Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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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.

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

Thursday, November 28th, 2019

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

Speaker: Seoyoung Kim (Queen's University)

Title: Artin's primitive root conjecture for function fields without Riemann Hypothesis.

Abstract: Artin's primitive root conjecture for function fields is known by Bilharz in his thesis in 1937, which was conditional on the proof of the Riemann hypothesis for global function fields, which was proved by Weil in 1948. In this talk, we suggest a simple proof of Artin's primitive root conjecture for function fields unconditional on the Riemann hypothesis for global function fields by using the technique from the proof of the prime number theorem by Hadamard and de la Vall/'ee Poussin. This is joint work with M. Ram Murty.

Lorne Campbell Lectureship - Olgica Milenkovic (UIUC)

Olgica Milenkovic (UIUC)

This is the second in a lecture series named in honour of Lorne Campbell, emeritus professor in the department, made possible by a generous donation from alumnus Vijay K. Bhargava, Professor of Electrical and Computer Engineering at the University of British Columbia.

Wednesday, November 27th, 2019

Time: 3:30 p.m.  Place: Jeffery Hall 127

Speaker: Olgica Milenkovic (UIUC)

Title: String reconstruction problems in molecular storage.

Abstract: String reconstruction problems frequently arise in many areas of genomic data processing, molecular storage, and synthetic biology. In the most general setting, they may be described as follows: one is given a single or multiple copies of a coded or uncodedstring, and the string copies are subsequently subjected to some form of (random) processing such as fragmentation or repeated transmission through a noise-inducing channel. The goal of the reconstruction method is to obtain an exact or approximate version of the string based on the processed outputs. Examples of string reconstruction questions include reconstruction from noisy traces, reconstruction from substrings and k-decks and reconstruction from compositional substring information. We review the above and some related problems and then proceed to describe coding methods that lead to strings that can be accurately reconstructed from their noisy traces, substrings and compositions. (This is a joint work with Ryan Gabrys, Han Mao Kiah, Srilakshmi Pattabiraman and Gregory Puleo.

Olgica Milenkovic is a professor of Electrical and Computer Engineering at the University of Illinois, Urbana-Champaign (UIUC), and Research Professor at the Coordinated Science Laboratory. She obtained her PhD from the University of Michigan, Ann Arbor. Her research interests include coding theory, bioinformatics, machine learning and signal processing.

Among her accolades, she received an NSF CAREER grant, the DARPA Young Faculty Award, the Dean’s Excellence in Research Award, and several best paper awards. She was elected a UIUC Center for Advanced Study Associate and Willett Scholar (2013) and became a Distinguished Lecturer of the Information Theory Society (2015). She is an IEEE Fellow and has served as Associate Editor and Guest-Editor-in-Chief of several leading IEEE journals.

Images from Olgica Milenkovic's Lecture - Nov. 28th, 2019

Lorne Campbell Lectureship - Olgica Milenkovic (UIUC)
Lorne Campbell Lectureship - Olgica Milenkovic (UIUC)
Lorne Campbell Lectureship - Olgica Milenkovic (UIUC)
Lorne Campbell Lectureship - Olgica Milenkovic (UIUC)

Department Colloquium - Undergraduate Summer Projects

Undergraduate Summer Projects

Friday, November 22nd, 2019

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

Speaker: Multiple Speakers

Title: Undergraduate Summer Projects.

This week colloquium will consists of ten 9 minutes presentations, starting at 2:30pm and
in the following order, by:

  • Rebecca Carter - RabbitMath animations: bringing dynamical systems to high school mathematics.
  • Daniel Cloutier - Computation of Beta Invariants on Toric Varieties I.
  • Keenan McPhail - Computation of Beta Invariants on Toric Varieties II.
  • Luca Sardellitti - Modelling and analyzing antibiotic resistance using artificial life
  • Adam Gronowski - Deep Variational Information Bottleneck.
  • Paul Wilson - Error control codes for two-way multiplying channels.
  • Ian Hogeboom-Burr - Comparison of information structures for zero-sum games and Blackwell ordering in standard Borel spaces.
  • Matt Spragge - Differential Equations Driven by Rough Paths.
  • Shikai Liu - Extensions of the Kalman lter I.
  • Linke Li - Extensions of the Kalman lter II.

Dynamics, Geometry, & Groups - Neil MacVicar (Queen's University)

Friday, November 22nd, 2019

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

Speaker: Neil MacVicar (Queen's University)

Title: Bratteli Diagrams and Cantor Minimal Systems.

Abstract: A Bratteli diagram is a kind of infinite graph for which a transformation can be defined on its path space. This talk will introduce the diagrams, their associated dynamical systems, and the relationship between these systems and systems described by a minimal homeomorphism acting on a Cantor space.

Number Theory Seminar - Richard Leyland

Thursday, November 21st, 2019

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

Speaker: Richard Leyland

Title: Isogenies of Elliptic Curves with Complex Multiplication.

Abstract: In my thesis work I seek to answer Mazur's Question which asks if there exists any isomorphisms of mod $N$ Galois representations attached to elliptic curves that are not induced by isogenies. The first step in answering this question is determining which isogenies of elliptic curves are defined over a field $F$. In this talk, I will show how to construct isogenies between CM elliptic curves by using ideals of the endomorphism rings. In particular, we will see that if the field of definition $F$ does not contain the CM field, then we can reduce the problem to finding cyclic isogenies.

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

Wednesday, November 20th, 2019

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

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

Title: Patterns in the Betti tables.

Abstract: We will examine some of the numerical restrictions on the Betti numbers appearing in the minimal free resolution of the homogeneous coordinate ring of a canonical curve. We will also highlight the consequences of these conditions on low genus curves.

Statistics & Biostatistics - Qingling Duan (Queen's University)

Wednesday, November 20th, 2019

Time: 11:30-12:30 Place: Jeffery Hall 225

Speaker: Qingling Duan (Queen's National Scholar in Bioinformatics, School of Computing and Dept. of Biomedical & Molecular Sciences, Queen's University)

Title: Statistical methods for the study of genomic risk factors of complex traits

Abstract: The overarching goal of my research program is to identify and characterize genomic factors that modulate multifactorial traits such as drug response, allergies and asthma. My team leads the collection and analysis of multiple types of ‘omics (i.e. genomics, transcriptomics, epigenomics and metagenomics) datasets from human cohorts. Specifically, we hypothesize that gene-gene and gene-environment interactions account in part for the missing heritability of complex traits. We test this using additive and multiplicative models in addition to network analysis and data integration to characterize novel biological pathways and underlying disease mechanisms. For example, we have identified main and interaction effects of genetic variants and environmental exposures (e.g., smoking, dog ownership, breastfeeding) on risk of early childhood asthma. In addition, we report novel gene networks associated with risk of asthma and response to chemotherapy among cancer patients. I am a lead investigator of the Canadian Healthy Infant Longitudinal Development (CHILD) cohort study and the Canadian Respiratory Research Network which supports the Canadian Chronic Obstructive Lung Disease (CanCOLD). My laboratory is currently funded by the Canadian Institute of Health Research, Queen’s University and the Canadian Foundation for Innovation.