UIUC Dept. of Mathematics Seminar Calendar

    November 2009          December 2009           January 2010    
 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  5  6  7          1  2  3  4  5                   1  2
  8  9 10 11 12 13 14    6  7  8  9 10 11 12    3  4  5  6  7  8  9
 15 16 17 18 19 20 21   13 14 15 16 17 18 19   10 11 12 13 14 15 16
 22 23 24 25 26 27 28   20 21 22 23 24 25 26   17 18 19 20 21 22 23
 29 30                  27 28 29 30 31         24 25 26 27 28 29 30
                                               31

Tuesday, December 1, 2009

Logic Seminar
1:00 pm in 345 Altgeld Hall, Tuesday, December 1, 2009

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Submitted by w-henson.

Jana Marikova (WIU)
O-minimal residue fields of o-minimal fields, I.
Abstract: Let R be an o-minimal field with a proper convex subring V, and let k be the corresponding residue field with residue map st: V \to k. We show that a certain first order axiom scheme in the language of (R,V) singles out exactly the structures (R,V) such that k_{ind}, the residue field with structure induced from R via st, is o-minimal. It has been shown in previous work that if (R,V) satisfies the above mentioned axiom scheme, then k_{ind} is o-minimal. The other direction is new and the proof uses a recent result by Shiota.

Analysis Seminar
2:00 pm in 241 Altgeld Hall, Tuesday, December 1, 2009

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Submitted by aimo.

Guan Yuan Zhang (Tsing Hua University, China)
The best bound of the area-length ratio in Ahlfors' covering surface theory
Abstract: Let $D$ be a closed disk in the complex plane and let $S$ be the unit Riemann sphere. A basic consequence of Ahlfors' theory of covering surfaces is that there exists an absolute constant $h$ such that for any nonconstant holomorphic mapping $f$ from $D$ into $S$, if $f$ does not take the three values $0$, $1$ and infinity, then $A/L < h$, where $A$ is the area of the image of $D$ and $L$ is the length of the image of the boundary of $D$, both counting multiplicities. We will introduce our recent work that give the precise bound of the ratio $A/L$. We indeed develop a new method whose starting points are a classical isoperimetric inequality of unit sphere due to F. Bernstein, a few simple observations, and some new results, such as the Triangle Lifting Lemma, the $4\pi$-Reducing Lemma, and a Theorem for treating non-convex vertices of polygonal boundary value curves of normal mappings defined in our paper.