Seminar Calendar
for events the day of Tuesday, October 5, 2010.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, October 5, 2010

Topology Seminar
11:00 am   in 241 Altgeld Hall,  Tuesday, October 5, 2010
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Submitted by mando.
 Emily Riehl (University of Chicago)Algebraic model structures Abstract: A model structure on a category provides a framework for doing homotopy theory whose main constructive tool consists of four classes of maps - the trivial cofibrations, fibrations, cofibrations, and trivial fibrations - which are defined so as to satisfy certain lifting properties with respect to each other. We'll present an algebraicization of Quillen's model structures that transform these properties into algebraic structure associated to the arrows in each of these classes. More precisely, the trivial cofibrations and fibrations are coalgebras and algebras for a comonad and monad, respectively, arising from the functorial factorization produced by a modified form of Quillen's small object argument. The same is true for the other pair, and there is a natural comparison between these two factorizations. Whenever a model structure is cofibrantly generated, this structural presentation exists and is equivalent to the usual property one, but this new perspective has several interesting features, which we describe. We conclude with a description of an "algebraic Quillen adjunction", which again exists in many familiar situations.

Harmonic analysis and Differential Equations Seminar
1:00 pm   in 347 Altgeld Hall,  Tuesday, October 5, 2010
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Submitted by berdogan.
 Brian Street (U. Wisconsin, Madison)Multi-parameter singular Radon transformsAbstract: We discuss singular (and maximal) Radon transforms where the singular kernel has a multi-parameter structure. We discuss operators of the form $f\mapsto \psi(x) \int f(\gamma(t,x)) K(t) dt,$ where $\psi$ is a $C^\infty$ cutoff function, $\gamma$ is a smooth function satisfying $\gamma(0,x)=x$, and $K$ is a singular kernel'' supported near $t=0$. The goal is to give finite-type'' conditions on $\gamma$ under which the above operator is bounded on $L^p$ (\$1

Logic seminar
1:00 pm   in Altgeld Hall 345,  Tuesday, October 5, 2010
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Submitted by vddries.
 Philipp Hieronymi (UIUC Math)Open definable sets in expansions of topological structuresAbstract: I consider the question of when an expansion of a topological structure has the property that every open set definable in the expansion is definable in the original structure. In joint work with Gareth Boxall, we answered the question in a fairly general setting and provided conditions which in practice are often easy to check. In this talk, I will discuss these results and some applications. On the way, I will introduce several basic notions and results from model theory and o-minimality. This talk will not assume much more than a very basic knowledge of first-order model theory and should hopefully be very understandable for new graduate students (and maybe even senior undergraduates).

Number Theory
1:00 pm   in 241 Altgeld Hall,  Tuesday, October 5, 2010
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Submitted by berndt.
 Paul Pollack (UIUC)Counting perfect numbersAbstract: A *perfect number* is a natural number n satisfying sigma(n)=2n. I will discuss the strategy introduced by Eduard Wirsing for bounding the number of perfect numbers below a given number x. As an application, we will prove a quantitative refinement of the following theorem of L.E. Dickson: For each fixed k, there are at most finitely many odd perfect numbers with <= k distinct prime factors.

2:00 pm   in 345 Altgeld Hall,  Tuesday, October 5, 2010
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Submitted by lukyane2.
 Anton Lukyanenko (UIUC)What is sub-Riemannian geometry and who cares?Abstract: I will define sub-Riemannian manifolds, describe how they arise in math and engineering, and mention some surprising properties.

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, October 5, 2010
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Submitted by nevins.
 Luca Scala (University of Chicago)Symmetric powers of tautological bundles on Hilbert schemes of points on a surfaceAbstract: By techniques by Danila and Le Potier, the comprehension of global sections of certain determinant line bundles on moduli spaces of sheaves over the projective plane can be reduced to the understanding of the cohomology of symmetric powers of some tautological line bundles on Hilbert schemes of points on P_2. We will discuss a work in progress on these symmetric powers, in order to understand their global sections, and some ideas to get their higher cohomology.

Study Seminar in Analysis and Geometry
3:00 pm   in 347 Altgeld Hall,  Tuesday, October 5, 2010
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Submitted by jmmackay.
 Jayadev Athreya (UIUC)Flows on nilmanifolds and theta sumsAbstract: We describe a part of the Forni program', which studies quantitative properties of parabolic dynamical systems by considering an appropriate renormalization system'. We'll review the paper `Equidistribution of nilflows and applications to theta sums' by L. Flaminio and G. Forni ( http://www.ams.org/mathscinet-getitem?mr=2218767 ). No background on equidistribution, nilflows, or theta sums will be assumed.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, October 5, 2010
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Submitted by west.
 Seog-Jin Kim (Konkuk University)Dynamic coloring of sparse graphsAbstract: A dynamic coloring of a graph G is a proper coloring of V(G) such that each vertex neighborhood of size at least 2 receives at least two distinct colors.  The list dynamic chromatic number chd(G) is the least integer k such that for every assignment of k-element lists to each vertex, there is a dynamic coloring of G with each vertex color chosen from its list. We prove that chd(G)≤4 if Mad(G)<8/3, where Mad(G) is the maximum average degree over subgraphs of G.  Also, chd(G)≤4 if G is a planar graph of girth at least 7.  Furthermore, if k≥4, then chd(G)≤k if Mad(G)<4k/(k+2).  All these results are sharp and are joint work with Won-Jin Park.