UIUC Dept. of Mathematics Seminar Calendar

    September 2010          October 2010          November 2010    
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Tuesday, October 19, 2010

Topology Seminar
11:00 am in 241 Altgeld Hall, Tuesday, October 19, 2010

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Submitted by mando.

Anna-Marie Bohmann (University of Chicago)
The equivariant generating hypothesis
Abstract: Freyd's generating hypothesis is a long-standing conjecture in stable homotopy theory. The conjecture says that if a map between finite spectra induces the zero map on homotopy groups, then it must actually be nullhomotopic. We formulate the appropriate version of this conjecture in the equivariant setting. We then give some results about this equivariant version and compare them to the nonequivariant results. In particular, we show that the rational version of this conjecture holds when the group of equivariance is finite, but fails when the group is S1. This result uses Greenlees's description of the rational S1-equivariant homotopy category.

Differential Geometry Seminar
1:00 pm in 243 Altgeld Hall, Tuesday, October 19, 2010

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Submitted by clein.

Spencer Dowdall (U Chicago Math)
Dilatation vs self-intersection number for point-pushing pseudo-Anosovs
Abstract: This talk is about the dilatations of pseudo-Anosov mapping classes obtained by pushing a marked point around a filling curve. After reviewing this "point pushing" construction, I will give both upper and lower bounds on the dilatation in terms of the self-intersection number of the filling curve. I'll also give bounds on the least dilatation of any pseudo Anosov in the point-pushing subgroup and describe the asymptotic dependence on self-intersection number. All of the upper bounds involve analyzing explicit examples using train tracks, and the lower bound is obtained by lifting to the universal cover and studying the images of simple closed curves.

Geometry Seminar
2:00 pm in 243 Altgeld Hall, Tuesday, October 19, 2010

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Submitted by sba.

Vince Matsko (IMSA)
On Kepler's Laws
Abstract: Kepler's Laws are often derived using vector methods in a third-semester calculus course.� However, such a derivation was first given by Newton - who was born twelve years after Kepler's death. In this talk, we begin with a brief historical introduction to Kepler's world, with specific reference to his relationship with Tycho Brahe.� Without the precision of Tycho's calculations, Kepler would not have been able to derive his eponymous laws. Retrograde motion of planets will then be discussed, followed by a derivation of the law of equal areas.� Finally, Kepler's creation of a nested sequence of celestial spheres will be presented. Some understanding of calculus is necessary.� This talk is suitable for undergraduates.

Algebraic Geometry Seminar
3:00 pm in 243 Altgeld Hall, Tuesday, October 19, 2010

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Submitted by nevins.

Yusuf Mustopa (Michigan)
Ulrich Bundles on del Pezzo Surfaces
Abstract: Ulrich bundles occur naturally in a variety of algebraic and algebro-geometric topics, including determinantal and Pfaffian descriptions of hypersurfaces, the computation of resultants, and the representation theory of generalized Clifford algebras. In this talk I will discuss the connection between the existence of rank r Ulrich bundles on a degree-d del Pezzo surface X and the geometry of curves of degree dr on X, and how it can be used to study the moduli of Ulrich bundles on X. This is joint work with Emre Coskun and Rajesh Kulkarni.

Study Seminar in Analysis and Geometry
3:00 pm in 347 Altgeld Hall, Tuesday, October 19, 2010

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Submitted by jmmackay.

Patrick Reynolds (UIUC Math)
Limit groups and Λ-trees
Abstract: We will first define Λ-trees, give some basic properties, and explain how these objects generalize simplicial trees (and ℝ-trees). We will then explain a few ways in which group actions on Λ-trees arise in nature (e.g. certain morphisms of finitely generated groups into non-standard extensions of hyperbolic groups). We will then sketch a proof of Guirardel showing that the Limit Groups of Sela act freely on a "simple" type of Λ-trees.
We will give all the necessary definitions/background, so the talk will be accessible to a general audience.

Graph Theory and Combinatorics
3:00 pm in 241 Altgeld Hall, Tuesday, October 19, 2010

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Submitted by west.

Oliver Pechenik (UIUC Math)
A-Cordial Graphs
Abstract: If A is an abelian group, then a labeling f: V(G)→A of the vertices of some graph G induces an edge-labeling on G as well; the edge uv receives the label f(u)+f(v). A graph G is A-cordial if there is a vertex-labeling f: V(G)→A such that (1) the vertex color-classes differ in cardinality by at most 1, and (2) the induced edge color-classes also differ in cardinality by at most 1.

Almost all research on A-cordiality has focused on the case where A is cyclic. We investigate the non-cyclic case, looking particularly at the group Z₂×Z₂. We also introduce a generalization of A-cordiality to digraphs and non-abelian groups, and we show that there are infinitely many A-cordial digraphs for every group A.