UIUC Dept. of Mathematics Seminar Calendar

     October 2009          November 2009          December 2009    
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
              1  2  3    1  2  3  4  5  6  7          1  2  3  4  5
  4  5  6  7  8  9 10    8  9 10 11 12 13 14    6  7  8  9 10 11 12
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 18 19 20 21 22 23 24   22 23 24 25 26 27 28   20 21 22 23 24 25 26
 25 26 27 28 29 30 31   29 30                  27 28 29 30 31

Tuesday, November 3, 2009

Topology seminar
11:00 am in 241 Altgeld Hall, Tuesday, November 3, 2009

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Submitted by bertg.

Rekha Santhanam (Johns Hopkins University)
Equivariant Gamma Spaces
Abstract: In this talk we explain how Equivariant \Gamma spaces model equivariant infinite loop spaces. We then construct the equivariant analog of Segal's \Gamma categories, thus producing examples of equivariant infinite loop spaces.

Harmonic Analysis and Mathematical Physics
1:00 pm in 347 Altgeld Hall, Tuesday, November 3, 2009

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Submitted by laugesen.

Joe Lakey [email] (New Mexico State University)
Time- and band-limiting
Abstract: This talk will survey some of the classical and recent results concerning operators composed of a projection onto a compact set in time, followed by a projection onto a compact set in frequency. Such "time- and band-limiting" operators were studied by Landau, Slepian, and Pollak in a series of papers published in the Bell Systems Tech. Journal in the early 1960s. Among other important results, Landau and Pollak gave an initial precise statement of the "folklore" observation that the dimension of the space of signals that are essentially timelimited to a given duration and bandlimited to a given frequency bandwidth is the time-bandwidth product. Other useful versions were proved by Slepian in the early 1970s and by Landau and Widom in 1980.
Further progress on time- and bandlimiting has been intermittent, but genuine recent progress has been made in terms of numerical analysis, sampling theory, and extensions to multiband signals, all driven to some extent by potential applications in wireless communications.
After providing a brief outline of the historical developments in the mathematical theory of time- and bandlimiting, some details of the sampling theory and multiband setting will be given.

Graduate Student Probability Seminar
2:00 pm in 347 Altgeld Hall, Tuesday, November 3, 2009

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Submitted by hpark48.

Kunwoo Kim (Department of Mathematics, University of Illinois)
Effect of drift on noise
Abstract: Consider two processes on different time scales. When one process is driven by the other, as the driving process gets faster and faster, we can characterize the asymptotic behavior of the driven process by stochastic averaging. In this talk, we will consider the case where the driving force is the fast switching process and the drift term of the driven process is 'singular'. We will show via martingale problem of Strook and Varadhan that the law of the driven process converge to that of sticky, reflected, or sticky reflected Brownian motion depending on the drift term.

Graph Theory and Combinatorics
3:00 pm in 241 Altgeld Hall, Tuesday, November 3, 2009

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Submitted by west.

Timothy LeSaulnier (Department of Mathematics, University of Illinois)
Rainbow matchings in edge-colored graphs
Abstract: The color degree of a vertex v in an edge-colored graph is the number of distinct colors appearing on edges incident to v. A rainbow subgraph is a subgraph whose edges receive distinct colors. Wang and Li proved that every edge-colored graph with minimum color degree at least k contains a rainbow matching of size at least ⌈(5k-3)/12⌉. They conjectured that in fact there must be a rainbow matching of size at least ⌈k/2⌉. Toward this conjecture, we prove that every edge-colored graph with minimum color degree k contains a rainbow matching of size at least ⌊k/2⌋. In addition, we prove the full conjecture for triangle-free graphs and show that if a properly edge-colored graph G with minimum color degree k does not contain a rainbow matching of size ⌈k/2⌉, then G is a complete graph minus a matching. (This is joint work with Christopher Stocker, Paul Wenger, and Douglas B. West.)

Mathematics Colloquium
4:00 pm in 245 Altgeld Hall, Tuesday, November 3, 2009

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Submitted by clein.

Oscar Garcia-Prada (CSIC)
Geometry of surface group representations
Abstract: Given a compact real surface S and a semisimple Lie group G, we consider the moduli space R(S,G) of representations of the fundamental group of S in G (sometimes called the character variety). This moduli space plays a central role in many problems in geometry, topology and physics. By considering a complex structure on the surface S (thus making it a Riemann surface), the moduli space of representations is in bijection with a moduli space of holomorphic objects, known as Higgs bundles. We explain this correspondence and show how to use it to study the topology of R(S,G). We give special attention to the case where G is the isometry group of a non-compact Hermitian symmetric space. In this situation, the moduli space has special components that can be regarded in some sense as generalizations of the Teichmueller space of S (which can be identified with a component of the character variety when G=PSL(2,R)).