# Seminars and Colloquia - Spring 2010

**Dr. Colin Reid**

McMaster University

Combinatorics Seminar

1:00 p.m., August 31, 2010

HH-3017

"T-chromatic index for Steiner S(2; k; v)s"

Given a Steiner 2-design, S = (V, B); with general block size k, a block-colouring of S is a mapping Á : B -> C, where C is a set of colours. If |C| = n, then Á is an n-block-colouring. In this presentation we will discuss T-chromatic index for S(2, k, v)s for various configurations T. The T-chromatic index for a Steiner system S(2, k, v), S, is the minimum number of colours needed to colour the blocks of S such that there are no monochromatic copies of T. In particular, we focus on configurations containing 2 lines and configurations containing 3 lines for both S(2, 4, v)s and general S(2, k, v)s.

Jian Fang

Harbin Institute of Technology, China

2:00p.m., Friday, August 27, 2010

HH-3017

"Bistable Traveling Waves for Monotone Semiflows"

In this talk, I will report our recent research on traveling waves for monotone evolution systems with bistability structure. Under an abstract setting, we establish the existence of bistable waves for monotone (discrete and continuous-time) semiflows. This result is then extended to the cases of periodic habitat and weak compactness. We also illustate the abstract result by four examples: a time-periodic reaction-diffusion system, a parabolic system in a cylinder, a parabolic equation with variable diffusion, and a functional reaction-diffusion equation. This talk is based on a joint work with Dr. Xiaoqiang Zhao.

Tan Yongji

School of Math, Fudan University

Colloquium

2:00p.m., Thursday, August 26, 2010

HH-3017

"Identifying the intensity of the dust and smoke pollution sources"

To identify the intensity of the dust and smoke pollution sources is of interest. However, this problem is ill-posed in the case of multi-point sources. In this talk we set up some inversion mathematical models and develop some algorithms to overcome the difficulty of ill-poseness and obtain satisfactory results by using fewer measuring devices.

Dr. Litao Han

Renmin University of China

Colloquium

Monday, August 16, 2010

HH-3017

"Study on Epidemic Models of Two Interaction Species"

Some epidemic models of two interaction species (competition or predation) are studied. For the models of two competitive species, SIS and SIRS types are discussed for different incidence forms. The influence of the inter-infection of disease on transmission and its real significance are revealed. Namely, when two species coexist and disease persists in both of them, if the inter-infection is removed, it is found that three different cases may occur: 1) Disease still persists in both species; 2) Disease persists in one species, but dies out in the other species; 3) Disease dies out in both species. For the prey-predator models, SIS and SIR types are discussed for the different incidence forms. The influence of the predation-infection of disease on transmission and its real significance are revealed. Namely, when two species coexist and disease persists in the prey species, it is found that disease must persist in the predator species because of the predation-infection.

Dr. Eugene Chibrikov

Memorial University

Algebra Seminar

1:00p.m., Tuesday, May 12, 2010

HH-3017

"On free Sabinin algebras"

Sabinin algebras are algebraic objects that capture the local structure of analytic loops in the same way in which Lie algebras capture the local structure of Lie groups. They were introduced by L.Sabinin and P.Miheev in 1987. In this report we discuss some recent results concerning free Sabinin algebras and construct a linear basis of a free Sabinin algebra which is a generalization of Shirshov's scheme for choosing bases of free Lie algebras.