Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Department Colloquium - Kasun Fernando (University of Toronto)

Kasun Fernando (University of Toronto)

Friday, January 17th, 2020

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Kasun Fernando (University of Toronto)

Title: Error terms in the Central Limit Theorem.

Abstract: Expressing the error terms in the Central Limit Theorem as an asymptotic expansion (commonly referred to as the Edgeworth expansion) goes back to Chebyshev. In the setting of sums of independent identically distributed (iid) random variables, sufficient conditions for the existence of such expansions have been extensively studied. However, there is almost no literature that describe this error when the expansions fail to exist. In this talk, I will discuss the case of sums of iid non-lattice random variables with $d+1$ atoms. It can shown that they never admit the Edgeworth expansion of order d. However, using tools from Homogeneous Dynamics, it can shown that for almost all parameters the Edgeworth expansion of order $d-1$ holds and the error of the order $d-1$ Edgeworth expansion is typically of order $n^{-d/2}$ but the order $n^{-d/2}$ terms have wild oscillations (to be made precise during the talk). This is a joint work with Dmitry Dolgopyat.

Kasun Fernando is a postdoctoral fellow in the Department of Mathematics at the University of Toronto. He completed his Ph.D. in 2018 at the University of Maryland, College Park. His research is primarily focused on possible extensions of this theory of asymptotic expansions to more general settings that are not included in the classical theory, including the case of random variables arising as observations of chaotic dynamical systems.

Department Colloquium - Yi Xiong (Simon Fraser University)

Yi Xiong (Simon Fraser University)

Thursday, January 16th, 2020

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Yi Xiong (Simon Fraser University)

Title: Statistical Issues in Forest Fire Control.

Abstract: This talk presents statistical issues arising from forest fire (wildfire) control with a particular focus on studying the duration times in the presence of missing origin. A new methodology is proposed to tackle the issue of missing time origin with the aid of available longitudinal measures.  I present an intuitive and easy-to-implement estimator for the distribution together with a method to conduct semi-parametric regression analysis. The estimation procedure is also extended to accommodate the spatial correlation in the data. A collection of wildfire records from Alberta, Canada is used for illustration and motivation. The finite-sample performances of proposed approaches are examined via simulation. On-going work and future directions to overcome other challenges of making inference on the underlying wildfire process will be discussed.

Yi Xiong is a Ph.D. student in the Department of Statistics at Simon Fraser University, under the supervision of Dr. Joan Hu and Dr. John Braun. She is interested in developing statistical methods to analyze complex data including missing data, censored lifetime data and spatio-temporal data.

Department Colloquium - Michael Gallaugher (McMaster University)

Michael Gallaugher (McMaster University)

Monday, January 13th, 2020

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Michael Gallaugher (McMaster University)

Title: Clustering and Classification of Three-Way Data.

Abstract: Clustering and classification is the process of finding and analyzing underlying group structure in heterogenous data and is fundamental to computational statistics and machine learning. In the past, relatively simple techniques could be used for clustering; however, with data becoming increasingly complex, these methods are oftentimes not advisable, and in some cases not possible. One such such example is the analysis of three-way data where each data point is represented as a matrix instead of a traditional vector. Examples of three-way include greyscale images and multivariate longitudinal data. In this talk, recent methods for clustering three-way data will be presented including high-dimensional and skewed three-way data. Both simulated and real data will be used for illustration and future directions and extensions will be discussed.

Michael Gallaugher is a Ph.D. candidate in the Department of Mathematics and Statistics at McMaster University, working under the supervision of Dr. Paul D. McNicholas. His research interests lie in the area of clustering and classification which aims to find underlying group structure in heterogenous data.

Number Theory Seminar - Anup Dixit (Queen's University)

Monday, January 13th, 2020

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 422

Speaker: Anup Dixit (Queen's University)

Title: On Picard-type theorems involving $L$-functions.

Abstract: The little Picard's theorem states that any non-constant entire function takes all complex values or all complex values except one point. In a similar flavour, suppose $f$ is an entire function such that for complex values $a$ and $b$, the set of zeros of $f$ is same as the set where $f'$ takes values $a$ and $b$, then it is possible to show that $f$ is a constant function. Such results are called Picard-type theorems. In this talk, we will discuss similar questions for $L$-functions, where it is possible to prove much stronger results.

Department Colloquium - Dimitris Koukoulopoulos (U Montreal)

Dimitris Koukoulopoulos (Universite de Montreal)

Friday, January 10th, 2020

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Dimitris Koukoulopoulos (Université de Montréal)

Title: On the Duffin-Schaeffer conjecture.

Abstract: Given any real number $\alpha$, Dirichlet proved that there are infinitely many reduced fractions $a/q$ such that $|\alpha-a/q|\le 1/q^2$. Can we get closer to $\alpha$ than that? For certain "quadratic irrationals" such as $\alpha=\sqrt{2}$ the answer is no. However, Khinchin proved that if we exclude such thin sets of numbers, then we can do much better. More precisely, let $(\Delta_q)_{q=1}^\infty$ be a sequence of error terms such that $q^2\Delta_q$ decreases. Khinchin showed that if the series $\sum_{q=1}^\infty q\Delta_q$ diverges, then almost all $\alpha$ (in the Lebesgue sense) admit infinitely many reduced rational approximations $a/q$ such that $|\alpha-a/q|\le \Delta_q$. Conversely, if the series $\sum_{q=1}^\infty q\Delta_q$ converges, then almost no real number is well-approximable with the above constraints. In 1941, Duffin and Schaeffer set out to understand what is the most general Khinchin-type theorem that is true, i.e., what happens if we remove the assumption that $q^2\Delta_q$ decreases. In particular, they were interested in choosing sequences $(\Delta_q)_{q=1}^\infty$ supported on sparse sets of integers. They came up with a general and simple criterion for the solubility of the inequality $|\alpha-a/q|\le\Delta_q$. In this talk, I will explain the conjecture of Duffin-Schaeffer as well as the key ideas in recent joint work with James Maynard that settles it.

Dimitris Koukoulopoulos is an Associate Professor of Mathematics at the Université de Montréal. He received his PhD from the University of Illinois in 2010. He works in analytic number theory, especially probabilistic and multiplicative aspects of the subject. Among his accolades, he was the cowinner of the 2013 Paul R. Halmos - Lester R. Ford Award. He is the author of the recent book The Distribution of Prime Numbers, published by the AMS.

Curves Seminar - Mike Roth (Queen's University)

Wednesday, December 4th, 2019

Time: 1:30-3:00 p.m Place: Jeffery Hall 319

Speaker: Mike Roth (Queen's University)

Title: Special linear series, the Clifford index, and Green’s conjecture.

Abstract: We will introduce the ideas of linear series, and special linear series on a curve, the notation $g^{r}_{d}$, Clifford’s theorem on special linear series, and state Green’s conjecture for canonically embedded curves.

Geometry & Representation - Veronique Bazier-Matte (UQAM)

Monday, December 2nd, 2019

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 319

Speaker: Véronique Bazier-Matte (Université du Québec à Montréal)

Title: Quasi-cluster algebras.

Abstract:  In 2015, Dupont and Palesi defined quasi-cluster algebra from non-orientable surfaces. The goal of this talk is to compare cluster algebras and quasi-cluster algebras and to explain some conjectures about them.

Department Colloquium - Matthew Pratola (OSU)

Matthew Pratola (OSU)

Friday, November 29th, 2019

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Matthew Pratola (OSU)

Title: Bayesian Additive Regression Trees for Statistical Learning.

Abstract: Regression trees are flexible non-parametric models that are well suited to many modern statistical learning problems. Many such tree models have been proposed, from the simple single-tree model (e.g.~Classification and Regression Trees -- CART) to more complex tree ensembles (e.g.~Random Forests). Their nonparametric formulation allows one to model datasets exhibiting complex non-linear relationships between predictors and the response. A recent innovation in the statistical literature is the development of a Bayesian analogue to these classical regression tree models. The benefit of the Bayesian approach is the ability to quantify uncertainties within a holistic Bayesian framework. We introduce the most popular variant, the Bayesian Additive Regression Trees (BART) model, and describe recent innovations to this framework such as improved Markov Chain Monte Carlo sampling and a heteroscedastic variant (HBART). We conclude with some of the exciting research directions currently being explored.

Dr. Matthew Pratola is an associate professor of statistics at the Ohio State University. His research program is focused on two areas of statistical methodology: (1) statistical models and methodology for calibrating complex simulation models to real-world observations for parameter estimation, prediction and uncertainty quantification; and (2) statistical models and methodology for computationally scalable and flexible Bayesian non-parametric regression models for high-dimensional "big data" and parallel computation. His work is motivated by applied collaborations and has worked with researchers at the National Center for Atmospheric Research, Los Alamos National Laboratories, the Biocomplexity Institute of Virginia Tech, King Abdullah University of Science and Technology and the JADS Institute.