UIUC Dept. of Mathematics Seminar Calendar

      July 2011             August 2011           September 2011   
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
                 1  2       1  2  3  4  5  6                1  2  3
  3  4  5  6  7  8  9    7  8  9 10 11 12 13    4  5  6  7  8  9 10
 10 11 12 13 14 15 16   14 15 16 17 18 19 20   11 12 13 14 15 16 17
 17 18 19 20 21 22 23   21 22 23 24 25 26 27   18 19 20 21 22 23 24
 24 25 26 27 28 29 30   28 29 30 31            25 26 27 28 29 30   
 31

Tuesday, August 30, 2011

Ergodic Theory
11:00 am in 347 Altgeld Hall, Tuesday, August 30, 2011

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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.

Harmonic Analysis and Differential Equations
1:00 pm in 347 Altgeld Hall, Tuesday, August 30, 2011

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Robert Jerrard [email] (U. of Toronto)
Rigidity of Sobolev isometric embeddings
Abstract: 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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Cory Palmer (UIUC Math)
The Tree Packing Conjecture
Abstract: 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).