Seminar Calendar
for events the day of Tuesday, February 25, 2003.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, February 25, 2003

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, February 25, 2003
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Submitted by cpfrench.
 Kristine Bauer (Johns Hopkins)Classifying FunctorsAbstract: This is joint work in progress with Greg Arone, Dan Christensen and Dan Isaksen. Several classification theorems for degree n functors from Spaces to Spectra and Spectra to Spectra have already been discovered (Dwyer-Rezk, Chaoha, Goodwillie, Johnson-McCarthy). We look again at classifying degree n functors from Spaces to Spectra with an eye towards trying to classify degree n functors from Spaces to Spaces.

String Theory RAP
12:00 pm   in 341 Altgeld Hall,  Tuesday, February 25, 2003
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Submitted by mcortez.
 Matthew Ando (UIUC Math)Classical Scalar FieldsAbstract: 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, February 25, 2003
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Submitted by ford.
 Alexandru Zaharescu (UIUC Math)On the parity of partition functions.Abstract: For any subset S of the positive integers, let p_S(n) denote the number of partitions of n into parts taken from S. Working in the ring of formal power series in one variable over the field of two elements we develop new methods for deriving lower bounds for both the number of even values and the number of odd values taken by p_S(n) for n less than N. This is joint work with Bruce Berndt and Ae Ja Yee.

Several complex variables
1:00 pm   in 243 Altgeld Hall,  Tuesday, February 25, 2003
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Submitted by dror.
 Eugene Lerman (UIUC)Kaehler cutsAbstract: This is joint work with Dan Burns and Victor Guillemin. A symplectic cut of a manifold M with a Hamiltonian circle action is a symplectic quotient of M x C (C denotes the complex line). If M is Kaehler then, since C is Kaehler, the cut space is Kaehler as well. The symplectic structure on the cut is well understood. In the talk I will describe the complex structure (and hence the metric) on the cut. I will then generalize the construction to the case where M has a torus action and C is replaced by a toric Kaehler manifold.

Logic Seminar
1:00 pm   in 345Altgeld Hall,  Tuesday, February 25, 2003
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Submitted by evas.
 Paul Schupp (UIUC Math)Generic-case Complexity and Decision Problems in Group TheoryAbstract: There is now a realization in complexity theory that worst-case complexity does not necessarily give a good overall picture of a particular problem or algorithm. The classic example is Dantzig's Simplex Algorithm for Linear Programming. This algorithm is used thousands of times a day and alway runs very quickly in practice. The examples of Klee and Minty show that one can make the Simplex Algorithm take exponential time but a "typical" problem is not at all like a bad example. It turns out that the situation of many decision problems in group theory is very similar. Even if the worst case complexity of a problem is very high or the problem is even undecidable, the "generic-case" complexity is often very low on the groups usually studied in combinatorial/geometric group theory.

2:00 pm   in 241,altgeld hall,  Tuesday, February 25, 2003
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Submitted by zhu5.
 Xinyun ZhuVersal deformation and superpotentials for rational curves in smooth threefolds

Geometric Potpourri Seminar
2:00 pm   in 243 Altgeld Hall,  Tuesday, February 25, 2003
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Submitted by seminar.
 Gregory Galperin (Professor, EIU Mathematics Department)The multidimensional cube: its geometric, arithmetic, combinatorial, and "electrical" properties, and paradoxesAbstract: Abstract: A generalization of a square is a standard 3-dimensional cube K3, whose generalization, in turn, is a _tesseract_, a 4-dimensional cube K4 that can be obtained from K3 by moving the standard cube along the fourth dimension. A d-dimensional cube Kd is obtained from the cube K(d-1) in the same manner. After drawing the tesseract on the blackboard and calculating the number of its vertices, edges, plane faces, and three-dimensional faces, we present a simple formula for the number of faces of all dimensions from 0 to d (for each d = 1, 2, 3, ...). A natural modification of this formula, applied to an arbitrary polyhedron, leads to relationships between the number of polyhedron's faces of all dimensions, one of which is the famous Euler's formula for polyhedra. The rest of the hour will be devoted to some beautiful formulas associated with different arithmetic, geometric, and "electrical" properties of the d-dimensional cube. Two paradoxes of the multidimensional cube in large dimensions (starting with dimension 10) will also be presented. The talk is based on elementary notions of geometry and algebra. It will be absolutely clear for undergraduate students. Students of all levels are encouraged to attend the talk.

RAP "Metric Spaces of Non-Positive Curvature"
3:00 pm   in Altgeld Hall, room 347,  Tuesday, February 25, 2003
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Submitted by kapovich.
 Ilya Kapovich (UIUC)Ends and CAT(0) cubingsAbstract: We will discuss the theorem of Sageev-Gerasimov relating groups with more than one relative end to actions on CAT(0)-cubings. We will start by explaining how to reconstruct the integer grid decomposition of the plane into squares if we forget where the edges and the vertices were (but remember something else).

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, February 25, 2003
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Submitted by west.
 Douglas B. West (UIUC Math)Optimal decomposition of a complete graph into many partsAbstract: A k-decomposition of a graph G is a partition of its edge set to form k spanning subgraphs G1,...,Gk. The classical theorem of Nordhaus and Gaddum bounds the sum of the chromatic numbers over all 2-decompositions of Kn. For a graph parameter p, let p(k;G) denote the maximum of sumi p(Gi) over all k-decompositions of the graph G. We obtain upper and lower bounds on p(k;Kn) when p is the clique number, chromatic number, list chromatic number, or Szekeres-Wilf number (they all equal n+1 when k=2). The last three behave differently for large k. We also obtain bounds for the maximum of chi(k;G) over all graphs embedded on a given surface. The talk will present a portion of these results. This is joint work with Zoltan Furedi, Alexandr Kostochka, Riste Skrekovski, and Michael Stiebitz.

Model Theory of Separably Closed Fields Seminar
4:00 pm   in 143 Altgeld Hall,  Tuesday, February 25, 2003
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Submitted by seminar.
 Piotr Kowalski (Department of Mathematics, UIUC)Minimal types in seperably closed fields are Zariski