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

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

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, March 18, 2003
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Submitted by cpfrench.
 Halvard Fausk (Northwestern)A stable homotopy splitting theorem for finite groups.

String Theory RAP
12:00 pm   in 341 Altgeld Hall,  Tuesday, March 18, 2003
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Submitted by mcortez.
 Joshua Guffin (UIUC Physics Graduate Student)Path Integral QuantizationAbstract: The Path Integral formalism is much more powerful than the canonical quantization, because calculations are carried out with the fields as functions rather than operators. The path integral will be derived from quantum mechanics and lifted to field theory. The equivalence of functional derivatives on the path integral and the time ordered product (propagator) from canonical quantization will be demonstrated. Further information regarding this seminar may be found at: http://www.math.uiuc.edu/~katz/stringrap/

Differential Geometry Seminar
1:00 pm   in 347 Altgeld Hall,  Tuesday, March 18, 2003
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Submitted by mineyev.
 Karsten Große-Brauckmann (TU Darmstadt)On periodic isoperimetric problemsAbstract: While in euclidean space spheres solve the isoperimetric problem, there are many other solutions in the periodic setting. For particular symmetry groups of flat 3 tori (crystallographic groups), we will present and discuss candidate surfaces, along with known results on them, in particular the recent work of Hauswirth, Perez, Romon and Ros.

Analytic Number Theory
1:00 pm   in 241 Altgeld Hall,  Tuesday, March 18, 2003
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Submitted by ahlgren.
 Song Heng Chan   [email] (UIUC)A reciprocity theorem for a certain q-series found in Ramanujan's lost notebookAbstract: This beautiful reciprocity theorem was first proved by George Andrews, who used heavy machinery. We give four new proofs and also show that it is a two variable generalization of the quintuple product identity. This is joint work with Bruce Berndt, Boon Yeap, and Ae Ja Yee.

RAP on Lubin-Tate-Morava cohomology theories
1:00 pm   in 159 Altgeld Hall,  Tuesday, March 18, 2003
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Submitted by rezk.
 Rekha Santhanam (UIUC Math)Lubin-Tate deformation theory

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, March 18, 2003
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Submitted by evas.
 Itay Ben-Yaacov (UIUC Math)Uncountable categoricity in cats, cont.Abstract: Cats form a general model theoretic framework that makes it possible to treat in a uniform manner a wide range of classes: elementary classes, Banach-like structures, probability spaces and more. After giving the basic definitions I will speak about notions of topology and abstract distance which are intrinsic to a cat, as well as their relation to true extra-logical metrics. The topology (or metric) allows us to define "complete models", which are the analogue of models of a first order theory, and whose size is measured by their density character rather than by cardinality. It also allows us to define the correct analogues of $\lambda$-stability and Morley Rank, in a manner similar to that of Iovino in Banach spaces. Having developed these tools, we prove that a cat is categorical in one uncountable cardinal if and only if it is categorical in every uncountable cardinal, following ideas found in Shelah's lazy guide.

Several Complex Variables
1:00 pm   in 243 Altgeld Hall,  Tuesday, March 18, 2003
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Submitted by dror.
 David Catlin (Purdue)Embeddings of CR manifolds of higher codimension

Analysis Seminar
2:00 pm   in 354 Altgeld Hall,  Tuesday, March 18, 2003
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Submitted by junge.
 Taka Ozawa (University of Tokyo)On Connes' approximate embedding problem

2:00 pm   in 241 Altgeld Hall,  Tuesday, March 18, 2003
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Submitted by mullet.
 Joshua Mullet (UIUC Math)K3-Fibered Calabi-Yau Threefolds Over the Projective LineAbstract: We consider Calabi-Yau threefolds which have a fibration over P^1 with general fiber a K3 surface. We will prove some generalities and then give some examples.

Geometric Potpourri Seminar
2:00 pm   in 243 Altgeld Hall,  Tuesday, March 18, 2003
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Submitted by seminar.
 Dr. Wacharin Wichiramala (UIUC Department of Mathematics)A smaller cover for unit convex arcsAbstract: An interesting variant of Moser's well-known "worm problem" asks for the convex planar set of least area that can cover all unit convex arcs. Thirty years ago Wetzel noted that an isosceles right triangle T with unit hypotenuse and area 0.2500 is such a cover, and he showed that a small triangle can be clipped from the right angle vertex of T to give a cover with area about 0.2492. At that time he conjectured that the triangle T clipped at the minimum width (0.4389) of the unit broadworm is also a cover. Last year Johnson and Poole found a sophisticated way to prune the isosceles right triangle T near its right angle vertex to form a cover with area about 0.2466. I will describe a barbarian way to clip the triangle T to form a cover with area about 0.2464, thereby bringing the world record back to UIUC.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, March 18, 2003
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Submitted by west.
 Michael Plantholt (Illinois State University, Mathematics)A combined logarithmic bound on the chromatic index of multigraphsAbstract: For any multigraph G, the integer round-up phi(G) of the fractional chromatic index fr(G) yields the best general lower bound for the chromatic index chi'(G). For an upper bound, Kahn showed that for any positive constant c there exists a positive integer N such that chi'(G) < (1+c) fr(G) whenever fr(G) > N. We show that for any multigraph G with order n and at least one edge, chi'(G) <= phi(G) + log3/2 ( min {n+1 , phi(G)} ). Kahn's result follows as a corollary.

RAP "Metric Spaces of Non-Positive Curvature"
3:00 pm   in Altgeld Hall 347,  Tuesday, March 18, 2003
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Submitted by kapovitc.
 Ilya Kapovich (UIUC)Ends of groups and CAT(0) cubings (continued)

Mathematics in Science and Society (MSS)
4:00 pm   in 314 Altgeld Hall,  Tuesday, March 18, 2003
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Submitted by duursma.
 Andrew Odlyzko   [email] (Director, Digital Technology Center, University of Minnesota)Cryptography and economicsAbstract: Mathematical cryptography has provided a new application area for many areas that had formerly been regarded as belonging to pure mathematics. It has also provided a variety of interesting and important tools for ecommerce. The impact of these tools was widely expected to be revolutionary. Yet so far, although some of these mathematical techniques do play a vital role, most of the optimistic early expectations have been disappointed. The reason for this, which will be explored in this lecture, is that many of these tools, especially those providing strong privacy, conflict with the economic incentives that govern how ecommerce is conducted.

Nonstandard analysis and differential equations
5:00 pm   in 159 Altgeld Hall,  Tuesday, March 18, 2003
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Submitted by henson.
 C. Ward Henson (UIUC Math)Benoit's chapter in the NATO book, IIAbstract: This is a working seminar attached to the speaker's course in nonstandard analysis (NSA). The goal is to cover several papers in which NSA methods are applied to singular perturbation problems for ODEs. Knowledge of basic NSA is assumed. This week we are covering results from section 3 of the lectures by E. Benoit from a 1996 NATO advanced study institute.