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Seminar Calendar
for events the day of Tuesday, April 25, 2006.

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Tuesday, April 25, 2006

1:00 pm in 241 Altgeld Hall,Tuesday, April 25, 2006

Mod 4 Galois Representations

Chris Holden (U Wisconsin, Madison)

Abstract: Modular Galois Representations with cyclotomic determinant arise from the n-torsion of elliptic curves for n = 2, 3, 5. For n = 4, we show that not every such representation can be obtained in this manner.

1:00 pm in 345 Altgeld Hall,Tuesday, April 25, 2006

Title: An application of model theory to isomorphism of complete local rings.

Lou van den Dries (UIUC Math)

Abstract: Macintyre raised the question whether two complete local rings are isomorphic if their quotients by the same powers of their maximal ideal are isomorphic. I will show the answer is positive if the residue field is the field of real numbers.

1:00 pm in 347 Altgeld Hall,Tuesday, April 25, 2006

To Be Announced

Zoi Rapti (UIUC Math)

2:00 pm in 243 Altgeld Hall,Tuesday, April 25, 2006

Quasilinearity and curvature of Aleksandrov spaces

Prof. I. David Berg (UIUC Department of Mathematics)

Abstract: We show that a geodesic metric space M is an R0 domain in the sense of Aleksandrov (i.e., a Cat(0) space) if and only if |cosq| does not exceed 1, where cosq(u,v) is a certain metric analogue of the cosine of the angle in Euclidean space of the oriented geodesic segments u and v of M. We describe some consequences of this characterization, and we discuss analogous Rk results and appropriate rigidity theorems as time permits.

This reports on joint work with I. G. Nikolaev.

2:00 pm in 347 Altgeld Hall,Tuesday, April 25, 2006

Local and nonlocal isoperimetric and Cahn-Hilliard type problems

Peter Sternberg   [email] (Indiana University)

Abstract: I will describe some recent work linking the isoperimetric problem on the flat torus to minimizers of the Cahn-Hilliard energy in the periodic setting. The problems are partially motivated by the fact that they both arise through certain singular limits of an energy modeling phase separation in diblock co-polymers. It turns out that there are many open problems related to the 3-d periodic isoperimetric problem. I will also discuss a nonlocal isoperimetric problem that arises in the same context.

3:00 pm in 241 Altgeld Hall,Tuesday, April 25, 2006

Symmetrically Constrained Compositions

Carla Savage (North Carolina State University, Computer Science)

Abstract: We consider the problem of counting the compositions of an integer n into k parts p1,...,pk, where the parts must satisfy a set of linear constraints that are symmetric in the pi. Simple examples include integer-sided triangles (p1,p2,p3) satisfying pi + pj >= pk, and pairs (p1,p2) with 2p1 >= p2 and 2p2 >= p1.

Andrews, Paule, and Riese found a generalization of these families that they enumerated with the help of MacMahon's partition analysis. In this work, we formulate a further generalization and show how to reduce the enumeration problem to computing permutation statistics. In cases where those statistics can be computed, nice enumeration formulas emerge. This is joint work with Sunyoung Lee.

3:00 pm in 443 Altgeld Hall,Tuesday, April 25, 2006

A General Fatou Lemma for the Gelfand Integral, continued.

Peter Loeb (UIUC Math)

Abstract: In joint work with Yeneng Sun, a general Fatou Lemma is established for a sequence of Gelfand integrable functions from a vector Loeb space to the dual of a separable Banach space, or for a stronger conclusion, Banach lattice. A corollary sharpens previous results in the finite dimensional setting even for the case of scalar measures. Examples show that a vector measure space formed from Lebesgue spaces will not suffice as the underlying space for the result.

4:00 pm in 314 Altgeld Hall,Tuesday, April 25, 2006

5:00 pm in 343 Altgeld Hall,Tuesday, April 25, 2006

"Not-so-smooth" geometry

Valerie Peterson (UIUC Math)

Abstract: A large number of geometers work in the smooth (or differential) setting, but there is a great deal of interesting geometry that is not so smooth. This talk will focus on the "not so smooth" setting; in particular, on a special class of cell complexes. I will define and give examples of systems whose behavior is captured by these cell complexes (e.g. the protein chains described in the previous talk), and will share some tools that are useful in describing geometric properties of these complexes. I aim for the talk to be entirely self-contained. This is based on joint work with R. Ghrist and Z. Rapti.