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
 11 12 13 14 15 16 17   15 16 17 18 19 20 21   13 14 15 16 17 18 19
 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 10, 2009

Topology seminar
11:00 am in 241 Altgeld Hall, Tuesday, November 10, 2009

Del

Edit

Copy

Submitted by bertg.

Jennifer French (MIT)
Modeling local spaces as mapping spaces of ring spectra
Abstract: The motivation is to generalize the algebraic models for rational homotopy theory developed by Sullivan and Quillen, and for p-adic homotopy theory developed by Mandell. The natural context to generalize these models is as mapping spaces of (commutative) R-algebras, where R is an E-infinity ring spectrum. The main tool for understanding the homotopy groups of such a mapping space is the Goerss--Hopkins spectral sequence. We will explore these R-algebra mapping spaces as models for certain localizations of spaces in the cases R = Hk, where k is the algebraic closure of the field Fp, and the case that R is the K(1)-local sphere spectrum.

Logic Seminar
1:00 pm in 345 Altgeld Hall, Tuesday, November 10, 2009

Del

Edit

Copy

Submitted by w-henson.

Joseph Flenner (Notre Dame)
Relative decidability of henselian valued fields
Abstract: While logic has produced many results about the p-adics, among them a decision procedure due to Paul Cohen, the general theory of henselian valued fields presents an inherent difficulty: they are built on structures of arbitrary complexity in the residue field and value group. Ax-Kochen and Ersov, however, proved their completeness result for some henselian valued fields relative to the theories of the residue field and value group, and more recently, there have been some relative quantifier elimination theorems of Kuhlmann and others. In this spirit, we describe a structure of leading terms associated to a valued field, and outline a proof of decidability for henselian valued fields of characteristic 0 relative to the leading term structures.

Graph Theory and Combinatorics
3:00 pm in 241 Altgeld Hall, Tuesday, November 10, 2009

Del

Edit

Copy

Submitted by west.

Douglas B. West (Department of Mathematics, University of Illinois)
Decomposition of sparse graphs
Abstract: The maximum average degree of a graph is the maximum, over all subgraphs, of the average vertex degree in the subgraph. Let k be a nonnegative integer, and let m_k=4(k²+4k+3)/(k²+6k+6). We prove that every graph with maximum average degree less than m_k decomposes into a forest and a subgraph with maximum degree at most k. The proof is by the discharging method. The result is joint work with Mickael Montassier, Arnaud Pecher, Andre Raspaud, and Xuding Zhu.

The motivation for our result is its application to the misnamed parameter game coloring number, written col_g(G). Alice and Bob alternately choose vertices, producing an ordering. The value of col_g(G) is 1+d, where Alice can guarantee that every vertex has at most d earlier neighbors in the ordering and cannot guarantee fewer. Faigle et al. proved that col_g(T)≤ 4 when T is a forest, and Zhu proved that col_g(G)≤ col_g(G₁)+Δ(G₂) when G decomposes into G₁ and G₂. Hence our result implies that every graph with maximum average degree less than m_k has game coloring number at most 4+k.