Seminar Calendar
for Geometry Seminar 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.

Monday, August 31, 2009

CR Geometry Seminar
3:00 pm   in 345 Altgeld Hall,  Monday, August 31, 2009
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Submitted by jlebl.
Jiri Lebl (UIUC Math)
Normal forms, Hermitian operators, and CR maps of spheres and hyperquadrics
Abstract: We will prove and organize some results on the normal forms of Hermitian operators composed with the Veronese map. We apply this general framework to prove two specific theorems in CR geometry. First, extending a theorem of Faran, we will classify all real-analytic CR maps between any hyperquadric in $\C^2$ and any hyperquadric in $\C^3$, resulting in a finite list of equivalence classes. Second, we will prove that all degree-two CR maps of spheres in all dimensions are spherically equivalent to a monomial map, thus obtaining an elegant classification of all degree-two CR sphere maps.

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.

Tuesday, September 8, 2009

Graduate Student Topology and Geometry Seminar
3:00 pm   in 347 AH,  Tuesday, September 8, 2009
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Submitted by reldred2.
Rosona Eldred (UIUC Math)
Topological Defects in Ordered Systems
Abstract: Ordered systems, such as a crystal lattice, can have what are called 'topological defects'. We'll discuss order parameter spaces for crystals and magnets, then how the lower homotopy groups of the spaces are used to classify the defects. This is intended to be a general talk: there will be lots of pictures and no background in physics or topology assumed.

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.

Monday, September 14, 2009

CR Geometry Seminar
3:00 pm   in 345 Altgeld Hall,  Monday, September 14, 2009
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Submitted by jlebl.
John P. D'Angelo (UIUC Math)
Iterated commutators of complex vector fields

Tuesday, September 15, 2009

Geometry Seminar
2:00 pm   in 243 Altgeld Hall,  Tuesday, September 15, 2009
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Submitted by sba.
Scott Tichenor (UIUC Math)
Curves of Constant Width I: Examples and Constructions
Abstract: I will give a short introduction to curves of constant width including definitions and examples. I will then show several ways to construct curves of constant width including one construction that I believe can be extended to include the others.

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.)

Monday, September 21, 2009

CR Geometry Seminar
3:00 pm   in 345 Altgeld Hall,  Monday, September 21, 2009
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Submitted by jlebl.
Alexander Tumanov (UIUC Math)
Beltrami operator on the torus

Tuesday, September 22, 2009

Differential Geometry Seminar
1:00 pm   in 243 Altgeld Hall,  Tuesday, September 22, 2009
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Submitted by ekerman.
Isidora Milin (UIUC Math)
Orderability of Contactomorphism Groups of Lens Spaces
Abstract: A contact isotopy of a contact manifold is "positive" if during it, each point of the manifold moves in a positively transverse direction to the contact hyperplane distribution. The question of whether this notion induces a partial order on the universal cover of the identity component of the contactomorphism group - whether the contact manifold is "orderable" - turns out to be sensitive to the topology of the contact manifold, and is related to nonsqueezing phenomena in contact geometry, as studied by Eliashberg, Kim and Polterovich. I will begin by explaining this relation, and then describe a version of contact homology for domains that enables us to detect relevant contact nonsqueezings. This will be illustrated by standard contact sphere (not orderable) and lens spaces (orderable).

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.

Graduate Student Topology and Geometry Seminar
3:00 pm   in 347 Altgeld Hall,  Tuesday, September 22, 2009
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Submitted by reldred2.
Nat Stapleton (UIUC Math)
Abstracting Monoids
Abstract: We look at generalizations of monoids. Particularly we look at monoidal categories and their generalizations to monoidal infinity categories. As an example we present the monoidal infinity category of stable presentable infinity categories with colimit preserving functors and notice that it's unit is the infinity category of spectra with smash product.

Monday, September 28, 2009

CR Geometry Seminar
3:00 pm   in 345 Altgeld Hall,  Monday, September 28, 2009
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Submitted by jlebl.
Jiri Lebl (Department of Mathematics, University of Illinois)
Polynomials Constant on a Hyperplane and CR Maps of Hyperquadrics
Abstract: In joint work with Han Peters we have proved sharp degree estimates for polynomials constant on a hyperplane in dimension 3. The motivation for the work are CR maps of spheres and hyperquadrics.

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.

Monday, October 19, 2009

CR Geometry Seminar
3:00 pm   in 345 Altgeld Hall,  Monday, October 19, 2009
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Submitted by jlebl.
Cancelled

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

Differential Geometry Seminar
1:00 pm   in 243 Altgeld Hall,  Tuesday, October 27, 2009
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Submitted by ekerman.
Rebecca Goldin (George Mason University)
Full Orbifold K-theory of Abelian Symplectic Quotients
Abstract: We will begin with a review of one way in which orbifolds arise, which is via the symplectic of a Hamiltonian T-space, where T is an abelian Lie group. Our goal is to describe the full orbifold K-theory for this class of spaces. Toward that purpose, we introduce the *inertial K-theory* of a Hamiltonian T-space M and show that it surjects as a ring onto the full orbifold K-theory of the symplectic quotient, denoted M//T (at a regular value). This research essentially involves two ingredients: The fact (due to M. Harada and G. Landweber) that equivariant K-theory of M maps surjectivity onto the K-theory of M//T, and the invention of a fancy product on the inertial K-theory of M, so that it surjects onto the full orbifold K-theory of M//T. These ideas are based on a similar (though rational) story in cohomology which we will also discuss. This is joint work with T. Holm, M. Harada, and T. Kimura.

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.

Monday, November 2, 2009

CR Geometry Seminar
3:00 pm   in 345 Altgeld Hall,  Monday, November 2, 2009
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Submitted by jlebl.
Alexander Tumanov (Department of Mathematics, University of Illinois)
Iterated commutators, holomorphic dimension, and analytic discs.
Abstract: Following comments by Giuseppe Zampieri, I will present a simple proof of the main result of the 50 page paper by Diederich and Fornaess of 1978 on analytic sets in pseudoconvex boundaries.

Tuesday, November 3, 2009

Differential Geometry Seminar
1:00 pm   in 243 Altgeld Hall,  Tuesday, November 3, 2009
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Submitted by clein.
Eriko Hironaka (FSU & Harvard)
Small dilatation mapping classes from the simplest pseudo-Anosov braid
Abstract: By a recent theorem of Farb, Leininger and Margalit, the set of 3-manifolds `realizing' mapping classes with small dilatation (compared to Euler characteristic) is finite. We show that all known minimal dilatation mapping classes for small genus are realized on the complement of Rolfsen's 6_2^2 link in S^3, and discuss the plausibility that minimal dilatation mapping classes for all genus are realized on this manifold.

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).

Monday, November 9, 2009

CR Geometry Seminar
3:00 pm   in 345 Altgeld Hall,  Monday, November 9, 2009
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Submitted by jlebl.
Alexander Tumanov (Department of Mathematics, University of Illinois)
Iterated commutators, holomorphic dimension, and analytic discs II.
Abstract: Following comments by Giuseppe Zampieri, I will present a simple proof of the main result of the Annals paper by Diederich and Fornaess of 1978 on analytic sets in pseudoconvex boundaries.

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

Geometry Seminar
2:00 pm   in 243 Altgeld Hall,  Tuesday, November 17, 2009
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Submitted by sba.
Vincent Matsko (IMSA)
Envelopes of Conic Sections
Abstract: In one of the classic nineteenth-century geometry texts, Salmon's *A Treatise on Conic Sections*, conics are discussed in the context of the projective plane. As a result, the duality of conic sections and their envelopes is easily represented. This talk will extend ideas of previous talks based on Salmon. In particular, use of the tangential equation to produce an envelope of lines for a conic will be discussed. Several examples will be described, followed by a brief slide show of attempts at creating an art gallery of pleasing geometric forms. An introduction to all necessary ideas is included in the talk. Interested undergraduates are encouraged to attend.

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.

Thursday, November 19, 2009

Differential Geometry Seminar
3:00 pm   in 347 Altgeld Hall,  Thursday, November 19, 2009
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Submitted by clein.
Ken Bromberg (U. Utah)
The asymptotic dimension of the mapping class group
Abstract: We will show that the mapping class group has finite asymptotic dimension. A key piece of the proof is the construction of a quasi-tree that mapping class acts on. This construction works in a quite general setting for groups that have some aspect of negative curvature. We will describe this construction and explain how it relates to the asymptotic dimension of the mapping class group. This is joint work with K. Fujiwara and M. Bestvina.

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, 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