Mathematics

The Broughton Archipeligo Monitoring Program

Speaker: 
Stephanie Peacock
Date: 
Fri, Jul 15, 2011
Location: 
PIMS, University of Victoria
Conference: 
AMP Math Biology Workshop
Conference: 
2011 IGTC Summit
Abstract: 
This talk was one of the IGTC Student Presentations.

Patterns of Social Foraging

Speaker: 
Leah Keshet
Date: 
Fri, Jul 15, 2011
Location: 
PIMS, University of Victoria
Conference: 
AMP Math Biology Workshop
Conference: 
2011 IGTC Summit
Abstract: 
I will present recent results from my group that pertain to spatio-temporal patterns formed by social foragers. Starting from work on chemotaxis by Lee A. Segel (who was my PhD thesis supervisor), I will discuss why simple taxis of foragers and randomly moving prey cannot lead to spontaneous emergence of patchiness. I will then show how a population of foragers with two types of behaviours can do so. I will discuss conditions under which one or another of these behaviours leads to a winning strategy in the sense of greatest food intake. This problem was motivated by social foraging in eiderducks overwintering in the Belcher Islands, studied by Joel Heath. The project is joint with post-doctoral fellows, Nessy Tania, Ben Vanderlei, and Joel Heath.

Brains and Frogs: Structured Population Models

Speaker: 
Kerry Landman
Date: 
Sat, Jul 16, 2011
Location: 
PIMS, University of Victoria
Conference: 
AMP Math Biology Workshop
Conference: 
2011 IGTC Summit
Abstract: 
In diverse contexts, populations of cells and animals disperse and invade a spatial region over time. Frequently, the individuals that make up the population undergo a transition from a motile to an immotile state. A steady-state spatial distribution evolves as all the individuals settle. Moreover, there may be multiple releases of motile subpopulation. If so, the interactions between motile and immotile subpopulations may affect the final spatial distribution of the various releases. The development of the brain cortex and the translocation of threatened Maud Island frog are two applications we have considered.

A New Approach to the Bar-Cobar Duality

Speaker: 
André Joyal
Date: 
Mon, Jul 18, 2011
Location: 
PIMS, University of British Columbia
Conference: 
Category Theory 2011
Abstract: 
The bar-cobar duality is playing a fundamental role in the Koszul duality for algebras and operads. We use Sweedler theory of measurings to reformulate and extend the duality. This is joint work with Matthieu Anel.

Approximating Functions in High Dimensions

Speaker: 
Albert Cohen
Date: 
Mon, Mar 14, 2011
Location: 
University of British Columbia, Vancouver, Canada
Conference: 
IAM-PIMS-MITACS Distinguished Colloquium Series
Abstract: 
This talk will discuss mathematical problems which are challenged by the fact they involve functions of a very large number of variables. Such problems arise naturally in learning theory, partial differential equations or numerical models depending on parametric or stochastic variables. They typically result in numerical difficulties due to the so-called ''curse of dimensionality''. We shall explain how these difficulties may be handled in various contexts, based on two important concepts: (i) variable reduction and (ii) sparse approximation.

The Hypoelliptic Laplacian

Speaker: 
Jean-Michel Bismut
Date: 
Fri, Sep 23, 2011
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Colloquium Series
Abstract: 
If X is a Riemannian manifold, the Laplacian is a second order elliptic operator on X. The hypoelliptic Laplacian L_b is an operator acting on the total space of the tangent bundle of X, that is supposed to interpolate between the elliptic Laplacian (when b -> 0) and the geodesic flow (when b -> \infty). Up to lower order terms, L_b is a weighted sum of the harmonic oscillator along the fibre TX and of the generator of the geodesic flow. In the talk, we will explain the underlying algebraic, analytic and probabilistic aspects of its construction, and outline some of the applications obtained so far.

Virtual Lung Project at UNC: What's Math Got To Do With It?

Speaker: 
Gregory Forest
Date: 
Fri, Mar 18, 2011
Location: 
PIMS, University of British Columbia
Abstract: 
A group of scientists at the University of North Carolina, from theorists to clinicians, have coalesced over the past decade on an effort called the Virtual Lung Project. There is a parallel VLP at the Pacific Northwest Laboratory, focused on environmental health, but I will focus on our effort. We come from mathematics, chemistry, computer science, physics, lung biology, biophysics and medicine. The goal is to engineer lung health through combined experimental-theoretical-computational tools to measure, assess, and predict lung function and dysfunction. Now one might ask, with all due respect to Tina Turner: what's math got to do with it? My lecture is devoted to many responses, including some progress yet more open problems.

Sparse Optimization Algorithms and Applications

Speaker: 
Stephen Wright
Date: 
Mon, Apr 4, 2011
Location: 
PIMS, University of British Columbia
Conference: 
IAM-PIMS-MITACS Distinguished Colloquium Series
Abstract: 
In many applications of optimization, an exact solution is less useful than a simple, well structured approximate solution. An example is found in compressed sensing, where we prefer a sparse signal (e.g. containing few frequencies) that matches the observations well to a more complex signal that matches the observations even more closely. The need for simple, approximate solutions has a profound effect on the way that optimization problems are formulated and solved. Regularization terms can be introduced into the formulation to induce the desired structure, but such terms are often non-smooth and thus may complicate the algorithms. On the other hand, an algorithm that is too slow for finding exact solutions may become competitive and even superior when we need only an approximate solution. In this talk we outline the range of applications of sparse optimization, then sketch some techniques for formulating and solving such problems, with a particular focus on applications such as compressed sensing and data analysis.

As Geometry is Lost - What Connections are Lost? What Reasoning is Lost? What Students are Lost? Does it Matter?

Speaker: 
Walter Whitley
Date: 
Fri, Apr 29, 2011
Location: 
SFU Harbour Center
Location: 
PIMS, Simon Fraser University
Conference: 
Changing the Culture 2011
Abstract: 
In a North American curriculum preoccupied with getting to calculus, we witness an erosion of geometric content and practice in high school. What remains is often detached from "making sense of the world", and from reasoning (beyond axiomatic work in University). We see the essential role of geometry in science, engineering, computer graphics and in solving core problems in applications put aside when revising math curriculum. A second feature is that most graduates with mathematics degrees are not aware of these rich connections for geometry. We will present some samples of: what we know about early childhood geometry.; and then of the critical role of geometry and geometric reasoning in work in multiple fields outside of mathematics. With a perspective from "modern geometry", we note the critical role of transformations, symmetries and invariance in many fields, including mathematics beyond geometry. With these bookends of school mathematics in mind, we consider some key issues in schools, such as which students are lost when the bridge of geometry is not there to carry them through (caught in endless algebra) and possible connections other subjects. We also consider the loss within these other disciplines. We will present some sample investigations and reasoning which can be supported by a broader more inclusive set of practices and which pays attention to geometric features and reasoning in various contexts. In particular, we illustrate the use of dynamic geometry investigations, hands on investigations and reflections, and making connections to deeper parts of the rest of mathematics and science.

Changing the Culture of Homework

Speaker: 
Justin Grey
Speaker: 
Jamie Mulholand
Date: 
Fri, Apr 29, 2011
Location: 
SFU Harbour Center
Location: 
PIMS, Simon Fraser University
Conference: 
Changing the Culture 2011
Abstract: 
Who do your students think their homework is for? Does attaching credit to homework promote student understanding, or encourage students to find answers by whatever means necessary? Are they focused on calculating the answer, or seeing the big picture? Is their homework grade a true reflection of their own understanding of the material, or does it better reflect the understanding of their "support network"? In this workshop we will describe our efforts to improve student feedback and to promote good study skills in first and second year mathematics classes.
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