Department of Mathematics and Statistics at the University of Regina

09/10/2024

Speaker: Chi-Kwong Li, College of William & Mary and Institute for Quantum Computing, University of Waterloo

Title: Some matrix and graph techniques in quantum tomography problems

Place & Time: RIC 20 at 3:30 pm on Tuesday, September 17, 2024

Abstract:

Quantum tomography is a technique used to determine the state of a quantum system by making measurements on many identically prepared copies of that system. We discuss some recent results in the study of the quantum state tomography for quantum states and quantum systems of finite dimensional systems. The proofs of the results utilize matrix theory and graph theory. Experimental results using the IBM online quantum computers (qiskit) will be presented.

No quantum theory background is needed for the talk.

03/14/2024

03/02/2024

PIMS Distinguished Lecture
Friday March 8
Time: 3:30 PM
Room: RIC 209 (for the viewing party)
Also livestreamed, with registration in advance:

https://uregina-ca.zoom.us/meeting/register/tJIsfu-prjkuGtDbZtO3x00R_XvsKfMmV1aX

Speaker: Teena Gerhardt (Michigan State University)

Title: Interactions between topology and algebra: advances in algebraic K-theory

Abstract: The field of algebraic topology has exposed deep connections between topology and algebra. One example of such a connection comes from algebraic K-theory. Algebraic K-theory is an invariant of rings, defined using tools from topology, that has important applications to algebraic geometry, number theory, and geometric topology. Algebraic K-groups are difficult to compute, but advances in algebraic topology have led to many recent computations which were previously intractable. In this talk I will introduce algebraic K-theory and its applications, and discuss recent advances in this field.

This event is supported by PIMS.

02/11/2024

Happy International Day of Women and Girls in Science!

The purpose of the day is to achieve full and equal access to and participation in science for women and girls.

02/04/2024

Mathematics and Statistics Colloquium
February 9th, 2024
3:30 pm - 4:30 pm
RI 209

Speaker: Shaun Fallat

Title: What is a positive matrix?

Abstract: If I asked this question to non-experts, the typical response is: positive definite or entry-wise positive. Indeed, classically, these two classes of positive matrices represent fundamental distinct topics in Linear Algebra, and continue to receive considerable research attention today! However, there are many other notions of a ``positive matrix" that are studied both for their theoretical value and for their related interesting applications (the Riemann Hypothesis...). Matrix positivity has been an interest of mine since my first days as a graduate student and I continue to be fascinated by the different varieties of a positive matrix and their significance in matrix theory.

In this talk, I will (try) to introduce the subject of matrix positivity and survey the various type of positive matrices. I will discuss connections, differences, some related applications, and, hopefully, provide some rationale for the numerous type of positive matrices. Let me know if you can spot all 25 defined types of positive matrices during this lecture!

No previous knowledge is required and this talk will not be technical in the least. All are welcome to attend and hopefully you leave having learned something new about a positive matrix!

02/03/2024

PIMS Distinguished Lecture
Monday, February 12th
Time: 3:30PM
Room: Classroom Building 125
Registration in advance: https://uregina-ca.zoom.us/meeting/register/tJEodu6hqDkrH9d6E9z56xmnY9_mxaHZ8YwA

Speaker: David Haziza (University of Ottawa)

Title: Statistical inference in the presence of imputed survey data through regression trees and random forests

Abstract: In recent years, machine learning procedures have attracted much attention in National Statistical Offices (e.g., Statistics Canada). In particular, random forests are currently being scrutinized as an alternative to traditional imputation procedures. Item nonresponse in surveys is usually handled through some form of single imputation. Random forests provide flexible tools for obtaining a set of imputed values. Belonging to the class of non-parametric methods, random forests have the ability to capture nonlinear trends in the data and tend to be robust to the non-inclusion of interactions or predictors accounting for curvature. In this presentation, we will discuss the properties of imputed estimators based on random forests. Also, to the best of our knowledge, how to estimate the variance while accounting for sampling and nonresponse, has not been addressed in the literature. We propose a novel variance estimator based on the so-called reverse approach for variance estimation. We will present the results from a simulation study to assess the proposed methods in terms of bias and efficiency. Finally, the choice of hyper-parameters will also be discussed. Co-authors: Mehdi Dagdoug (McGill University) and Camelia Goga (Université de Bourgogne Franche Comté).

Welcome! You are invited to join a meeting: PIMS Distinguished Lecture. After registering, you will receive a confirmation email about joining the meeting.

01/26/2024

Mathematics and Statistics colloquium
February 2nd, 2024, 3:30 pm - 4:30 pm, RI 209

Speaker: Prateek Kumar Vishwakarma, University of Regina

Title: Plucker inequalities for weakly separated coordinates in totally nonnegative Grassmannian

Abstract: We show that the partial sums of the long Plucker relations for pairs of weakly separated Plucker coordinates oscillate around 0 on the totally nonnegative part of the Grassmannian. Our result generalizes the classical oscillating inequalities by Gantmacher--Krein (1941) and recent results on totally nonnegative matrix inequalities by Fallat--Vishwakarma (2023). In fact we obtain a characterization of weak separability, by showing that no other pair of Plucker coordinates satisfies this property.

Weakly separated sets were initially introduced by Leclerc and Zelevinsky and are closely connected with the cluster algebra of the Grassmannian. Moreover, our work connects several fundamental objects such as weak separability, Temperley--Lieb immanants, and Plucker relations, and provides a very general and natural class of additive determinantal inequalities on the totally nonnegative part of the Grassmannian.

We shall begin the talk with the introduction of totally nonnegative matrices and see its important connection with planar networks. Then we shall review some of the results discussed in my previous talk in this Colloquium on the topic to continue further with the more recent discovery. The talk will be self-contained.

11/22/2023

At just 15 years old, Atticus Hall has been cruising through university-level math and calculus classes, one number at a time.

11/20/2023

Mathematics and Statistics colloquium

Date: Friday, December 1, 2023 at 3:30 PM
Zoom Link
https://uregina-ca.zoom.us/j/94223382852?pwd=UzdqSG52UklTTm9GNVFvRGZKMlhHUT09

Zoom Password767870

Speaker: Kevin McGregor, York University

Title: Community modelling techniques in microbiome data

Abstract: The microbiome is the collection of microorganisms colonizing the human body and plays an integral part in human health. Community modelling is an important kind of analysis in microbiome studies, as species in the human microbiome are known to be metabolically linked. In this talk I will outline various statistical techniques I have developed in recent years to perform community modelling in the microbiome, including both co-occurrence estimation and Bayesian dimension reduction techniques. These methods will be highlighted in metagenomic sequencing data from a pediatric multiple sclerosis dataset from Dr. Heather Armstrong at the University of Manitoba. I will also show how such techniques are applicable in other count-based sequencing platforms such as single-cell RNA-sequencing data.

Zoom is the leader in modern enterprise video communications, with an easy, reliable cloud platform for video and audio conferencing, chat, and webinars across mobile, desktop, and room systems. Zoom Rooms is the original software-based conference room solution used around the world in board, confer...

10/31/2023

Mathematics and Statistics Colloquium
Date and Place : November 3, 2023, RI 209
Time: 3:30 pm - 4:30 pm
Speaker: Douglas Farenick

Title: Bipartite entanglement in tensor cones of Toeplitz and Fejer-Riesz operator systems

Abstract: In the 1960s, Namioka and Phelps considered the various ways one might define the tensor product of cones, where the cones are assumed to be proper cones in finite-dimensional real vector spaces. The most basic of these possibilities results in what is called the separable cone; the dual of the separable cone constitutes a larger cone, containing the separable cone. Any cone residing between these two is called a tensor cone, and elements of a tensor cone that do not belong to the separable cone are said to be entangled.
In quantum information theory, the proper cones of interest are those generated by density operators, yielding the familiar notion of a separable state. The dual of the cone of separable states is cones of block-positive operators, wherein one finds the entanglement witnesses studied in quantum theory.
At present there is considerable interest in returning to the abstract ideas put forward by Nakioma and Phelps, and the long-standing open problem characterising the context in which the separable cone and its dual coincide has only recently been resolved. In this lecture, I explain some of my own investigations into tensor cones arising from the tensor product of Toeplitz and Fejer-Riesz operator systems.