Seminar Calendar
for Algebraic Geometry events the next 12 months of Saturday, August 1, 2009.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery. 
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Tuesday, August 25, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, August 25, 2009
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Submitted by katzs.
Sheldon Katz   [email] (UIUC Math)
A classical perspective of algebraic geometry
Abstract: This is an expository talk, designed to be accessible to graduate students with little or no prior exposure to algebraic geometry.

Tuesday, September 1, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, September 1, 2009
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Submitted by llpku.
Rahul Pandharipande (Princeton University)
Quivers, curves, and the tropical vertex group
Abstract: Elements of the tropical vertex group are formal families of symplectomorphisms of the 2-dimensional algebraic torus. I will talk about commutators in the tropical vertex group and their relationship to quivers and curve counts. The latter is joint work with Gross and Siebert.

Wednesday, September 2, 2009

Algebraic Geometry Seminar
4:00 pm   in 343 Altgeld Hall,  Wednesday, September 2, 2009
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Submitted by nevins.
Kevin McGerty (Imperial College)
Rational Cherednik algebras and microlocal versions of the KZ functor
Abstract: We show how the relation of the rational Cherednik algebra in type A with the Hilbert scheme of points in the plane allows one to construct a family of exact functors which generalize the KZ functor of Ginzburg-Guay-Opdam-Rouquier.

Friday, September 4, 2009

Algebra, Geometry and Combinatorics Seminar
3:00 pm   in 445 Altgeld Hall,  Friday, September 4, 2009
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Submitted by llpku.
Zach Teitler (Texas A&M University)
Ranks of polynomials
Abstract: The Waring rank of a polynomial of degree d is the least number of terms in an expression for the polynomial as a sum of dth powers. The problem of finding the rank of a given polynomial and studying rank in general has been a central problem of classical algebraic geometry, related to secant varieties; in addition, there are applications to signal processing and computational complexity. Other than a well- known lower bound for rank in terms of catalecticant matrices, there has been relatively little progress on the problem of determining or bounding rank for a given polynomial (although related questions have proved very fruitful). I will describe new upper and lower bounds, with especially nice results for some examples including monomials and cubic polynomials. This is joint work with J.M. Landsberg.

Thursday, September 10, 2009

Algebraic Geometry Seminar
3:00 pm   in 241 Altgeld Hall,  Thursday, September 10, 2009
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Submitted by llpku.
Pierrette Cassou-Nogučs (Université Bordeaux I)
On polynomial maps
Abstract: I will give a survey on polynomial maps from \mathbb{C}^2 to \mathbb{C} and to \mathbb{C}^2 and discuss some questions about those maps.

Tuesday, September 15, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, September 15, 2009
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Submitted by llpku.
Benjamin Howard (University of Michigan)
The relations among invariants of points on the projective line
Abstract: We consider the coordinate rings of GIT quotients of n points on the projective line modulo automorphisms of the line. In particular we wish to describe such rings by generators and relations. Kempe found generators in 1894. We describe the full ideal of relations in these generators. (This is joint work with John Millson, Andrew Snowden, and Ravi Vakil.)

Tuesday, September 22, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, September 22, 2009
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Submitted by llpku.
Christian Schnell (University of Illinois at Chicago)
Complex analytic Neron models
Abstract: I will present a global construction of the Neron model for degenerating families of intermediate Jacobians; a classical case would be families of abelian varieties. The construction is based on Saito's theory of mixed Hodge modules; a nice feature is that it works in any dimension, and does not require normal crossing or unipotent monodromy assumptions. As a corollary, we obtain a new proof for the theorem of Brosnan-Pearlstein and Saito that, on an algebraic variety, the zero locus of an admissible normal function without singularities is an algebraic subvariety.

Friday, October 2, 2009

Algebra, Geometry and Combinatorics Seminar
3:00 pm   in 445 Altgeld Hall,  Friday, October 2, 2009
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Submitted by llpku.
Eugene Mukhin (Indiana University-Purdue University Indianapolis)
Algebraic Bethe Ansatz
Abstract: The method of algebraic Bethe Ansatz can be used to connect the Representation Theory (over complex numbers) to many areas of mathematics, including Integrable Systems (the KDV and KP hierarchies, the Calogero-Moser system), Special Functions (orthogonal and multiple orthogonal polynomials, hypergeometric solutions of the KZ equations), Algebraic Geometry (Schubert Calculus, the B. and M. Shapiro conjecture), Combinatorics (Kostka polynomials, Capelli identities, crystalls). These relations produce a number of difficult and important theorems. I will survey some recent results in this area. (Based on a joint project with V. Tarasov and A. Varchenko.)

Tuesday, October 6, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, October 6, 2009
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Submitted by llpku.
Li Li (University of Illinois)
Hilbert schemes of points on a Deligne-Mumford stack
Abstract: I will first review the definition and properties of Hilbert schemes of points on a Deligne-Mumford stack, then talk about how are our Hilbert schemes related to quiver varieties and multigraded Hilbert schemes.

Tuesday, October 13, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, October 13, 2009
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Submitted by llpku.
Wenchuan Hu (Institute of Advanced Study)
Topological aspects on Chow varieties
Abstract: The topological invariants of Chow varieties can be calculated by the homotopy theoretic method. In this talk I will discuss this method in calculating the Euler Characteristic of Chow varieties. This result has been obtained by Blaine Lawson and Stephen Yau by using a fixed point formula with a torus action. Our calculation in a direct and simple way. This technique also can be generalized to Chow varieties with certain group actions and other cases. Furthermore, I will also talk about the application of the method on l-adic Euler-Poincare Characteristic of Chow varieties over arbitrary algebraic closed field.

Tuesday, October 20, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, October 20, 2009
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Submitted by llpku.
Henry Schenck (University of Illinois)
On the equivariant Chow cohomology of nonsimplicial toric varieties
Abstract: For a toric variety X determined by a polyhedral fan P in a lattice N, the (rational) equivariant Chow cohomology is a graded Sym(N) module. We study the Chern classes of the associated reflexive sheaf on Proj(N). The first two Chern classes depend only on the combinatorics of P, but c_3 depends on the geometry of codimension two intersections of facets of P.

Tuesday, October 27, 2009

Algebraic Geometry Seminar joint with Algebra,Geometry and Combinatorics Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, October 27, 2009
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Submitted by llpku.
Matthew Satriano (University of California, Berkeley)
Stacky Resolutions of Singular Schemes
Abstract: Given a singular scheme X, one way to study it is through a resolution of singularities, which is oftentimes hard to control. In certain cases, however, one can construct a smooth stack which well-approximates X and can serve as a replacement for the resolution of singularities. In this talk, I describe two cases where such a stack exists and give applications to Invariant Theory, Hodge Theory, and toric Artin stacks.

Tuesday, November 3, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, November 3, 2009
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Submitted by llpku.
Bruce Reznick (Department of Mathematics, University of Illinois)
Higher Laws of Inertia
Abstract: Newton's Law of Inertia says that if a real quadratic form is written as a linear combination of the squares of real linear forms, then there are computable lower bounds on the numbers of positive and negative coefficients. It seems natural to wonder what happens in higher (even) degree. It turns out that a similar law applies for binary forms in degree 4, but fails in degree 6 (and probably higher).

Tuesday, November 10, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, November 10, 2009
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Submitted by llpku.
Pramod N. Achar (Louisiana State University)
Positivity, coherent sheaves, and representation theory
Abstract: A number of questions in representation theory involve an endomorphism algebra endowed with a natural Z-grading; sometimes, deep consequences follow if it can be shown that the negative-degree components vanish. I will explain several instances of such "positivity phenomena" in derived categories of coherent sheaves, following work of Arkhipov, Bezrukavnikov, Ginzburg, and others. I will then discuss a new approach to proving positivity theorems, followed by some potential applications.

Tuesday, November 17, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, November 17, 2009
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Submitted by llpku.
Steven Bradlow (University of Illinois)
Sp(4,R)-Higgs bundles: a Higgs bundle case study
Abstract: Using G=Sp(4,R) as a special case, we will describe what G-Higgs bundles are and how they can be used to study maps from surface groups into non-compact real Lie groups.

Tuesday, December 1, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, December 1, 2009
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Submitted by llpku.
Michael Broshi (University of Notre Dame)
G-Bundles over curves
Abstract: Let X be a Dedekind scheme and G a flat affine group scheme of finite type on X. We give a description of G-bundles on schemes over X inspired by Chevalley's theorem for algebraic groups over a field. As an application, we show that the fibred category of G-bundles over a smooth proper curve over a field is an Artin stack.

Tuesday, January 26, 2010

Graduate Student Algebraic Geometry Working Seminar
1:00 pm   in 347 Altgeld Hall,  Tuesday, January 26, 2010
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Submitted by mim2.
Stephen Maguire   [email] (UIUC Math)
Understanding First-Order Deformations (Part 1)
Abstract: We will concentrate on deformation theory and its applications to moduli theory, Mori Program, and birational geometry this semester. We are using Robin Hartshorne's book titled Deformation Theory. I will give the definition of deformation, talk about why we should care about such a thing, and give a proof that H0(Y, NY/X) parametrizes the deformation of a closed subscheme Y in X.

Mathematics Colloquium - Special Lecture 2009-10
4:00 pm   in 245 Altgeld Hall,  Tuesday, January 26, 2010
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Submitted by seminar.
Sam Payne (Stanford University and Clay Mathematics Institute)
Nonarchimedean algebraic geometry
Abstract: The usual norm on the complex numbers and its associated analytic geometry (holomorphic functions and differential forms) have been fundamental tools for understanding the geometry and topology of complex algebraic varieties since the beginnings of the subject. Nonarchimedean norms, such as the p-adic norm on the rational numbers, also have an associated analytic geometry which has been used in number theory, but is just beginning to be applied in other areas of mathematics, such as algebraic geometry and dynamical systems. This talk will be an introduction to nonarchimedean geometry with an explanation of its combinatorial manifestation in tropical geometry and relations to intersection theory.

Please join us for refreshments at 3:30 p.m. in the Common Room, 321 Altgeld Hall.

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.

Tuesday, March 30, 2010

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, March 30, 2010
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Submitted by nevins.
Travis Schedler (MIT)
To Be Announced

Tuesday, April 6, 2010

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, April 6, 2010
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Submitted by nevins.
David Smyth (Harvard)
To Be Announced

Tuesday, April 13, 2010

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, April 13, 2010
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Submitted by nevins.
Gwyn Bellamy (Edinburgh)
To Be Announced