UIUC Dept. of Mathematics Seminar Calendar

     October 2009          November 2009          December 2009    
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
              1  2  3    1  2  3  4  5  6  7          1  2  3  4  5
  4  5  6  7  8  9 10    8  9 10 11 12 13 14    6  7  8  9 10 11 12
 11 12 13 14 15 16 17   15 16 17 18 19 20 21   13 14 15 16 17 18 19
 18 19 20 21 22 23 24   22 23 24 25 26 27 28   20 21 22 23 24 25 26
 25 26 27 28 29 30 31   29 30                  27 28 29 30 31

Tuesday, February 10, 2009

Topology seminar
11:00 am in 241 Altgeld Hall, Tuesday, February 10, 2009

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Submitted by bertg.

Bert Guillou (Department of Mathematics, University of Illinois)
Enriched Categories and Equivariant Stable Homotopy Theory
Abstract: I will begin by describing some joint work with J.P. May on enriched model categories. As an application, we are able to obtain a new model for the equivariant stable homotopy category of a compact Lie group. When the group is finite, I will give another description of the latter using K-theory.

Tuesday, February 17, 2009

Topology seminar
11:00 am in 241 Altgeld Hall, Tuesday, February 17, 2009

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Submitted by mando.

Barry Walker (Northwestern)
The V Operator in Algebraic Topology
Abstract: Motivated by the definition of Katz' modular forms we construct a theory of generalized Bernoulli numbers on formal groups. The V operator is the effect on the quotient obtained by the subgroup of p-torsion points. The V operator is now intimately related to the Adams operations in the Lubin-Tate cohomology theores. We can use this definition to describe the effect of the K(1) local logarithm on infinite complex projective space for E_1. An interesting question is then: what the role the Ando Condition plays in this story? The answer is compatible with the obstruction theory to orientations of Ando, Blumberg Gepner, Hopkins and Rezk. If there's time we will try to say something abou tthe U operator and future work.

Tuesday, March 3, 2009

Wednesday, March 4, 2009

Graduate Student Geometry & Topology Seminar
1:00 pm in 147 Altgeld Hall, Wednesday, March 4, 2009

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Submitted by fricano1.

Christopher Lee [email] (UIUC Math)
An Invitation to G-Manifolds
Abstract: This talk serves as an introduction to the general theory of manifolds equipped with actions of compact Lie groups. After a (hopefully) brief definition session, we begin in earnest by considering the local picture given by the Slice Theorem and its consequences. We then attempt to extend our understanding globally by restricting our attention to torus actions. We will make progress by classifying closed surfaces admitting faithful circle actions and will catch a glimpse of results from higher dimensions.

Tuesday, March 10, 2009

Topology seminar
11:00 am in 241 Altgeld Hall, Tuesday, March 10, 2009

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Submitted by mando.

Pokman Cheung (MIT)
Vertex algebras and the Witten genus
Abstract: This is the first report on an ongoing project aimed at finding a geometric interpretation of the Witten genus in terms of conformal vertex algebras (CVAs). Such an interpretation was first discovered by Gorbounov, Malikov and Schechtmann (GMS) for a special type of manifolds. In this talk, I will attempt to describe: (i) the GMS sheaves of CVAs and their relation with the Witten genus, and (ii) certain sheaves of dg CVAs that provide fine resolutions of the GMS sheaves. The role of (ii) for the Witten genus is the same as the role of the Dolbeault resolution for the Todd genus. The speaker hopes to find a generalization of (ii) for all smooth string manifolds, from which we may learn more about the geometry of these manifolds as well as what geometric notions are classified by tmf.

Tuesday, March 31, 2009

Tuesday, April 7, 2009

Topology seminar
11:00 am in 241 Altgeld Hall, Tuesday, April 7, 2009

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Submitted by bertg.

Kirsten Wickelgren (Stanford)
Obstructions to homotopy sections of curves over number fields
Abstract: Grothendieck's anabelian conjectures say that hyperbolic algebraic curves over number fields should be K(pi,1)'s in algebraic geometry. It follows that conjecturally the rational points on such a curve are the sections of etale pi_1 of the structure map. These conjectures are analogous to equivalences between fixed points and homotopy fixed points of Galois actions on related topological spaces. We use cohomological obstructions of Jordan Ellenberg's coming from nilpotent approximations to the curve to study the sections of etale pi_1 of the structure map. We will relate Ellenberg's obstructions to Massey products, and explicitly compute mod 2 versions of the first and second for P^1-{0,1,infty}.

Tuesday, April 14, 2009

Topology seminar
11:00 am in 241 Altgeld Hall, Tuesday, April 14, 2009

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Submitted by bertg.

Andrew Salch (Johns Hopkins University)
A computational motivation for topological Langlands correspondences.
Abstract: We describe the most effective known method for computing the stable homotopy groups of spheres at odd primes; this uses formal modules over p-adic number rings, together with base-change properties of the "chromatic filtration," i.e., local cohomology on the moduli stacks of formal modules, to construct the Adams-Novikov E_2-term. A consequence of these methods is the appearance of denominators of special values of Artin L-functions in the orders of the stable homotopy groups of spheres. We describe the role this phenomenon plays in motivating the (still very speculative) study of topological Langlands correspondences.

Tuesday, April 21, 2009

Tuesday, April 28, 2009

Tuesday, August 25, 2009

Tuesday, September 1, 2009

Tuesday, September 8, 2009

Wednesday, September 9, 2009

Tuesday, September 15, 2009

Tuesday, September 22, 2009

Tuesday, September 29, 2009

Tuesday, October 6, 2009

Topology seminar
11:00 am in 241 Altgeld Hall, Tuesday, October 6, 2009

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Submitted by bertg.

Megan Guichard Shulman (University of Chicago)
RO(Z/p)-graded cohomology of some classifying spaces
Abstract: When dealing with G-spaces for a finite group G, there are many reasons to think that RO(G)-graded Bredon cohomology is the ``correct'' equivariant cohomology theory to consider. Unfortunately, it is also very difficult to compute with. Gaunce Lewis calculated the RO(Z/p)-graded cohomology of complex projective spaces in the 1980s, and William Kronholm calculated the RO(Z/2)-graded cohomology of some real projective spaces in his 2008 thesis, but to date no other calculations have been done. In this talk, I will describe an equivariant spectral sequence which can be used in conjunction with the equivariant Serre spectral sequence and the equivariant cohomology of complex projective spaces to identify the RO(Z/p)-graded cohomology of the equivariant classifying space B_{Z/p} O(2).

Tuesday, October 13, 2009

Topology seminar
11:00 am in 241 Altgeld Hall, Tuesday, October 13, 2009

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Jeremiah Heller (Northwestern University)
Vanishing Theorems for Real Algebraic Cycles
Abstract: Homotopy groups of topological spaces of cycles on an algebraic variety form rich and intriguing invariants of the variety. Some of these homotopy groups are classical topological invariants (e.g. singular homology in the complex case, Bredon homology in the real case) and some are classical geometric invariants (e.g. cycles modulo algebraic equivalence). However most of these homotopy groups remain quite mysterious and difficult to compute. We discuss recent joint work with M. Voineagu where we show that the k-th homotopy group of the space of "reduced" r-cycles on a real variety vanishes for k larger than dim(X)-r. This is the real analogue of the (still open) Friedlander-Mazur conjecture for homotopy groups of cycles on a complex variety. Additionally we compute equivariant homotopy groups of spaces of cycles on a real variety in terms of Bredon homology in some cases.

Tuesday, October 20, 2009

Topology seminar
11:00 am in 241 Altgeld Hall, Tuesday, October 20, 2009

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Julie Bergner (UC Riverside)
Algebraic theories and (\infty, n)-categories
Abstract: One approach to the comparison of simplicial monoids and Segal monoids, or diagrams of simplicial sets which look like simplicial monoids but only up to homotopy, makes use of the algebraic theory of monoids. One can then construct more complicated algebraic theories in order to extend this comparison to more general simplicial categories and Segal categories with a given fixed object set. This approach becomes extremely useful in the most general comparison of simplicial categories and Segal categories, two of the models for (\infty, 1)-categories. Thus, it is expected that having algebraic theories corresponding to n-categories with a fixed set of objects would be helpful in comparing analogous models for (\infty, n)-categories. In this talk we'll look at work in progress in this direction.

Tuesday, October 27, 2009

Topology seminar
11:00 am in 241 Altgeld Hall, Tuesday, October 27, 2009

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Submitted by bertg.

John Francis (Northwestern University)
Invariants of E_n-algebras
Abstract: E_n-algebras are less commutative analogues of E-infinity algebras, which arise naturally from such objects as n-fold loop spaces, (oo,n)-categories, topological field theories, and Poisson algebras. After introducing the basic features of the theory of E_n-algebras, I'll describe some sophisticated invariants, which are E_n variants of Quillen cohomology and Hochschild cohomology, and I'll prove a relation between them first conjectured by Kontsevich. Finally, I'll discuss how E_n-Hochschild cohomology is the Lie algebra of the group of automorphisms of an n-category.

Tuesday, November 3, 2009

Tuesday, November 10, 2009

Topology seminar
11:00 am in 241 Altgeld Hall, Tuesday, November 10, 2009

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Submitted by bertg.

Jennifer French (MIT)
Modeling local spaces as mapping spaces of ring spectra
Abstract: The motivation is to generalize the algebraic models for rational homotopy theory developed by Sullivan and Quillen, and for p-adic homotopy theory developed by Mandell. The natural context to generalize these models is as mapping spaces of (commutative) R-algebras, where R is an E-infinity ring spectrum. The main tool for understanding the homotopy groups of such a mapping space is the Goerss--Hopkins spectral sequence. We will explore these R-algebra mapping spaces as models for certain localizations of spaces in the cases R = Hk, where k is the algebraic closure of the field Fp, and the case that R is the K(1)-local sphere spectrum.

Tuesday, November 17, 2009

Wednesday, December 2, 2009