Seminar Calendar
for events the day of Tuesday, August 30, 2011.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, August 30, 2011

Ergodic Theory
11:00 am   in 347 Altgeld Hall,  Tuesday, August 30, 2011
 Del Edit Copy
Submitted by jathreya.
 Joe Rosenblatt (UIUC)Large Deviations for Sequences of Operators and Maximal Functions Abstract: We consider the integrability of $\phi(f^*)$ for various maximal functions $f^*$ and various increasing functions $\phi$. We show that for some of the standard maximal functions arising in harmonic analysis and ergodic theory, there is never integrability of $\phi(f^*)$ for all Lebesgue integrable functions $f$ except in cases where the growth of $\phi$ is slow enough so that the integrability follows from the standard weak maximal inequalities.

Topology Seminar
11:00 am   in 241 Altgeld Hall,  Tuesday, August 30, 2011
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Submitted by franklan.
 Charles Rezk (UIUC)Quasi-elliptic cohomology and stringy power operationsAbstract: I'll describe some work of Nora Ganter, in which she (1) constructs an equivariant cohomology theory (which I'll call "quasi-elliptic") as an "extension" of equivariant K-theory, and (2) describes a very interesting family of power operations for this theory.

Logic Seminar
1:00 pm   in Altgeld Hall,  Tuesday, August 30, 2011
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Submitted by sabok.
 Lou van den Dries (UIUC Math)Model theory of transseriesAbstract: Transseries are like power series in a variable 1/x, but may also contain terms like exp(x), exp(exp(x)), log(x), and the like. They are the elements of a differential field with a natural valuation. It is conjectured that the theory of this structure is model complete. I will discuss the work done on this conjecture in the last 15 years, and in particular the progress made in the last two years. This is joint work with Matthias Aschenbrenner and Joris van der Hoeven.

Harmonic Analysis and Differential Equations
1:00 pm   in 347 Altgeld Hall,  Tuesday, August 30, 2011
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Submitted by laugesen.
 Robert Jerrard   [email] (U. of Toronto)Rigidity of Sobolev isometric embeddingsAbstract: It has been known for about 50 years that a $C^2$ isometric embedding of the n-dimensional Euclidean unit ball into $(n+k)$-dimensional Euclidean space enjoys certain rigidity properties if $1 \leq k < n$. For example, its image cannot be contained in a ball of radius much less than 1. This is easily seen to be false if $k \geq n$, and there are dramatic counterexamples, due to Nash and Kuiper, showing that it is also false if one considers isometric embeddings that are merely $C^1$. We consider isometric embedding of the Euclidean n-ball into $R^{n+k}$ that belong to the Sobolev space $W^{2,p}$ for certain choices of $p \geq n$. Maps with this regularity may fail to be $C^1$. Nonetheless, we show that if $p \leq k+1$ then an isometric embedding is $C^{1, \alpha}$ for some positive $\alpha$, and enjoys rigidity properties similar to those of $C^2$ isometric embeddings. These results are believed, but not known, to be optimal. This is joint work with Reza Pakzad.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, August 30, 2011
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Submitted by west.
 Cory Palmer (UIUC Math)The Tree Packing ConjectureAbstract: The Gyárfás Tree Packing Conjecture asserts that any set of trees with $1, 2, 3,\ldots, n-1$ edges packs (edge-disjointly) into the complete graph on $n$ vertices. Gyárfás and Lehel proved that the conjecture is true when all but two of the $n-1$ trees are stars. They also proved the conjecture when the set of trees is made up of only stars and paths. We strengthen the first result by showing that a generalization of the conjecture holds if all but three of the $n-1$ trees are stars. We also show that any four trees of orders $n, n-1, n-2, n-3$ can be packed into the complete graph on $n$ vertices. Finally, we discuss some generalizations of the tree packing conjecture. (This is joint work with Balázs Keszegh and Dániel Gerbner).