Scientific

Models for the Spread of Cholera

Speaker: 
Pauline van den Driessche
Date: 
Thu, Jan 18, 2018
Location: 
PIMS, University of Manitoba
Conference: 
PIMS-UManitoba Distinguished Lecture
Abstract: 
There have been several recent outbreaks of cholera (for example, in Haiti and Yemen), which is a bacterial disease caused by the bacterium Vibrio cholerae. It can be transmitted to humans directly by person-to-person contact or indirectly via contaminated water. Random mixing cholera models from the literature are first formulated and briefly analyzed. Heterogeneities in person-to-person contact are introduced, by means of a multigroup model, and then by means of a contact network model. Utilizing an interplay of analysis and linear algebra, various control strategies for cholera are suggested by these models. Pauline van den Driessche is a Professor Emeritus in the Department of Mathematics and Statistics at the University of Victoria. Her research focuses on aspects of stability in biological models and matrix analysis. Current research projects include disease transmission models that are appropriate for influenza, cholera and Zika. Most models include control strategies (e.g., vaccination for influenza) and aim to address questions relevant for public health. Sign pattern matrices occur in these models, and the possible inertias of such patterns is a current interest.

Some specialization problems in Geometry and Number Theory

Speaker: 
Umberto Zannier
Date: 
Fri, Mar 2, 2018
Location: 
PIMS, University of British Columbia
Conference: 
PIMS-UBC Math Distinguished Colloquium
Abstract: 
We shall survey over the general issue of `specializations which preserve a property', for a parametrized family of algebraic varieties. We shall limit ourselves to a few examples. We shall start by recalling typical contexts like Bertini and Hilbert Irreducibility theorems, illustrating some new result. Then we shall jump to much more recent instances, related to algebraic families of abelian varieties. ** Please note, this video was recorded using an older in room system and has substantially diminished video quality.**

Reconfiguration of Triangulations of a Planar Point Set

Speaker: 
Anna Lubiw
Date: 
Thu, Feb 15, 2018
Location: 
PIMS, University of Manitoba
Conference: 
PIMS-UManitoba Distinguished Lecture
Abstract: 
In a reconfiguration problem, the goal is to change an initial configuration of some structure to a final configuration using some limited set of moves. Examples include: sorting a list by swapping pairs of adjacent elements; finding the edit distance between two strings; or solving a Rubik’s cube in a minimum number of moves. Central questions are: Is reconfiguration possible? How many moves are required? In this talk I will survey some reconfiguration problems, and then discuss the case of triangulations of a point set in the plane. A move in this case is a flip that replaces one edge by the opposite edge of its surrounding quadrilateral when that quadrilateral is convex. In joint work with Zuzana Masárová and Uli Wagner we characterize when one edge-labelled triangulation can be reconfigured to another via flips. The proof involves combinatorics, geometry, and topology. Anna Lubiw is a professor in the Cheriton School of Computer Science, University of Waterloo. She has a PhD from the University of Toronto (1986) and a Master of Mathematics degree from the University of Waterloo (1983). Her research is in the areas of Computational Geometry, Graph Drawing and Graph Algorithms. She was named the Ross and Muriel Cheriton Faculty Fellow in 2014, received the University of Waterloo outstanding performance award in 2012 and was named a Distinguished Scientist by the Association for Computing Machinery in 2009. She serves on the editorial boards of the Journal of Computational Geometry and the Journal of Graph Algorithms and Applications.

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
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