ISU Discrete Math Seminar

ISU DISCRETE MATHEMATICS SEMINAR
Archive: 2005-2006

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Date	Name	Title
Jan. 23	Irvin R. Hentzel	Finite Division Rings
Jan. 30	Richard Kramer	Definability in Geometry and the Product Rule for Derivations, Part I
Feb. 6	Richard Kramer	Definability in Geometry and the Product Rule for Derivations, Part II
Feb. 13	Leslie Hogben	Introduction to Matrix Completions
Feb. 20	Luz DeAlba	The Q-matrix Completion Problem
Feb. 27	Y. T. Poon	Product of differences of complex numbers and the determinantal conjecture.
March 6	Chi-Kwong Li, College of William and Mary	Spectrum preserving maps
March 20	Ryan Martin	On the Editing Distance in Graphs
March 27 4:10 PM	Fan Chung, UC-San Diego	Random graphs and Internet graphs This is a Women in Mathematical Sciences Distinguished Lecture
April 3	Leslie Hogben	A new graph parameter for minimum rank
April 10	Steve Willson	Reconstructing phylogenetic networks from distances between leaves
April 17	Ryan Martin	Introduction to Expander Graphs
April 24	Rana Mikkelson & Olga Pryporova	Spectrally Arbitrary Sign Pattens

Feb. 27: Y. T. Poon, Product of differences of complex numbers and the determinantal conjecture.

Let R={a_1,...,a_n}, S={c_1,...,c_n} be two sets of complex numbers, and
T = {∏_j=1ⁿ (a_j-c_σ(j)) : σ є S_n} ,
where S_n denotes the set of all permutations of {1,2,...,n}. We will give some necessary and sufficient conditions for T to be a subset of a straight line in the complex plane. The set T is related to the Marcus and de Oliveira conjecture on determinant.

March 6: Chi-Kwong Li, Spectrum preserving maps

We discuss recent results on spectrum preserving maps on
operators. Previous research on this topic often impose assumptions on the maps such as linearity, additivity, multiplicatively, etc. We show that most of these assumptions can be removed, and one can still obtain nice structure for spectrum preserving maps.

March 27: Fan Chung, Random graphs and Internet graphs

We will discuss some recent developments on random graphs with given expected degree distributions.Such ramdom graphs can be used to model various very large graphs arising in Internet and telecommunications. In turn, these "massive graphs" shed insights and lead to new directions for random graph theory. For example, it can be shown that the sizes of connected components depend primarily on the average degree and the second-order average degree under certain mild conditions. Furthermore, the spectra of the adjacency matrices of some random power law gra phs obey the power law while the spectra of the Laplacian follow the semi-circle law. We will mention a number of related results and problems that a re suggested by various applications of massive graphs.

Fall 05 Seminars

Date	Name	Title
Aug. 30	Sung-Yell Song	Characterizations of Strongly Regular Graphs
Sept. 6	Sung-Yell Song	Characterizations of Strongly Regular Graphs: Bose-Mesner Algebras
Sept. 13	Leslie Hogben and Rana Mikkelson	Rational Realization of Maximum Eigenvalue Multiplicity of Symmetric Tree Sign Patterns
Sept. 20	Sung-Yell Song	Characterizations of Strongly Regular Graphs
Sept. 27	Jozsef Balogh	On k-sets, convex quadrilaterals, and the rectilinear crossing number of K_n
Oct. 4	Maria Axenovich	On graphs with small number of subgraphs with distinct sizes
Oct. 11	Maria Axenovich	On graphs with small number of subgraphs with distinct sizes
Oct. 18	Bhaba Sarma	Energy of Graphs
Oct. 25	Ryan Martin	An application of Szemeredi’s Regularity Lemma
Nov. 1	Ryan Martin	An application of Szemeredi’s Regularity Lemma
Nov. 8	Ryan Martin	An application of Szemeredi’s Regularity Lemma
Nov15	Doug Ray, Jake Manske	The NFL superfan problem
Nov 29	Alex Burstein	Patience Sorting and Barred Pattern Avoidance
Dec. 6	NO SEMINAR

Archives: S06, F05, S05, F04, S04

Leslie Hogben's Home Page
Ryan Martin's Home Page

Discrete Math Seminar 2005-2006. Updated by Ryan Martin: 2006 Dec. 23.