# NIU Department of Mathematical Sciences

# Upcoming Colloquia and Seminars

**September 15-21, 2014**

### Math Department Colloquium

**Friday, September 19**, 4:00-5:00 p.m. in DU 348

Speaker:

**Casian Pantea**, West Virginia Univ.

Title:

*Chemical reaction theory: dynamics from structure*

**Abstract:**Much attention has been paid recently to bistability and switch-like behavior that might be resident in important biochemical reaction networks. It turns out that large classes of extremely complex networks cannot give rise to multistationarity, no matter what their reaction rates might be. In turn, absence of multistationarity in a reaction network is often a consequence of the corresponding vector field being injective. In this talk I will give an overview of some old and new injectivity results in vector fields associated with a bichemical reaction network. The talk will be aimed largely at mathematicians who are inexpert in biology or chemistry, and will assume no prior knowledge of how differential equations come about in these scientific fields.

Coffee and refreshments at 3:30 in Watson 322

### Seminars

Algebra Seminar: | Thursday, Sept. 18, 3:00-4:00 p.m. in DU 412 | |

Speaker: | Harvey Blau | |

Topic: | All-Involution Table Algebras and Finite Projective Space
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Abstract: | Table algebras all of whose nontrivial basis elements are involutions (in the sense of Zieschang), which serve as a counterpoint to the generic Hecke algebras parametrized by Coxeter groups, are classified. If two-generated, they are a family (discovered by Blau and Chen for all n at least 3) which for suitable n arise from schemes defined by affine planes of order n-1. Otherwise, the basis involutions correspond to the points of a finite projective space, whose incidence geometry determines the algebra multiplication. This joint work with Gang Chen generalizes to table algebras a previous result of van Dam for association schemes. |

Complex Analysis Seminar: | Tuesday, Sept. 30, 12:00-12:50 p.m. in DU 310 | |

Speaker: | Doug Macclure | |

Topic: | Classification of Quasiregular Poincare Linearizers
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Abstract: | Koenig's Linearization Theorem proves the existence and uniqueness of Poincare linearizers in the complex plane. Hinkkanen, Martin, and Mayer extended the existence portion of the theorem to higher dimensions in the setting of quasiregular mappings. Here, we have shown that in the quasi-world, given a uniformly quasiregular function f and repelling fixed point x_0, Poincare linearizers are unique up to composition with a quasiconformal map. Linearizers of a function f given repelling fixed point x_0 are unique up to composition with a linear map when we assume differentiability of the function f at a repelling fixed point, and the linearizer L at 0. There are also other conditions we can impose on the linearizers which gives even stronger equivalencies. We will also show that linearizers are automorphic with respect to a quasiconformal group. Finally, we provide an example of a quasiregular linearizer in 3-dimensions, and show it is related to other linearizers of the function f given repelling fixed point x_0 by composition with a quasiconformal map. |