Mathematics

The Mathematics of Social Evolution

Speaker: 
Troy Day
Speaker: 
Dave McLeod
Date: 
Thu, Mar 22, 2018
Location: 
PIMS, University of Manitoba
Conference: 
PIMS-UManitoba Distinguished Lecture
Abstract: 
How social traits evolve remains an open question in evolutionary biology. Two traits of particular interest are altruism (where an individual incurs a cost to help others) and spite (where an individual incurs a cost to harm others). Both traits should be evolutionarily disadvantageous because any benefits arising from these behaviours are also available to “cheaters” who do not pay the cost of displaying altruism or spite themselves. In this talk I will show how stochasticity can sometimes reverse the direction of evolution and drive the emergence of these behaviours. I will start with an individual-based evolutionary model and then approximate it using a system of stochastic differential equations (SDEs). These SDEs are then be reduced to a single SDE on a “slow manifold” governing the evolutionary dynamics. A rather complete analysis of this SDE is then possible, showing exactly when and how stochasticity can drive the evolution of altruism and spite. Biography: Tryo Day is a Professor and former CRC in the Department of Mathematics and Statistics at Queen’s University. His research interests involve evolutionary theory, including the evolution of pathogen virulence, drug resistance, social traits, and epigenetic inheritance. Dr. Day is coauthor (with James Stewart) of the textbooks “Biocalculus: Calculus, Probability and Statistics for the Life Sciences”, and (with Sarah P. Otto) “A Biologist’s Guide to Mathematical Modeling”. He is an Elected Fellow of the Royal Society of Canada and the AAAS, and is the recipient of a Killam Research Fellowship, a Steacie Fellowship, the CAIMS Research Prize, and the Steacie Prize.

Philosophy of Mathematics as a Design Science

Speaker: 
Jeremy Avigad
Date: 
Thu, Mar 15, 2018
Location: 
PIMS, University of Calgary
Conference: 
The Calgary Mathematics & Philosophy Lectures
Abstract: 
n the history of philosophy, much has been made of the disagreements between W. V. O. Quine and Rudolf Carnap on the nature of mathematical and scientific knowledge. But when the dust settles, the points of agreement are more substantial: mathematical and scientific reasoning are shaped by the rules of our language, and these rules are, in turn, adopted for pragmatic scientific reasons. In this talk, I will take this perspective seriously, and regard mathematics as a system of conventions and norms that is designed to help us make sense of the world and reason efficiently. Like any designed system, it can perform well or poorly, and the philosophy of mathematics has a role to play in helping us understand the general principles by which it serves its purposes well. To that end, I will consider models of mathematical language currently implemented in interactive theorem provers, which support the formalization and verification of mathematical theorems. Using these models, as well as reflection on ordinary mathematical practice, I will try to extract some insights as to how mathematical language works, and what makes it so effective.

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.

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.
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