room 312, Friday, February 21, 11:00 AM
  
  
• Thursday, February 27, 2014, 4:15 -- 5:15 PM, room 312 LeConte
  Speaker: Tyler Lewis
  Title: "Tor may be computed in either component, with an application to the calculation of socle degrees."
  
  
• Thursday, March 6, 2014, 4:15 -- 5:15 PM, room 312 LeConte
  Speaker: Tyler Lewis
  Title: "Tor may be computed in either component, with an application to the calculation of socle degrees. Part 2."
  
  
• Thursday, March 20, 2014
  Today's seminar is replaced by the colloquium
  Speaker: Karl Schwede, Penn. State University.
  
  Title: Singularities of polynomials in characteristic zero and characteristic p
  
  Time and Place: Thursday, March 20 at 4:30 in LC 412.
  
  Abstract: We will consider solution sets to polynomial equations. For example, consider y^2 = x^3, the solution set has a singularity at the origin (a cusp). I will talk about different ways to measure singularities such as this one. First I will discuss the multiplier ideal, a way to measure singularities via integration. Second I will discuss the test ideal, a way to measure singularities if one considers them over a finite field. It has been known for nearly two decades that these two independently introduced notions are closely related. I will discuss recent joint work with Manuel Blickle and Kevin Tucker which shows that these two objects are in fact aspects of the same phenomenon.