Seminar Calendar
for events the day of Thursday, September 23, 2010.

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Thursday, September 23, 2010

Number Theory
1:00 pm   in 241 Altgeld Hall,  Thursday, September 23, 2010
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Submitted by berndt.
Joseph Vandehey (UIUC)
Information, probability, and randomness in even and odd continued fractions
Abstract: Ustinov gave a wonderful, short solution to the following problem: given a random irrational x and its sequence of continued fraction convergents $p_n/q_n$, along with a large $R >0$, what is the probability that the first time $q_n > R$ the continued fraction digits $a_{n-k},a_{n-k+1},\ldots,a_{n+k}$ all take some given values? We will present the solution to the more complicated case of even continued fractions and odd continued fractions. This talk is based on joint research with Florin Boca done for this summer's REGS.

Joint Group Theory/Differential Geometry Seminar
1:00 pm   in 347 Altgeld Hall,  Thursday, September 23, 2010
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Submitted by clein.
Chris Leininger (UIUC Math)
Right-angled Artin subgroups of the mapping class group
Abstract: I'll talk about coarse geometric properties of Right-angled Artin subgroups of the mapping class group. This is joint work with Matt Clay and Johanna Mangahas.

Commutative Algebra Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, September 23, 2010
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Submitted by asecele2.
Hal Schenck (UIUC)
Euler characteristic of line bundles on simplicial torics via the Stanley-Reisner ring
Abstract: We combine work of Cox on the homogeneous coordinate ring of a toric variety and results of Eisenbud-Mustata-Stillman and Mustata on cohomology of toric and monomial ideals to obtain a simple formula for computing $\chi(\mathcal&ob;O&cb;_X(D))$ for a divisor $D$ on a complete simplicial toric variety $X_&ob;\Sigma&cb;$. The main point is to use Alexander duality to pass from the toric irrelevant ideal, which appears in the computation of $\chi(\mathcal&ob;O&cb;_X(D))$, to the Stanley-Reisner ideal of $\Sigma$, which is used in defining the Chow ring of $X_\Sigma&.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, September 23, 2010
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Submitted by clein.
Krzysztof Burdzy (University of Washington)
Archimedes' principle for Brownian liquid
Abstract: I will present a mathematical model illustrating Archimedes' principle. The model is not quite realistic but, surprisingly, there seem to be no earlier rigorous results on Archimedes' principle in mathematical literature. The same mathematical model illustrates two other physical phenomena -- the formation of liquid surface and centrifuge effect. The two main mathematical techniques used in this project are the Dirichlet form approach to reflected Brownian motion and sphere packing. Joint work with Zhenqing Chen and Soumik Pal.