Seminar Calendar
for events the day of Tuesday, February 18, 2003.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, February 18, 2003

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, February 18, 2003
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Submitted by cpfrench.
 Ernesto Lupercio (U Wisconsin Math)TWISTED ORBIFOLD K-THEORYAbstract: String theory has recently motivated the study of the so-called twisted K-theory of a space. Witten has asked for the correct generalization of this functor to the category of orbifolds. An orbifold locally looks like a finite group acting on a manifold. In this talk I will survey several aspects of this circle of ideas and I will explain my work with Bernardo Uribe on Gerbes over orbifolds and twistings in K-theory.

String Theory RAP
12:00 pm   in 341 Altgeld Hall,  Tuesday, February 18, 2003
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Submitted by mcortez.
 Dror Varolin (UIUC Math)Quantum MechanicsAbstract: Further information on this seminar may be found at: http://www.math.uiuc.edu/~katz/stringrap/

Several Complex Variables
1:00 pm   in 243 Altgeld Hall,  Tuesday, February 18, 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.

Number Theory Seminar
1:00 pm   in 241 Altgeld Hall,  Tuesday, February 18, 2003
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Submitted by ford.
 Heini Halberstam (UIUC Math)Sparse sieves

RAP on Lubin-Tate-Morava cohomology theories
1:00 pm   in 159 Altgeld Hall,  Tuesday, February 18, 2003
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Submitted by rezk.
 David Gepner (UIUC)Formal group laws and complex cobordismAbstract: Lazard's theorem on the universal formal group law.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, February 18, 2003
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Submitted by evas.
 Anand Pillay (UIUC Math)Countable simple unidimensional theoriesAbstract: I will discuss a recent proof that countable simple unidimensional theories are supersimple under some mild assumption. This assumption, "the weak non finite cover property" is related to the theory of lovely pairs.

2:00 pm   in 241 Altgeld Hall,  Tuesday, February 18, 2003
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Submitted by jacox.
 Jonathan Cox   [email] (UIUC)Riemann-Roch Theorems and Enumerative GeometryAbstract: What happens to a bundle when you push it forward? Riemann-Roch theorems answer this question. This information, together with appropriate exact sequences of bundles, gives relations in Chow ring of a space which then allow computation of certain integrals. The integrals give enumerative information about the space. I will give examples for Grassmannians and, at least conjecturally, for moduli spaces of stable curves.

Geometric Potpourri Seminar
2:00 pm   in 243 Altgeld Hall,  Tuesday, February 18, 2003
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Submitted by seminar.
 Jeff Erickson (Professor, Department of Computer Science, UIUC)Intersecting nonconvex polyhedra: theory, practice, and bothAbstract: Computing intersections between nonconvex objects is a common problem in graphics, spatial databases, scientific computing, and other application areas. There are intersection algorithms that are provably always better than brute force, but they are too complicated to be practical. Most practical heuristics for computing intersections use a hierarchy of bounding volumes for each object. In the worst case, all such heuristics can be forced to behave as badly as brute force---if the two objects each have n features, the heuristics can be forced to take Omega(n^2) time---but the examples that lead to this worst-case behavior are quite contrived. I will explain bounding volume hierarchies, describe some worst-case examples, and show that under some realistic assumptions about the shapes of the objects, bounding volume hierarchies are provably efficient.

Algebraic Geometry Seminar
3:00 pm   in 345 Altgeld Hall,  Tuesday, February 18, 2003
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Submitted by mcortez.
 Lawrence Ein (University of Illinois at Chicago)Log Canonical Thresholds and Birational RigidtyAbstract: Log canonical threshold is natural invariant from higher dimensional geometry. We discuss the comparison of this new invariant with the more classical invariants such as multiplicity. As an application of this comparison, we show that the automorphism group of the function field of a smooth hypersurface of degree n in P^n is a finite group for 4<= n<=12. This generalizes the classical result of Iskovskikh, Manin Pukhlikov and others.

RAP "Spaces of Non-Positive Curvature"
3:00 pm   in Altgeld Hall, room 347,  Tuesday, February 18, 2003
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Submitted by kapovich.
 Professor Richard Bishop (UIUC)Metrics on the extension of a CAT(0) space by its boundaryAbstract: The extension of a CAT(0) space is the union of the space and its boundary at infinity. The cone topology of the extension generalizes the cone topology in the Riemannian case originally defined by Eberlein and O'Neill. We show that there are bounded length metrics on the extension which induces the cone topology

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, February 18, 2003
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Submitted by west.
 Jozef Skokan (UIUC Math)Tree representations of Kn,nAbstract: A graph is chordal if and only if it is the intersection graph of some family of subtrees of a tree. Applying "tolerance" allows larger families of graphs to be represented. A graph G is in the family [D,d,t] if there is a tree with maximum degree D and subtrees corresponding to the vertices of G such that each subtree has maximum degree at most d and vertices of G are adjacent if and only if the subtrees corresponding to them have at least t common vertices. It is known that [3,3,1] and [3,3,2] both equal the family of chordal graphs. Since a complete bipartite graph with partite sets of size at least 2 is not chordal, we study the minimum t such that Kn,n is in [3,3,t]. In this talk, we provide bounds for t in terms of n and discuss related problems.