# Fall 2010

## Fall 2010

**Dr. Hamid Usefi**

University of Toronto

Colloquium

1:00 p.m., Friday, November 19, 2010

HH-3017*The isomorphism problem for enveloping algebras*

Given Lie algebras L and H with isomorphic enveloping algebras, the isomorphism problem asks whether L and H are isomorphic. Theanswer to the isomorphism problem in positive characteristic is NO. In this talk, I will review the past and recent results and discuss a conjecture in characteristic zero and some recent evidence regarding the validity of the conjecture. In positive characteristic the isomorphism problem makes sense for restricted Lie algebras. I will also mention some developments in this area.

**Dr. Zhuang Niu**

Department of Mathematics and Statistics, Memorial University

Algebra Seminar

1:00p.m., Wednesday, November 17, 2010

HH-3017*An introduction to K-theory for operator algebras*

I will give a brief introduction to the (topological) K-theory for operator algebras, and discuss some basic properties and some simple applications.

**Dr. Karen Chandler**

Dalhousie University

Colloquium

12:00p.m., Tuesday, November 16, 2010

HH-3014*Counting polymonials with higher-order singularities*

**Dr. Emilie Dufresne**

Mathematisches Institute, Universität Basel

10:00 a.m., Wednesday, November 10, 2010

SN-2098*Well-behaved separating algebras*

The study of separating invariants has become quite popular in recent years. For an algebraic group action on an affine variety, a separating algebra is a subalgebra of the ring of invariants which separates any two points separated by invariants. Part of the appeal of separating invariants is that they can have better structural and computational properties than the ring of invariants. For example, there always exist a finite separating set, a beautiful, but unfortunately very non-constructive result. The first part of this talk focuses on well-behaved separating algebras for invariants of representations of finite groups, and the second part, on invariants of algebraic actions the additive groups on a vector space. For finite groups, we show that the close relationship between separating invariants and the ring of invariants imposes limits on the good properties which can be expected from separating algebras. The additive group, however, is not reductive. Thus, no such relationship exists, and moreover, for some actions, the invariants are not finitely generated. We discuss how finite separating set can be constructed for some examples. (Includes a discussion of joint work with Jonathan Elmer and Martin Kohls.)

**Dr Mikhail Kotchetov**

Department of Mathematics and Statistics, Memorial University

Algebra Seminar

1:00pm, Wednesday, November 3, 2010

HH-3017*"Gradings on the exceptional Lie algebras F_4 and G_2"*

All gradings by abelian groups are classified on the following algebras over an algebraically closed field F: the simple Lie algebra of type G_2 (char F different from 2, 3), the exceptional simple Jordan algebra (char F different from 2), and the simple Lie algebra of type F_4 (char F different from 2).

**Dr. Alex Nielson**

Max Planck Institute for Gravitational Physics in Potsdam, Germany

Colloquium

3:30pm, Wednesday, October 20, 2010

HH-3026

*Black hole horizons for dynamical space times.*

The event horizon and trapping horizon are two different ways of defining the boundary of a black hole. I will present some of the differences between these approaches and show how they lead to the boundary of a black hole being at different locations in simple dynamical black hole space times. I will also present some recent numerical work on the foliation dependence of trapping horizons and their uniqueness properties. The talk will give an overview of the current state of black hole horizon research and should be suitable to a general mathematical audience.

**Dr. Brajendra Sutradhar**

Memorial Univeristy

World Statistics Day Seminar

2:00-3:00pm, Wednesday, October 20, 2010

HH-3017*Socio-economic Data Collection, Management and Inferences*

The history of data collection for real life inferences goes back to 1662 when John Graunt (a tradesman/ demographer) from London, England tabulated the number of burials and deaths from a plague epidemic that used to recur in those days. He collected small samples from communities to help estimating the total population of the city and country based on the proportion of plague deaths. This statistical thinking continues today around the needs of states including the united nations (state of states) to base policy on demographic and economic data. The data collection and their analysis can be quite complex depending on the nature of population frame for the data of interest. Some examples are: Challenges involved in HIV, employment and unemployment data collection, and their analysis, for a developing and/or under-developed country. In this talk, I will take you to a brief journey with me to the past few centuries to see what statisticians have been doing toward this challenging problem. I will briefly talk about the challenges with experimental data that belongs to hypothetical population as opposed to a large finite existent population for socio-economic data. In the end, I will present some challenges for the analysis for SLID (survey of labour and income dynamics ) longitudinal data collected by Statistics Canada.

**Prof. Bovas Abraham**

University of Waterloo

Colloquium

12.00PM, October 15, 2010

HH 3017*Stochastic Volatility Modeling and Gamma Processes *

Studies on financial time series indicate that a sequence of returns on some financial assets such as stocks, currency, and commodities often exhibit time-dependent variances (volatility clustering) and have excess kurtosis in the marginal distributions. In general, there are two types of models for time-dependent variances: (i) Observation-driven models such as the autoregressive conditional heteroscedastic (ARCH) and Generalized ARCH (GARCH) models, and (ii) Parameter-driven models. In the latter models, it is assumed that the time-dependent variances are random variables generated by an underlying (latent) stochastic process and such models are referred to as stochastic volatility (SV) models. In such contexts it is common to assume that the conditional distribution of returns is normal (or student t) and the volatility sequence evolves as an autoregressive sequence with log normal marginals. Maximum likelihood (ML) estimation of such models is difficult. In this talk we briefly consider simulated ML (SML) and MCMC methods. In addition we discuss models for returns in which the return volatilities evolve according to a stationary gamma auroregressive (GAR) process. Parameters of such models can be obtained by moment methods. Simulations indicate that these estimates are reasonable. We also illustrate with some stock return data that the GAR models capture the leptokurtic nature of return distributions and the slowly decaying autocorrelation functions of squared returns.

**Dr. Rui Peng**

Department of Mathematics and Statistics, Memorial University

Applied Dynamical Systems Seminar

2:30pm, Thursday, October 14, 2010

HH-3017*Effect of a Protection Zone in the Diffusive Leslie Predator-prey Model*

In this talk, we consider the diffusive Leslie predator-prey model with large intrinsic predator growth rate, and investigate the change of behavior of the model when a simple protection zone for the prey is introduced. We will show the existence of a critical patch size of the protection zone, determined by the first Dirichlet eigenvalue of the Laplacian over the protection zone and the intrinsic growth rate of the prey, so that there is fundamental change of the dynamical behavior of the model only when protection zone is above the critical patch size. We show that the asymptotic profile of the population distribution of the Leslie model is governed by a standard boundary blow-up problem, and classical or degenerate logistic equations. This is a joint work with Drs. Yihong Du and Mingxin Wang.

Dr. Qiong Yi

University of Ottawa and Canadian Blood Services

Colloquium

2:00p.m., Friday, October 1, 2010

HH-3017

"Assessing Reliability (Agreement) for Continuous Measurements"

Reliability or agreement assessment is an important step in various applications. There exists a large volume of literatures on its use and on underlying methodology; In 2008 alone, more than 1600 papers could be found on PubMed. Many statistical methods (indexes) have been proposed to assess reliability. This presentation will review some of them, discuss their advantages and limitations, and illustrate their use by analyzing an example data.

Dr. Paul Peng

Queens' University

Colloquium

2:00p.m., Friday, September 24, 2010

HH-3017

"Cure Model Selection under a Unified Cure Model"

We review cure models and a unified cure model based on the Box-Cox transformation. We propose a novel interpretation for the unified cure model, which leads to a natural extension of the cure model. The extended cure model is capable to model data that the original model may not fit. Our empirical study shows that Akaike's information Criterion is informative and the score test performs better than the likelihood ratio test in determining an adequate simple cure model for data. We apply the test methods and AIC to some real data sets to examine the appropriateness of the cure model considered for them in the literature.

Dr. Shaofen Zou

Hunan University, China

2:00p.m., Tuesday, September 7, 2010

HH-3017

"Multiple Epidemic Waves in Delayed SIR Models on Complex Networks"

A delayed SIR epidemic model on a scale-free network is considered. We address the effect of time lag on the shape and multiple peaks of epidemic curves and show that when the transmission rate is above a threshold, large delay can cause multiple waves with larger amplitudes in the second and subsequent waves.