Seminar Calendar
for Algebraic Geometry events the year of Monday, November 23, 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, January 27, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, January 27, 2009
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Submitted by nevins.
Arthur B. Coble (Department of Mathematics, University of Illinois)
Organizational meeting
Abstract: We'll meet to discuss speakers for this semester's seminar. We will also discuss a proposal to have a working seminar this semester (on a topic to be decided).

Wednesday, February 4, 2009

Graduate Student Topology and Geometry Seminar
1:00 pm   in 147 Altgeld Hall,  Wednesday, February 4, 2009
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Submitted by fricano1.
Nat Stapleton (Department of Mathematics, University of Illinois)
HKR and Algebraic Geometry
Abstract: We will explore the Hopkins-Kuhn-Ravenel generalized character isomorphism for Morava E-theory in the language of finite flat group schemes and p-divisible groups. If there is enough time we will discuss generalizations.

Tuesday, February 17, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, February 17, 2009
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Submitted by nevins.
William Haboush (Department of Mathematics, University of Illinois)
The Fundamental Lemma, Part I

Thursday, February 19, 2009

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, February 19, 2009
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Submitted by nmd.
Allen Knutson (Cornell University)
Why do matrices commute? Algebraic geometry meets statistical mechanics
Abstract: The matrix equations M^2 = 0 are quadratic, so to derive the linear equation Trace(M)=0 from them requires nonalgebraic operations. Are there corresponding "surprising" equations implied by the matrix equation XY=YX? This question was posed in the '60s, and still nobody knows. Even the (normalized) volume of this space &ob;(X,Y) : XY=YX&cb; is very difficult to compute for large matrices, and until recently was only known to start 1,3,31,1145.

I'll talk about a bunch of related spaces of matrices, some of which are provably harder and some easier to understand than the commuting scheme &ob;(X,Y) : XY=YX&cb;, and the volumes of these spaces. Then I'll explain how physicists came up with the same set of numbers from a statistical mechanical model (making them much easier to compute), and why they are indeed the same.

Some of this work is joint with Paul Zinn-Justin.


Tuesday, February 24, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, February 24, 2009
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Submitted by nevins.
Bill Haboush (UIUC Math)
The Fundamental Lemma, II
Abstract: This will be the second lecture introducing the Fundamental Lemma (following T. Hales's article).

Tuesday, March 3, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, March 3, 2009
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Submitted by nevins.
Bill Haboush (University of Illinois)
Statement of the Fundamental Lemma, III
Abstract: This is the third in a series of talks leading up to a precise statement of the Fundamental Lemma (recently proven by Ngo). It is based on the paper of T. Hales, "A statement of the fundamental lemma."

Tuesday, March 10, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, March 10, 2009
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Submitted by nevins.
Susan Sierra (University of Washington)
Transversality and noncommutative geometry
Abstract: Let Z and Y be closed subvarieties of a variety X. We say that Z and Y are _homologically_transverse_ if the higher Tor's of their structure sheaves all vanish. Now let G be an algebraic group acting on X. We give conditions on Z that ensure that for any Y, the general translate of Z under the action of G is homologically transverse to Y. This result generalizes a recent result of Miller and Speyer for transitive group actions and ultimately goes back to the classical Kleiman-Bertini theorem. We give applications to noncommutative algebraic geometry, including the classification of noncommutative surfaces.

Tuesday, March 17, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, March 17, 2009
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Submitted by nevins.
Donghoon Hyeon (Marshall University)
A new look at the moduli space of hyperelliptic curves
Abstract: There are two natural ways to compactify the moduli space of smooth hyperelliptic curves of genus g: one is to take the closure in the moduli space of stable curves of genus g, and the other is to construct the GIT quotient of semistable binary forms of degree 2g + 2. Avritzer and Lange showed that there is a projective birational morphism f from the former to the latter extending the natural isomorphism between the loci of smooth curves. By carrying out a log minimal model program, we prove that f decomposes into a series of divisorial contractions collapsing the boundary divisors in natural order. We also obtain a conjectural formula for critical values in the log MMP for the moduli of stable hyperelliptic curves which are also expected to be critical values for the log MMP for the moduli of stable curves. They are then identified with the values from a formula obtained by considering the GIT stability of curves. This suggests that log canonical models can be constructed as GIT quotients of Hilbert scheme of curves that are 'rationally' semistable.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, March 17, 2009
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Submitted by west.
Hal Schenck (UIUC Math)
Graphs, hyperplane arrangements, and algebra
Abstract: Associated to a simple graph G with vertex set V is a hyperplane arrangement A, which is a finite set of hyperplanes in the vector space K|V| (typically K is the complex or real numbers). Each edge (i,j) of G gives rise to a hyperplane, defined by the vanishing of the linear form xi-xj. I'll spend the first half of the talk describing examples and the basic translation between graph-theoretic concepts and the analogous concepts in algebraic geometry. In the second part I'll describe two basic algebraic objects associated to arrangements, as well as several open conjectures about these objects.

Thursday, March 19, 2009

Special Algebraic Geometry Seminar
1:00 pm   in 243 Altgeld Hall,  Thursday, March 19, 2009
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Submitted by nevins.
Bill Haboush (UIUC Math)
The statement of the fundamental lemma
Abstract: This continues our series on the statement of the Fundamental Lemma, recently proven by Ngo.

Tuesday, March 31, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, March 31, 2009
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Submitted by nevins.
Davesh Maulik (MIT)
Gromov-Witten Theory of K3 Surfaces

Tuesday, April 14, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, April 14, 2009
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Submitted by nevins.
Elizabeth Csima (UIUC)
The reduction of the fundamental lemma to the Lie algebra case

Wednesday, April 29, 2009

Graduate Student Topology and Geometry Seminar
1:00 pm   in Altgeld Hall 147,  Wednesday, April 29, 2009
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Submitted by reldred2.
Pat Szuta (UIUC Math)
Hochschild, Negative, Cyclic, and Periodic Homologies of Exact Categories
Abstract: K-theory is a powerful tool with applications in algebraic geometry, algebraic topology and number theory, with two main flavors, Algebraic and Topological. Analogous to how homology groups can be used to approximate homotopy groups, we use topological Hochschild Homology (and related equivariant constructions) to approximate Algebraic K-theory. In this talk, we'll discuss Hochschild, Negative, Cyclic, and Periodic homologies of exact categories (categories with exact sequences). Our primary focus will be on the relationship between these theories as invariants of rings.

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.