Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Department Colloquium - Dengdeng Yu (University of Toronto)

Dengdeng Yu (University of Toronto)

Thursday, February 6th, 2020

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

Speaker: Dengdeng Yu (University of Toronto)

Title: Causal Inference with 2D Treatment: An Application to Alzheimer’s Studies

Abstract: Alzheimer's disease is a progressive form of dementia that causes problems with memory, thinking and behavior. It is important to identify the changes of certain brain regions that lead to behavioral deficits. In this paper, we study how hippocampal atrophy affects behavioral deficits using data from the Alzheimer's Disease Neuroimaging Initiative. The special features of the data include a 2D matrix-valued imaging treatment and more than $6$ million of potential genetic confounders, which bring significant challenges to causal inference. To address these challenges, we propose a novel two-step causal inference approach, which can naturally account for the 2D treatment structure while only adjusting for the necessary variables among the millions of covariates. Based on the analysis of the Alzheimer's Disease Neuroimaging Initiative dataset, we are able to identify important biomarkers that need to be accounted for in making causal inference and located the subregions of the hippocampus that may affect the behavioral deficits. We further evaluate our method using simulations and provide theoretical guarantees.

Dengdeng Yu is a postdoctoral fellow at the Department of Statistical Sciences at the University of Toronto and the Canadian Statistical Sciences Institute (CANSSI). He obtained his Ph.D. degree in Statistics from the University of Alberta in 2017. His research interests include high-dimensional and functional data analysis, neuroimaging and imaging genetics data analysis, and quantile regression.

Curves Seminar - Mike Roth (Queen's University)

Wednesday, February 5th, 2020

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

Speaker: Mike Roth (Queen's University)

Title: K3 surfaces and Lazarsfeld-Mukai bundles.

Abstract: The talk will be a short introduction to some aspects of K3 surfaces, including their relation with canonical embeddings of curves, as well as details of the construction of a particular kind of vector bundle on a K3 surface, obtained by starting with a $g^{r}_{d}$ on a curve on that surface.

This vector bundle construction appeared in Lazarsfeld’s proof of the Petri conjecture, but has also been one of the main starting points for investigating Green’s conjecture. In particular, it will be used in future lectures giving a recent proof due to Kemeny of Green’s conjecture for generic curves of even genus.

Number Theory Seminar - M. Ram Murty (Queen's University)

Monday, February 3rd, 2020

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

Speaker: M. Ram Murty (Queen's University)

Title: On the normal number of prime factors of Fourier coefficients of modular forms.

Abstract: Using recent advances in the theory of Galois representations, we will indicate how to prove that for a prime $p$, the $p$-th Fourier coefficient of any modular form (with integer coefficients) has $\log \log p$ prime factors for almost all primes $p$. This is joint work in progress with Kumar Murty and Sudhir Pujahari. It extends my earlier joint work with Kumar Murty where only eigenforms were considered.

Department Colloquium - Gregory G. Smith (Queen's University)

Gregory G. Smith (Queen's University)

Friday, January 31st, 2020

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

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

Title: The geometry of closed subsets.

Abstract: How can we understand the spaces embedded in a fixed projective space? There are different ways to answer this question. After examining a few, we will focus on a geometric approach. Ultimately, we aim to determine when the natural parameter space (the so called Hilbert scheme) is smooth.

Gregory G. Smith is a Professor of Mathematics at Queen's University. His research interests include algebraic geometry, commutative algebra, computer algebra and combinatorics. He was elected a fellow of the Canadian Mathematical Society in 2018. He also received the 2012 Coxeter-James Prize and 2007 André Aisenstadt Prize.

Clone of Curves Seminar - Mike Roth (Queen's University)

Wednesday, January 29th, 2020

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

Speaker: Mike Roth (Queen's University)

Title: An overview of Brill-Noether theory.

Abstract: The object of Brill-Noether theory is to answer the question : which $g^{r}_{d}$’s can a generic curve of genus $g$ have?

The relevance to Green’s conjecture is that this then allows us to compute the Clifford index of a generic curve of genus $g$.

The lecture will be an overview of Brill-Noether theory, including a sketch of the main lines of argument.

Number Theory Seminar - Seoyoung Kim (Queen's University)

Monday, January 27th, 2020

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

Speaker: Seoyoung Kim (Queen's University)

Title: On the density of irreducible polynomials which generate $k$-free polynomials over function fields.

Abstract: Let $M \in \FF_{q}[t]$ be a polynomial, and let $k \geq 2$ be an integer. In this talk, we will compute the asymptotic density of irreducible monic polynomials $P\in\FF_{q}[t]$ for which $P+M$ is not divisible by the $k$-th power of any irreducible polynomial.

Department Colloquium - Hok Kan Ling (Columbia University)

Hok Kan Ling (Columbia University)

Monday, January 27th, 2020

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

Speaker: Hok Kan Ling (Columbia University)

Title: Shape-constrained Estimation and Testing.

Abstract: Shape-constrained inference has been gaining more attention recently. Such constraints are sometimes the direct consequence of the problem under investigation. In other times, they are used to replace parametric models while retaining qualitative shape properties that exist in problems from diverse disciplines. In this talk, I will first discuss the estimation of a monotone density in s-sample biased sampling models, which has been long missing in the literature due to certain non-standard nature of the problem. We established the asymptotic distribution of the maximum likelihood estimator (MLE) and the connection between this MLE and a Grenander-type estimator. In the second part of the talk, a nonparametric likelihood ratio test for the hypothesis testing problem on whether a random sample follows a distribution with a decreasing, k-monotone or log-concave density is proposed. The obtained test statistic has a surprisingly simple and universal asymptotic null distribution, which is Gaussian, instead of the well-known chi-square for generic likelihood ratio tests. We also established rates of convergence of the maximum likelihood estimator under weaker conditions than the existing literature that are of independent interest.

Hok Kan (Brian) Ling is a Ph.D. candidate in the Department of Statistics at Columbia University, working under the supervision of Dr. Zhiliang Ying. His research interests primarily lie in the areas of multivariate statistics, latent variable models, event history analysis, nonparametric estimation, semiparametric models and shape-restricted statistical inference.