Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Dynamics, Geometry, & Groups - Rylee Lyman (Tufts University)

Friday, January 24th, 2020

Time: 10:30 a.m Place: Jeffery Hall 319

Speaker: Rylee Lyman (Tufts University)

Title: Train tracks and pseudo-Anosov braids in automorphisms of free products.

Abstract: The Nielsen–Thurston classification of surface homeomorphisms says that every homeomorphism of a surface either has a finite power isotopic to the identity, preserves the isotopy class of some essential multi-curve, or is isotopic to a pseudo-Anosov map, the most interesting kind. Bestvina and Handel introduced a similar classification for automorphisms of free groups. Here the analogue of a pseudo-Anosov homeomorphism is a train track map for an outer automorphism which is fully irreducible, a homotopy equivalence of a graph with extra structure. The analogy really is correct: pseudo-Anosov mapping classes of once-punctured surfaces induce fully irreducible outer automorphisms preserving a nontrivial conjugacy class and vice-versa. We discuss extensions of the train track theory to automorphisms of free products. Here the analogy is to mapping classes of punctured spheres. We show that fully irreducible automorphisms of free products of finite subgroups of SO(2) may be represented as pseudo-Anosov braids on orbifolds if and only if they preserve a non-peripheral conjugacy class.

Department Colloquium - Siliang Gong (University of Pennsylvania)

Siliang Gong (University of Pennsylvania)

Thursday, January 23rd, 2020

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

Speaker: Siliang Gong (University of Pennsylvania)

Title: Per-family Error Rate Control for Gaussian Graphical Models via Knockoffs.

Abstract: Driven by many real applications, the estimation of and inference for Gaussian Graphical Models (GGM) are fundamentally important and have attracted much research interest in the literature. However, it is still challenging to achieve overall error rate control when recovering the graph structures of GGM. In this paper, we propose a new multiple testing method for GGM using the knockoffs framework. Our method can control the overall finite-sample Per-Family Error Rate up to a probability error bound induced by the estimation errors of knockoff features. Numerical studies demonstrate that our method has competitive performance compared with existing methods. This is joint work with Qi Long and Weijie Su.

Siliang Gong is a postdoctoral fellow in the Department of Biostatistics at the University of Pennsylvania. She completed her Ph.D. in statistics at the University of North Carolina at Chapel Hill in 2018. She works on high-dimensional data analysis and statistical machine learning.

Math Club - Ivan Dimitrov (Queen's University)

Thursday, January 23rd, 2020

Time: 5:30 - 6:30 p.m Place: Jeffery Hall 319

Speaker: Ivan Dimitrov (Queen's University)

Title: Proof of the Sensitivity Conjecture.

Abstract:  Last year Hao Huang proved that, if $P$ is a set of $2^{n-1} +1$ vertices of an n-dimensional cube, it contains a vertex with at least $\sqrt{n}$ neighbours in $P$. This settled the nearly 30-year old Sensitivity Conjecture. I will present Huang’s proof and show that the estimate $\sqrt{n}$ is sharp.

Curves Seminar - Gregory G. Smith (Queen's University)

Wednesday, January 22nd, 2020

Time: 4:00-5:30 p.m Place: Jeffery Hall 319

Speaker: Gregory G. Smith (Queen's University)

Title: Green-Lazarsfeld nonvanishing.

Abstract: By exploiting vector bundle techniques for Koszul cohomology, we see how non-trivial geometry leads to non-trivial syzygies.  In particular, this establishes one part of Green’s conjecture.

Number Theory Seminar - Francesco Cellarosi (Queen's University)

Monday, January 20th, 2020

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

Speaker: Francesco Cellarosi (Queen's University)

Title: Smooth arithmetical sums over k-free integers.

Abstract: We use partial zeta functions to analyse the asymptotic behaviour of certain smooth arithmetical sums over smooth $k$-free integers. This is joint work with Ram Murty.

Dynamics, Geometry, & Groups - Kasun Fernando (U of T)

Friday, January 17th, 2020

Time: 10:30 a.m Place: Jeffery Hall 319

Speaker: Kasun Fernando (University of Toronto)

Title: Edgeworth Expansions for (mostly) hyperbolic dynamical systems.

Abstract: Given a dynamical system which shows hyperbolicity on a large part of phase space, one would expect it to exhibit good statistical properties like rapid decay of correlations, the Central Limit Theorem (CLT), Large Deviation Principle and etc. In this talk, I will discuss sufficient conditions for such mostly hyperbolic dynamical systems to admit Edgeworth expansions in the CLT. Our focus is on systems that admit a Young tower with return times with an exponentially decaying tail. This is an on-going joint work with Françoise Pène.

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.