Heavy tailed distributions have been shown to be consistent with data in a variety of systems with multiple time scales. Recently, increasing attention has appeared in different phenomena related to climate. For example, correlated additive and multiplicative (CAM) Gaussian noise, with infinite variance or heavy tails in certain parameter regimes, has received increased attention in the context of atmosphere and ocean dynamics. We discuss how CAM noise can appear generically in many reduced models. Then we show how reduced models for systems driven by fast linear CAM noise processes can be connected with the stochastic averaging for multiple scales systems driven by alpha-stable processes. We identify the conditions under which the approximation of a CAM noise process is valid in the averaged system, and illustrate methods using effectively equivalent fast, infinite-variance processes. These applications motivate new stochastic averaging results for systems with fast processes driven by heavy-tailed noise. We develop these results for the case of alpha-stable noise, and discuss open problems for identifying appropriate heavy tailed distributions for these multiple scale systems. This is joint work with Prof. Adam Monahan (U Victoria) and Dr. Will Thompson (UBC/NMi Metrology and Gaming).

Rendering objects or oneself invisible to others has fascinated us since the dawn of human civilization. Illustration of such vanishing acts are often made in sci-fi movies. Even though this idea of making oneself invisible to others sounds out of reach, lately it is gaining traction in the scientific community. This has led to the emergence of a fascinating field of meta-materials which deals with the design and study of assemblies of ordinary materials such that the assembly as a whole behaves in an exotic manner. This talk will try to present some elementary ideas involved in the theory of invisibility cloaking. The talk is intended for non-experts and will be accessible to people familiar with basic notions in multivariable calculus.

Let G be a group and w a word map on G. Shalev and others computed bounds for |w(G)|/|G| when G is a finite simple group of Lie type and showed that the lower bound is c/n except for type A_n and {}^2A_n. He further conjectured that the same bound is expected for these cases as well. In this talk, we present our exploration in this direction

In socioeconomic and Biological studies, observations on individuals are often observed longitudinally on a Likert-type scale with substantially large proportion of zeros. This leads to a special case of mixture structured data where extra-variation occurs. Obviously the standard ordinal data analysis fails to provide appropriate statistical inference. We propose a suitable zero inflated semi parametric ordinal model that takes into account the non linear link between the ordinal response and a covariate. A sieve maximum likelihood estimator(MLE) is proposed for the regression parameter of interest. We also propose a test for the zero proportion in this semi parametric model. A simulation study has been carried out to investigate the performance of the estimator as well as the test.

We will see a two variable zeta function associated with a graph due to Dino Lorenzini. I will mainly spend time discussing divisor theory on graphs that arises in the definition of this zeta function.

We aim to provide a proof of the fundamental theorem of algebra based on winding numbers of curves. If time permits, we will discuss a second proof using the notion of degree of a smooth map between compact manifolds.

In this talk, we shall briefly recall the dilation theory on the unit disk and the bidisk developed by Sz.-Nagy -- Foias in 1950s and by Ando in 1963, respectively. We shall give two new proofs of Ando's dilation theorem and discuss a couple of classification results.

The Sally module was introduced by W. Vasconcelos in 1994. This module is a mediator that relates the homological properties of the blow-up algebras to the Hilbert coefficients. In this series of talks we will discuss basic properties of the Sally module. We will derive some well-known results on the Hilbert coefficients using this approach.

The Sally module was introduced by W. Vasconcelos in 1994. This module is a mediator that relates the homological properties of the blow-up algebras to the Hilbert coefficients. In this series of talks we will discuss basic properties of the Sally module. We will derive some well-known results on the Hilbert coefficients using this approach.