Seminar Calendar
for events the day of Tuesday, April 29, 2003.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, April 29, 2003

Max Newman Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, April 29, 2003
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Submitted by seminar.
 Matthew Ando (UIUC, Department of Mathematics)All bundles are orientable if you're twisted enough

String Theory RAP
12:00 pm   in 341 Altgeld Hall,  Tuesday, April 29, 2003
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Submitted by mcortez.
 Rahul Biswas (UIUC Physics Graduate Student)Getting Einstein's Equations from String TheoryAbstract: Further information regarding this seminar may be found at: http://www.math.uiuc.edu/~katz/stringrap/

Number Theory Seminar
1:00 pm   in 241 Altgeld Hall,  Tuesday, April 29, 2003
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Submitted by ford.
 Heekyoung Hahn (UIUC Math)Ramanujan's letter to Hardy on Waring's Problem for g(4) and G(4) Abstract: First we briefly mention the history of Waring's problem. We then discuss Ramanujan's idea for getting a better bound for G(4). Finally we give a proof of Ramanujan's identity which he claimed should lead to an upper bound for G(4).

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, April 29, 2003
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Submitted by evas.
 Maya Saran (UIUC Math)How special are the meager and null ideals?Abstract: The sigma-ideal of meager subsets of 2^omega and the sigma-ideal of null subsets of 2^omega (null w.r.t. the usual product measure on 2^omega) have some nice properties: each is a ccc sigma-ideal, has a Borel basis, is index-invariant and translation invariant. Kunen asked whether these two ideals and their intersection were the ONLY sigma-ideals on 2^omega with all these properties. Roslanowski and Shelah answered this question in the negative; I will present their construction. I will also briefly mention related results of Kechris and Solecki.

Geometric Potpourri Seminar
2:00 pm   in 243 Altgeld Hall,  Tuesday, April 29, 2003
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Submitted by seminar.
 John M. Maki, John E. Wetzel, and Wacharin Wichiramala (UIUC, Department of Mathematics)Drapeability ReduxAbstract: An arc of length one in the plane is _drapeable_ if it lies in the convex hull of a convex arc of unit length. A unit arc is _admissible_ if the open line segment that joins its endpoints lies in the unbounded open connected component of the complement of its trace (draw a picture!). A unit arc is _circumscribed_ if its open endpoint line segment lies in the complement of the unbounded open connected component of the complement of its trace (draw another picture!). In a GeoPot seminar last October, Wetzel conjectured that every admissible unit arc is drapeable and that every circumscribed unit arc is drapeable. * Wetzel will begin with five minute survey, for context. * Maki will prove that every unit arc whose endpoints are no more than 0.222 apart is drapeable. (The smallest possible distance between the endpoints of a non-drapeable unit arc is not known.) * Wichiramala will prove the first conjecture, that every admissible arc is drapeable; and as time permits he will suggest an approach to the proof of the second conjecture. Kyung-won Hwang participated in some of this work.

2:00 pm   in 241,Altgeld Hall,  Tuesday, April 29, 2003
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Submitted by zhu5.
 Xinyun Zhu (UIUC Math)Gorenstein Threefold singularities with small resolutions via invariant theory for weyl groups, by Sheldon Katz and David R.Morrison

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, April 29, 2003
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Submitted by west.
 Hemanshu Kaul (UIUC Math)Small-world graphs - new random graph modelsAbstract: We are interested in two basic parameters of a graph G: lG is the average distance between two vertices in the graph, and CG (the clustering coefficient) is the average density of the subgraphs induced by vertex neighborhoods. Naturally evolving massive networks like the social networks of acquaintances (used to model the spread of diseases, rumors, etc.), the internet, the power grid, airline traffic, etc., share common characteristics like short average distance and high clustering coefficient. In the past, these networks have been modelled by the classical random graphs Gn,p, but Gn,p does not show any local clustering, making it a bad model for these networks. Recently, several random graph models have been proposed to incorporate the "small world effect" - average distance like that of the random graph, but much higher clustering coefficient. We will discuss some of these models and their properties. In addition to the small world effect, some of the above mentioned networks, like the internet and telephone call graphs, have been observed to have the property that the number of vertices of degree k is proportional to k-c for some constant c > 0. Graphs having this property are called power law graphs. If time permits, we will also discuss some variations on Gn,p whose degree distribution follows the power law.

RAP "Metric Spaces of Non-Positive Curvature"
3:00 pm   in Altgeld Hall,  Tuesday, April 29, 2003
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Submitted by kapovitc.
 Ilya Kapovich (UIUC)What is a building?Abstract: We will discuss Tits' notion of a building.

Student Awards Ceremony
4:00 pm   in 245 Altgeld Hall,  Tuesday, April 29, 2003
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Submitted by seminar.
 Please join us as we honor the recipients of the 2003 Department of Mathematics student awards. A reception will follow in the Commons Room, 3rd Floor Altgeld Hall

Nonstandard analysis and differential equations
5:00 pm   in 159 Altgeld Hall,  Tuesday, April 29, 2003
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Submitted by henson.
 Yevgeniy Gordon (Eastern Illinois Univ.)The relation of "relative standardness" in nonstandard analysis, and its applications.Abstract: Concepts of "relative standardness" were introduced by the speaker (in 1989, in the framework of Nelson's Internal Set Theory) and by I. Peraire (axiomatically). These will be discussed and some problems concerning possible applications of these notions to ODEs will be formulated.

Model Theory of Separably Closed Fields Seminar
5:00 pm   in 145 Altgeld Hall,  Tuesday, April 29, 2003
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Submitted by seminar.
 Piotr Kowalski (Department of Mathematics, UIUC)Minimal types in separably closed fields, continued