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

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.

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

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.

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

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.

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

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.

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

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: