UIUC Dept. of Mathematics Seminar Calendar

      March 2008             April 2008              May 2008      
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                    1          1  2  3  4  5                1  2  3
  2  3  4  5  6  7  8    6  7  8  9 10 11 12    4  5  6  7  8  9 10
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 23 24 25 26 27 28 29   27 28 29 30            25 26 27 28 29 30 31
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Tuesday, April 22, 2008

Topology Seminar
11:00 am in 241 Altgeld Hall, Tuesday, April 22, 2008

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Submitted by rezk.

Jacob Lurie (MIT Math)
Algebraic Groups over the Sphere Spectrum

Joint Differential Equations and Stochastic Analysis
2:00 pm in 345 Altgeld Hall, Tuesday, April 22, 2008

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Submitted by berdogan.

Jim Colliander (University of Toronto)
Rough blowup solutions of the mass critical NLS
Abstract: We study the singularity formation for the cubic focusing L^2-critical nonlinear Schrodinger equation on R^2. In a series of recent works, Merle and Raphael have completely described the so called log-log blowup regime and proven its stability in the energy space H^1. Our aim in this paper is to investigate the stability of this blowup regime under rough perturbations in the direction of developing a theory at the level of the critical space L^2. By blending the Merle, Raphael techniques with the quantitative I-method developed by Keel, Staffilani, Takaoka, Tao and the speaker for the study of the Cauchy problem for rough data, we obtain the stability of the log-log regime in H^s for all s>0. This talk reports on joint work with Pierre Raphael.

Geometric Potpourri Seminar
2:00 pm in 243 Altgeld Hall, Tuesday, April 22, 2008

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Submitted by j-wetzel.

Dr. Vincent J. Matsko (Illinois Mathematics and Science Academy, Aurora, IL)
The illustrated Salmon
Abstract: Conic Sections, a 19th century geometry text by George Salmon, contains a wealth of information about conics and their representations. In the new version of Mathematica, dynamic interactivity allows many of these interesting ideas to be illustrated graphically.
The use of homogeneous coordinates and linear algebra to describe conics in a projective plane allows for the elegant and brief coding of graphical displays. See how several sections of Salmon are illustrated using such techniques. Mathematica notebooks shown in the talk may be downloaded and modified to illustrate other results.
No previous knowledge is required. A brief overview of the projective plane and homogeneous coordinates will be offered for those unfamiliar with these ideas. The talk should be accessible to undergraduates who have some familiarity with linear algebra.

Graph Theory and Combinatorics
3:00 pm in 241 Altgeld Hall, Tuesday, April 22, 2008

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Submitted by west.

Suil O (UIUC Math)
Balloons, cut-edges, and matchings in regular graphs of odd degree
Abstract: A balloon in a graph G is a maximal 2-edge-connected subgraph of G that is incident to exactly one cut-edge of G. For a graph G, let b(G) be the number of balloons, let c(G) be the number of cut-edges, and let α'(G) be the maximum size of a matching. We obtain sharp bounds on these parameters for (2r+1)-regular graphs. Upper bounds on c(G) and lower bounds on α'(G) follow from upper bounds on b(G). We prove that b(G)≤ [(2r-1)n+2]/[4r²+4r-2] and that c(G)=[2rb(G)-2]/[2r-1]-1 when c(G) attains its maximum. We also prove that α'(G)≥ n/2-[rb(G)]/[2r+1], simplifying the recent proof by Henning and Yeo of the resulting lower bound on α'(G) for (2r+1)-regular graphs (about n/2 - n/(4r) for large r). All the bounds are sharp for each r, holding with equality for infinitely many n.