Seminar Calendar
for events the day of Thursday, September 18, 2008.

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Thursday, September 18, 2008

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, September 18, 2008
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Submitted by kapovitc.
Brent Solie (Department of Mathematics, University of Illinois)
The Bestvina-Feighn Combination Theorem
Abstract: The Bestvina-Feighn Combination Theorem gives a set of sufficient conditions under which a graph of groups where all vertex and edge groups are word-hyperbolic defines a group that is again word-hyperbolic. We will discuss the proof of this theorem and some applications.

Number Theory Seminar
1:00 pm   in 241 Altgeld Hall,  Thursday, September 18, 2008
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Submitted by seminar.
Pace Nielsen (University of Iowa)
A Covering System with Minimum Modulus 40
Abstract: A covering system is a set of congruence classes, with distinct moduli, for which each integer lives in at least one of the congruence classes. It is an open question of Paul Erdos whether covering systems exist where the minimum modulus can be chosen arbitrarily large. We introduce the readers to some new ways of picturing covering systems, and sketch the proof that there is a covering system with smallest modulus equal to 40.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, September 18, 2008
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Submitted by aimo.
Ken Stolarsky (Department of Mathematics, University of Illinois)
Analytic and algebraic properties of Chebyshev-like polynomials
Abstract: We shall survey various analytic and functional properties of Chebyshev polynomials and see how they extend to wider classes of polynomials. Some particular attention will be paid to the discriminants and zero distributions of such polynomials. If time permits, some open problems and connections with number theory will be given. Please note that there will be substantial overlap with the talk given on Tuesday in the number theory seminar.

Differential Geometry Seminar
3:00 pm   in 347 Altgeld Hall,  Thursday, September 18, 2008
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Submitted by ekerman.
Richard Hind (Notre Dame)
Symplectic embeddings in Euclidean space
Abstract: We will describe some constructions of and restrictions on symplectic embeddings, motivated by a question of Hofer related to the possibility of higher order sympectic capacities. This is joint work with Ely Kerman.

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, September 18, 2008
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Submitted by jmccullo.
Phil Griffith (Department of Mathematics, University of Illinois)
Heitmann's Direct Summand Theorem and the Ranks of Back Syzygies
Abstract: I will discuss the implication of Heitmann's direct summand theorem in dimension three with respect to application of the improved new intersection theorem in the context of the syzygy theorem.