UIUC Dept. of Mathematics Seminar Calendar

    February 2010            March 2010             April 2010     
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
     1  2  3  4  5  6       1  2  3  4  5  6                1  2  3
  7  8  9 10 11 12 13    7  8  9 10 11 12 13    4  5  6  7  8  9 10
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 28                     28 29 30 31            25 26 27 28 29 30

Tuesday, March 9, 2010

Topology seminar
11:00 am in 241 Altgeld Hall, Tuesday, March 9, 2010

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Submitted by bertg.

Eugene Lerman (UIUC)
A combinatorial category of dynamical systems.
Abstract: This is joint work with Lee DeVille. We revisit the groupoid formalism of coupled cell networks as developed by Golubitsky, Stewart and their collaborators and extend it to continuous-time dynamical systems on manifolds. In particular we develop a combinatorial model for the category of modular complex dynamical systems.

Logic Seminar
1:00 pm in 345 Altgeld Hall, Tuesday, March 9, 2010

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Submitted by w-henson.

Slawomir Solecki (UIUC Math)
Groups generated by generic measure preserving transformations
Abstract: We show that for a generic measure preserving transformation T, the closed group generated by T is isomorphic to a subgroup of L_0(measure,S1) that is the image of a closed linear subspace of L_0(measure,R) via the exponential map. Using certain factorization theorems, we analyze unitary representations of the group of continuous functions with values in S1. This analysis together with a result of del Junco and Lemanczyk allows us to show that the closed group generated by the generic measure preserving transformation T is not isomorphic to the whole group L_0(measure,S1).

Probability Seminar
2:00 pm in 347 Altgeld Hall, Tuesday, March 9, 2010

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Submitted by rsong.

Prof. Jin Feng (University of Kansas)
Some Hamilton-Jacobi PDE in space of probability measures and its associated compressible Euler equations
Abstract: We introduce a class of action integrals defined over probability measure-valued path space. We show that minimal action exists and satisfies a compressible Euler equation in a weak sense. Moreover, we prove that both Cauchy and resolvent formulations of the associated Hamilton-Jacobi equation, in the space of probability measures, are well posed. There are two keys to the arguments. One is a relaxation on formulation of the problem motivated from the point of view of thermodynamics, the other is introduction of a regularization term which is related to particle symmetries. Both are probabilistic in nature.

Geometry Seminar
2:00 pm in 243 Altgeld Hall, Tuesday, March 9, 2010

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Submitted by sba.

Clark Kimberling (U. Evansville)
Space curves composed of circles
Abstract: The cylinders x^2 + y^2 = 1 and x^2 + z^2 = 1 meet in a curve that lies on a sphere. The curve also lies on a cube, and it resembles the "baseball curve" formed by the stitching on a baseball. It is a member of a family of thirteen smooth curves composed of circular arcs such that the curve lies on a sphere and also on a regular polyhedron. These curves will be presented and discussed with the help of Mathematica animations. The material represents a preprint jointly authored with Peter Moses. The talk will be accessible to undergraduates.

Harmonic Analysis and Differential Equations Seminar
3:00 pm in Altgeld Hall, Tuesday, March 9, 2010

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Submitted by xcli.

Jingwei Guo (University of Wisconsin at Madison)
Some new bounds in lattice point problem
Abstract: Lattice point problem, an old problem in number theory, is about estimating lattice points in large domains. Tools from analytic number theory and harmonic analysis can be applied in the estimation. If we assume the domain is compact convex, with smooth boundary and nonzero Gaussian curvature, several improvements have been made. I will introduce a new bound obtained by a careful application of oscillatory integral methods. If curvature is allowed to vanish, the bound could become much worse. If time permits, I will discuss the case in two dimension and introduce a generic estimate with an exponent independent of the domain.

Graph Theory and Combinatorics
3:00 pm in 241 Altgeld Hall [25-minute talk], Tuesday, March 9, 2010

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Submitted by west.

Jane Butterfield (UIUC Math)
Online Ramsey games for triangles in random graphs
Abstract: In the online F-avoidance edge-coloring game with r colors, a graph on n vertices is generated by at each stage randomly adding a new edge. The player must color each new edge as it appears; his goal is to avoid a monochromatic copy of F. Let N₀(F,r,n) be the threshold for the number of edges that the player is almost surely able to paint before he loses. Even when F = K₃, the order of magnitude for N₀(F,r,n) is unknown for r ≥ 3. In particular, the only known upper bound is from the offline threshold. We improve the upper bound for the online triangle-avoidance game with r colors, separating it from the offline bound. This supports a conjecture of Marciniszyn, Spöhel, and Steger that the known lower bound is tight for cliques and cycles for all r. (Joint work with J. Balogh)

Mathematics in Science and Society (MSS)
4:00 pm in Music Building, Room 1201, Tuesday, March 9, 2010

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Submitted by rdeville.

William Sethares (University of Wisconsin)
Beat-Based Signal Processing
Abstract: The input to an automated beat-tracking algorithm is a recording of a piece of music. The output of the beat tracking algorithm is a sequence of times that are intended to represent when 'beats' occur: when listeners 'tap their feet'.

The ability to detect beat timepoints is information about the naturally occurring points of division within a musical signal, and it makes sense to exploit these points when manipulating the sound. Signal processing techniques can be applied on a beat-by-beat basis or the beat can be used to control the parameters of a continuous process. Applications include beat-synchronized special effects, spectral mappings with harmonic and/or inharmonic destinations, and a variety of sound manipulations that exploit the beat structure. A series of sound examples demonstrate.

Graduate Analysis Seminar
4:00 pm in 243 Altgeld Hall, Tuesday, March 9, 2010

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Submitted by wgreen4.

Austin Rochford (UIUC Math)
The Approximation Property of Operator Spaces
Abstract: We will give a brief introduction to operator spaces and then explore the operator space counterpart of Grothedieck's approximation property for Banach spaces. In particular, we will explore the relationship between the operator space approximation property and Tomiyama's slice mapping property. Time permitting we will give some examples that arise from group C* and von Neumann algebras. These examples will reveal a link between the operator space approximation property and Fourier analysis on general locally compact groups.