Seminar Calendar
for Algebraic Geometry events the month of Tuesday, February 9, 2010.

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Questions regarding events or the calendar should be directed to Tori Corkery. 
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Tuesday, February 2, 2010

Graduate Student Algebraic Geometry Working Seminar
1:00 pm   in 347 Altgeld Hall,  Tuesday, February 2, 2010
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Submitted by mim2.
Mee Seong Im   [email] (UIUC Math)
Understanding First-Order Deformations (Part 2)
Abstract: This is the second of a series of lectures from Robin Hartshorne's Deformation Theory. I will discuss structures such as a (sub)scheme flat over the dual numbers (this is thought of as an infinitesimal thickening a scheme evenly spread out over the base), some applications of the Ti functors (e.g., given a k-algebra B where k is a field, deformations of B over the dual numbers are classified by T1(B/k,B) and its obstructions lie in T2(B/k,B)), the infinitesimal lifting property, and deformation of rings (this has to do with finding various extensions of a ring B by a B-module). I will also talk about when trivial deformations and trivial extensions are the only possibility for a scheme. Since this is a seminar for graduate students, I will attempt to provide as many examples as possible during the lecture.

Monday, February 8, 2010

CR Geometry/Algebraic Geometry Seminar
4:00 pm   in 243 Altgeld Hall,  Monday, February 8, 2010
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Submitted by nevins.
Kevin Tucker (University of Michigan)
Jumping Numbers and Multiplier Ideals on Algebraic Surfaces
Abstract: Jumping numbers and multiplier ideals are recently defined invariants of singularities on complex algebraic varieties. We will give an introduction and overview while paying particular attention to the case of algebraic surfaces. Several new and interesting results will also be presented. These include the theorem that the jumping numbers of the germ of a plane curve (a priori analytic invariants) depend only on the topological type of the curve.

Tuesday, February 9, 2010

Graduate Student Algebraic Geometry Working Seminar
1:00 pm   in 347 Altgeld Hall,  Tuesday, February 9, 2010
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Submitted by mim2.
Steve Maguire   [email] (UIUC Math, 1-3PM)
Higher Order Deformations and Obstruction Theory (Part 3)
Abstract: I will talk about higher order deformations and obstruction theory applied to subschemes, invertible sheaves, vector bundles and coherent sheaves. Jimmy Shan and I will prove when a locally free sheaf over a scheme X can be deformed when X is deformed, the necessity and the sufficiency of the vanishing of its obstruction for the existence of global deformation, and which group the automorphism of the deformed sheaf is isomorphic to. The first hour will be devoted to lecture while the second hour (2-3PM) will be devoted to working on problems from Hartshorne's book.

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, February 9, 2010
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Submitted by nevins.
Kevin Tucker (University of Michigan)
On the Number of Log Canonical Centers and Compatibly F-Split Subvarieties
Abstract: In this talk, I will explain joint work with Karl Schwede which gives identical enumerative bounds for two very different mathematical objects. The first, log canonical centers, are certain loci of singularities arising in the study of higher dimensional complex algebraic geometry. They are particularly important for inductive arguments and adjunction theorems in the minimal model program. The second arise in positive characteristic and are those subvarieties which inherit a fixed splitting of Frobenius. These compatibly F-split subvarieties have been very useful in both representation theory and commutative algebra. In the process of describing our result and giving an idea of the proof, I hope to also impart the mathematical philosophy that (mysterious) connections between complex algebraic geometry and positive characteristic commutative algebra can lead to new and interesting results in both of these areas.

Tuesday, February 16, 2010

Graduate Student Algebraic Geometry Working Seminar
1:00 pm   in 347 Altgeld Hall,  Tuesday, February 16, 2010
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Submitted by mim2.
Mee Seong Im   [email] (UIUC Math, 1-3PM)
Higher Order Deformations (Part 4)
Abstract: Higher Order Deformations applied to Cohen-Macaulay in codimension 2 and complete intersections and Gorenstein in codimension 3. More specific details to be announced.

Tuesday, February 23, 2010

Graduate Student Algebraic Geometry Working Seminar
1:00 pm   in 347 Altgeld Hall,  Tuesday, February 23, 2010
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Submitted by mim2.
To be Announced (UIUC Math, 1-3PM)
To Be Announced (Part 5)
Abstract: To be announced.