UIUC Dept. of Mathematics Seminar Calendar

      July 2009             August 2009           September 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  4                      1          1  2  3  4  5
  5  6  7  8  9 10 11    2  3  4  5  6  7  8    6  7  8  9 10 11 12
 12 13 14 15 16 17 18    9 10 11 12 13 14 15   13 14 15 16 17 18 19
 19 20 21 22 23 24 25   16 17 18 19 20 21 22   20 21 22 23 24 25 26
 26 27 28 29 30 31      23 24 25 26 27 28 29   27 28 29 30         
                        30 31

Tuesday, August 25, 2009

Topology seminar
11:00 am in 241 Altgeld Hall, Tuesday, August 25, 2009

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No meeting this week.

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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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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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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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

Tuesday, December 1, 2009

Topology seminar
11:00 am in 241 Altgeld Hall, Tuesday, December 1, 2009

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Simona Paoli (Penn State Altoona)
Homotopical Properties of weakly globular models of homotopy types
Abstract: Homotopy n-types are an important class of topological spaces: they amount to CW complexes whose homotopy groups vanish in dimension higher than n. The problem of modelling homotopy types is relevant both in higher category theory and homotopy theory and received contributions from both areas. There is a particularly simple model of homotopy types in the path connected case, consisting of n-fold categories internal to groups, also called cat$^n$-groups. This model, however, has the disadvantage that is it does not have an algebraic description of the Postnikov decomposition nor it is easy to establish algebraically when a map of cat$^n$-groups is a weak equivalence. In this talk we introduce a new model of connected n-types through a subcategory of cat$^n$-groups, which we call weakly globular, for which the above issues are resolved in transparent way. We also describe other homotopical properties of this model, and discuss the relevance of these structures for higher category theory.

Tuesday, December 8, 2009

Tuesday, January 26, 2010

Tuesday, February 2, 2010

Tuesday, February 9, 2010

Tuesday, February 16, 2010

Topology seminar
11:00 am in 241 Altgeld Hall, Tuesday, February 16, 2010

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Angelica Osorno (MIT)
An infinite loop space machine for symmetric monoidal 2-categories
Abstract: In recent work of Baas-Dundas-Richter-Rognes, the authors prove that the classifying space of 2-vector bundles, K(Vect) is equivalent to the algebraic K-theory of the connective K-theory spectrum ku. In this talk we will show that K(Vect) is the group completion of the classifying space of the 2-category of 2-vector spaces, which is a symmetric monoidal 2-category. We will explain how to use the symmetric monoidal structure to produce a $\Gamma$-2-category, which will give an infinite loop space structure on K(Vect). Then we will show that the equivalence mentioned above is a map of infinite loop spaces.