Mathematics

Math Outreach: Many Needs, Many Ways

Speaker: 
Melania Alvarez
Date: 
Thu, Oct 26, 2017
Location: 
PIMS, University of Manitoba
Conference: 
PIMS-UManitoba Distinguished Lecture
Abstract: 
Math Outreach: Many Needs, Many Ways I will present a wide range of math educational outreach activities involving elementary, middle and secondary level students. By expecting children to succeed, introducing new and exciting ways to teach mathematics, and promoting role models, the Pacific Institute for the Mathematical Sciences (PIMS) is making a significant difference in the way students view science and technology and their own mathematical ability. These activities are designed to transform the way students look at mathematics and empower them to see themselves as fully capable of succeeding at math. I will describe PIMS outreach programs specifically designed for First Nations schools in British Columbia. We have also developed a variety of programs to support teachers, in particular I will describe our must recent one: a 4-week Summer School for Elementary School Teachers. At this camp, teachers work with mathematicians, educators and math specialists to increase their mathematical knowledge and capability and boost their confidence, as well as foster a positive attitude towards learning mathematics. WORKSHOPS: 1) Bar Model Workshop (Friday, October 27, 1:00 - 2:15 pm) The main purpose of this workshop is to show how the Bar Model method can be used not only as a problem solving technique, but also to develop in students a deeper understanding of fundamental concepts in mathematics. 2) Kindergarten to Grade 2: An important foundation for success (Friday, October 27, 2:30 - 3:45 pm) What students learn during these early years will make a significant difference in how they approach mathematics later on. Research is showing that mathematics knowledge and skills are the most important predictors not only for later math achievement but also for achievement in other content areas (Claessens A. and Engel M., 2013). This workshop presents connection of various concepts and ideas, teaching sequencing, and hands-on fun activities for retention.

Depth Functions in Multivariate & Other Data Settings: Concepts, Perspectives, Tools, & Applications

Speaker: 
Robert Serfling
Date: 
Thu, Sep 28, 2017
Location: 
PIMS, University of Manitoba
Conference: 
PIMS-UManitoba Distinguished Lecture
Abstract: 
Depth functions were developed to extend the univariate notions of median, quantiles, ranks, signs, and order statistics to the setting of multivariate data. Whereas a probability density function measures local probability weight, a depth function measures centrality. The contours of a multivariate depth function induce closely associated multivariate outlyingness, quantile, sign, and rank functions. Together, these functions comprise a powerful methodology for nonparametric multivariate data description, outlier detection, data analysis, and inference, including for example location and scatter estimation, tests of symmetry, and multivariate boxplots. Due to the lack of a natural order in dimension higher than 1, notions such as median and quantile are not uniquely defined, however, posing a challenging conceptual arena. How to define the middle? The middle half? Interesting competing formulations of depth functions in the multivariate setting have evolved, and extensions to functional data in Hilbert space have been developed and more recently, to multivariate functional data. A key question is how generally a notion of depth function can be productively defined. This talk provides a perspective on depth, outlyingness, quantile, and rank functions, through an overview coherently treating concepts, roles, key properties, interrelations, data settings, applications, open issues, and new potentials.

Graph Searching Games and Probabilistic Methods

Speaker: 
Anthony Bonato
Date: 
Thu, Nov 30, 2017
Location: 
PIMS, University of Manitoba
Conference: 
PIMS-UManitoba Distinguished Lecture
Abstract: 
The intersection of graph searching and probabilistic methods is a new topic within graph theory, with applications to graph searching problems such as the game of Cops and Robbers and its many variants, Firefighting, graph burning, and acquaintance time. Graph searching games may be played on random structures such as binomial random graphs, random regular graphs or random geometric graphs. Probabilistic methods may also be used to understand the properties of games played on deterministic structures. A third and new approach is where randomness figures into the rules of the game, such as in the game of Zombies and Survivors. We give a broad survey of graph searching and probabilistic methods, highlighting the themes and trends in this emerging area. The talk is based on my upcoming book (with the same title) co-authored with Pawel Pralat (to be published by CRC Press in late 2017).

Random Maps 10

Speaker: 
Gregory Miermont
Date: 
Tue, Jun 19, 2012
Location: 
PIMS, University of British Columbia
Conference: 
PIMS-MPrime Summer School in Probability
Abstract: 
N.B. Due to a problem with the microphone, the audio for this recording is almost entirely missing. It is displayed here in the hope that the whiteboard material is still useful. The study of maps, that is of graphs embedded in surfaces, is a popular subject that has implications in many branches of mathematics, the most famous aspects being purely graph-theoretical, such as the four-color theorem. The study of random maps has met an increasing interest in the recent years. This is motivated in particular by problems in theoretical physics, in which random maps serve as discrete models of random continuum surfaces. The probabilistic interpretation of bijective counting methods for maps happen to be particularly fruitful, and relates random maps to other important combinatorial random structures like the continuum random tree and the Brownian snake. This course will survey these aspects and present recent developments in this area.

Random Maps 2

Speaker: 
Gregory Miermont
Date: 
Tue, Jun 5, 2012
Location: 
PIMS, University of British Columbia
Conference: 
PIMS-MPrime Summer School in Probability
Abstract: 
The study of maps, that is of graphs embedded in surfaces, is a popular subject that has implications in many branches of mathematics, the most famous aspects being purely graph-theoretical, such as the four-color theorem. The study of random maps has met an increasing interest in the recent years. This is motivated in particular by problems in theoretical physics, in which random maps serve as discrete models of random continuum surfaces. The probabilistic interpretation of bijective counting methods for maps happen to be particularly fruitful, and relates random maps to other important combinatorial random structures like the continuum random tree and the Brownian snake. This course will survey these aspects and present recent developments in this area.

The orbit intersection problem for linear spaces and semiabelian varieties

Speaker: 
Khoa Nguyen
Date: 
Thu, Oct 19, 2017
Location: 
PIMS, University of Calgary
Conference: 
PIMS CRG in Explicit Methods for Abelian Varieties
Abstract: 
We will introduce the Dynamical Mordell-Lang problem by Ghioca and Tucker. After that, we explain the “orbit intersection problem” for linear spaces and semi-abelian varieties. This is joint work with Ghioca.

Diophantine equations for fun (and profit?)

Speaker: 
Michael Bennett
Date: 
Thu, Sep 21, 2017
Location: 
PIMS, University of Calgary
Conference: 
Louise and Richard K. Guy Lecture Series
Abstract: 
Michael Bennett (President, Canadian Mathematical Society; Professor of Mathematics, University of British Columbia) Diophantine equations are one of the oldest, frequently celebrated and most abstract objects in mathematics. They crop up in areas ranging from recreational mathematics and puzzles, to cryptography, error correcting codes, and even in studying the structure of viruses. In this talk, Dr. Bennett will attempt to show some of the roles these equations play in modern mathematics and beyond.

Triangular bases of integral closures

Speaker: 
Jens Bauch
Date: 
Thu, Sep 28, 2017
Location: 
PIMS, University of Calgary
Conference: 
PIMS CRG in Explicit Methods for Abelian Varieties
Abstract: 
Triangular bases of integral closures

Hybrid Krylov Subspace Iterative Methods for Inverse Problems

Speaker: 
James Nagy
Date: 
Fri, May 5, 2017
Location: 
PIMS, University of Manitoba
Conference: 
Mathematical Imaging Science
Abstract: 
Inverse problems arise in many imaging applications, such as image reconstruction (e.g., computed tomography), image deblurring, and digital super-resolution. These inverse problems are very difficult to solve; in addition to being large scale, the underlying mathematical model is often ill-posed, which means that noise and other errors in the measured data can be highly magnified in computed solutions. Regularization methods are often used to overcome this difficulty. In this talk we describe hybrid Krylov subspace based regularization approaches that combine matrix factorization methods with iterative solvers. The methods are very efficient for large scale imaging problems, and can also incorporate methods to automatically estimate regularization parameters. We also show how the approaches can be adapted to enforce sparsity and nonnegative constraints. We will use many imaging examples that arise in medicine and astronomy to illustrate the performance of the methods, and at the same time demonstrate a new MATLAB software package that provides an easy to use interface to their implementations. This is joint work with Silvia Gazzola (University of Bath) and Per Christian Hansen (Technical University of Denmark).

Rufus Bowen Conference - Lunchtime Speeches

Speaker: 
Brian Marcus
Date: 
Wed, Aug 2, 2017
Location: 
PIMS, University of British Columbia
Conference: 
Current Trends in Dynamical Systems and the Mathematical Legacy of Rufus Bowen
Abstract: 
These speeches were given during the remembrance lunch as part of the conference "Current Trends in Dynamical Systems and the Mathematical Legacy of Rufus Bowen".
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