UIUC Dept. of Mathematics Seminar Calendar

    September 2009          October 2009          November 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  4  5                1  2  3    1  2  3  4  5  6  7
  6  7  8  9 10 11 12    4  5  6  7  8  9 10    8  9 10 11 12 13 14
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 20 21 22 23 24 25 26   18 19 20 21 22 23 24   22 23 24 25 26 27 28
 27 28 29 30            25 26 27 28 29 30 31   29 30

Tuesday, October 27, 2009

Topology seminar
11:00 am in 241 Altgeld Hall, Tuesday, October 27, 2009

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Submitted by bertg.

John Francis (Northwestern University)
Invariants of E_n-algebras
Abstract: E_n-algebras are less commutative analogues of E-infinity algebras, which arise naturally from such objects as n-fold loop spaces, (oo,n)-categories, topological field theories, and Poisson algebras. After introducing the basic features of the theory of E_n-algebras, I'll describe some sophisticated invariants, which are E_n variants of Quillen cohomology and Hochschild cohomology, and I'll prove a relation between them first conjectured by Kontsevich. Finally, I'll discuss how E_n-Hochschild cohomology is the Lie algebra of the group of automorphisms of an n-category.

Harmonic Analysis and Mathematical Physics
1:00 pm in 347 Altgeld Hall, Tuesday, October 27, 2009

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Submitted by ekirr.

Boaz Ilan [email] (U. of California, Merced)
Solitons at the interface between bands and gaps
Abstract: Solitons or localized bound states arise in nonlinear wave systems including nonlinear optics, ultra-cold atomic systems, and water waves. In some cases solitons can be very stable while in others highly unstable and can undergo collapse (singularity formation). We study solitons in focusing Nonlinear Schrödinger (NLS) equations with periodic potentials. Rigorous asymptotic analysis reveals that when a soliton bifurcates from a band edge into a gap, the soliton profile is constructed from a linear Bloch wave that is slowly modulated by a bound state solution of a homogenized NLS equation. A consequence of the analysis is that in the L2-critical case, the soliton power (L2 norm) is below the threshold for collapse. Direct computations of soliton dynamics in L2-critical NLS equations elucidate these results.

Differential Geometry Seminar
1:00 pm in 243 Altgeld Hall, Tuesday, October 27, 2009

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Submitted by ekerman.

Rebecca Goldin (George Mason University)
Full Orbifold K-theory of Abelian Symplectic Quotients
Abstract: We will begin with a review of one way in which orbifolds arise, which is via the symplectic of a Hamiltonian T-space, where T is an abelian Lie group. Our goal is to describe the full orbifold K-theory for this class of spaces. Toward that purpose, we introduce the *inertial K-theory* of a Hamiltonian T-space M and show that it surjects as a ring onto the full orbifold K-theory of the symplectic quotient, denoted M//T (at a regular value). This research essentially involves two ingredients: The fact (due to M. Harada and G. Landweber) that equivariant K-theory of M maps surjectivity onto the K-theory of M//T, and the invention of a fancy product on the inertial K-theory of M, so that it surjects onto the full orbifold K-theory of M//T. These ideas are based on a similar (though rational) story in cohomology which we will also discuss. This is joint work with T. Holm, M. Harada, and T. Kimura.

Number Theory Seminar
1:00 pm in 241 Altgeld Hall, Tuesday, October 27, 2009

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Submitted by ahlgren.

Harold Diamond (UIUC Math)
Weak logarithmic density estimates for Beurling generalized numbers
Abstract: An infinite collection of real numbers $p_1, p_2, ... $ satisfying $1 < p_1 \le p_2 \le ...$ is called a sequence $P$ of Beurling generalized (g-) primes, and the semigroup $N_P$ it generates under multiplication is called the associated Beurling g-integers. We say that $N_P$ satisfies an upper (resp. lower) logarithmic density condition if $(1/\log x) \sum_{n_i \le x} 1/n_i$ is bounded above (resp. below). We show that these conditions are connected with the behavior of the g-zeta function near its pole. The case of logarithmic density is the famous tauberian theorem of Hardy, Littlewood, and Karamata.

Study Seminar in Analysis and Geometry
3:00 pm in 441 Altgeld Hall, Tuesday, October 27, 2009

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Submitted by jmmackay.

Patrick Reynolds (Department of Mathematics, University of Illinois)
Rips' Theorem
Abstract: Rips theory is, roughly speaking, a collection of tools allowing one to deduce certain structure in a group $G$ acting nicely on an $\mathbb{R}$-tree. We will introduce the techniques of Rips Theory and present a "detailed sketch" of a proof of Rips' Theorem, that a finitely generated group acting freely on an $\mathbb{R}$-tree is a free product of closed surface groups and free abelian groups. We will present all definitions, assuming only a small amount of knowledge of basic covering theory, and will give examples when possible. If time permits we will mention some applications.

Graph Theory and Combinatorics
3:00 pm in 241 Altgeld Hall, Tuesday, October 27, 2009

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Submitted by west.

Suil O (UIUC Math)
Matchings, edge-connectivity and eigenvalues in regular graphs
Abstract: The matching number of a graph is the maximum size of a matching in it. We previously characterized the graphs having the smallest maximum number among connected (2k+1)-regular graphs with n vertices; the extremal graphs have cut-edges. In this talk, we prove a lower bound for the maximum matching in a t-edge-connected r-regular graph with n vertices, for t≥ 2 and r≥ 4; various special cases were obtained earlier. We also characterize the graphs achieving equality.

We also study the relationship between eigenvalues and matchings in t-edge-connected r-regular graphs. We give a condition on anappropriate eigenvalue that guarantees a lower bound on the matching number in a t-edge-connected r-regular graph; this generalizes a recent result of Cioaba, Gregory, and Haemers.