Colloquia — Summer 2010

Thursday, June 17, 2010

Title: The \(\sigma\)-flows in the Novikov-Veselov Equation
Speaker: Jen-Hsu Chang, National Defense University
Time: 3:00pm‐4:00pm
Place: PHY 118

Sponsor: Wen-Xiu Ma


The \(\sigma\)-flows in the Novikov-Veselov equation are used to describe a dynamical system on the \(n\)-th elementary symmetric product of roots of the related Gould-Hopper polynomials. We investigate the root dynamics of the related Gould-Hopper polynomials. One can solve the initial value problem of the root dynamics and the Lax equation is established. In some cases, they are the solutions of the Goldfish Model, a limiting case of the Ruijesenaars-Schneider system. The asymptotic behavior of the root dynamics is also discussed.

Wednesday, June 9, 2010

Title: Symmetric Quandle Invariants for Spatial Graphs
Speaker: Kanako Oshiro, Graduate School of Science
Hiroshima University
Hiroshima, Japan
Time: 11:00am‐12:00pm
Place: PHY 108

Sponsor: Masahiko Saito


A spatial \(n\)-valent graph is a finite graph embedded in \(R^{3}\) such that the valency of each vertex of the graph is \(n\).

A symmetric quandle is a quandle with a good involution. By using a symmetric quandle, un-oriented (classical or surface) link invariants were introduced by S. Kamada and were used for several studies.

In this talk, we introduce a symmetric quandle invariant for un-oriented spatial \(n\)-valent graphs.

Wednesday, June 2, 2010

Title: The Holy grail: discovering the genetic origin of phenotypic traits
Speaker: Paola Bonizzoni, Università Degli Studi di Milano-Bicocca
Milano, Italy
Time: 11:00am‐12:00pm
Place: PHY 108

Sponsor: Nataša Jonoska


Discovering the impact of genetic differences on the expression of different phenotypic traits such as disease susceptibility or drug resistance is one of the main goals in genetics. This could be achieved through comparing genetic sequences of different individuals to identify chromosomal regions where genetic variants are shared. The main source of this information is represented by the single nucleotide polymorphism (SNP) variations possessed by individuals in a population and compiled into “haplotypes”. The parsimony principle for analyzing this data provides an appealing mathematical formulation of the haplotype inference problem that leads to new and challenging combinatorial problems on graphs and sequences. In this talk, we review the main results and the most recent advances for this problem and show some possible areas for future research.

Friday, May 28, 2010

Title: Hom-Algebras and Cohomology
Speaker: Abdenacer Makhlouf, Haute Alsace University
Mulhouse, France
Time: 3:00pm‐4:00pm
Place: PHY 120

Sponsor: Mohamed Elhamdadi


We will introduce some new algebraic structures, called Hom-Algebras, which relates to associative algebras and Lie algebras. Their deformations and cohomology will be discussed, and examples will be given. The talk will be self-contained.

Friday, May 7, 2010

Title: Minimal Shape Preserving Projections
Speaker: Gregorz Lewicki, Jagiellonian University
Krakow, Poland
Time: 3:00pm‐4:00pm
Place: PHY 120

Sponsor: Lesław Skrzypek


Let \(X\) be a Banach space and let \(V\subset X\) be a linear subspace of \(X\). Denote by \(\mathcal{P}(X,V)\) a set of all linear, continuous projections from \(X\) onto \(V\). Assume \(\mathcal{P}(X,V)\neq\emptyset\), and fixed a cone \(S\subset X\). (A cone in \(X\) is a convex set closed under nonnegative scalar multiplication.) Let $$\mathcal{P}_{S}(X,V)=\{P\in \mathcal{P}(X,V)\mid PS\subset S\}$$ and $$\lambda_{S}(V,X)=\inf\left\{\|P\|:P\in \mathcal{P}_{S}(X,V)\right\}.$$ During my talk I would like to present some results concerning the following problems:

  1. under what conditions \(\mathcal{P}_{S}(X,V)\neq\emptyset\);
  2. calculation or estimation \(\lambda_{S}(X,V)\);
  3. finding \(P_o\in\mathcal{P}_{S}(X,V)\) such that \(\lambda_{S}(X,V)=\left\|P_o\right\|\).