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 Events
Martin Barlow, UBC
Fri 3 Apr 2009, 3:30pm
Department Colloquium
WMAX 110 (PIMS)
The Ant in the Labyrinth: Random Walks and Percolation
WMAX 110 (PIMS)
Fri 3 Apr 2009, 3:30pm-4:00pm

Abstract

Percolation was introduced by Broadbent and Hammersley in 1957. The simplest version to describe is on the Euclidean lattice Zd. Let p be a fixed probability between 0 and 1. Each bond in Zd is retained with probability p, and removed with probability 1-p, independently of all the others. The percolation cluster containing a point x, denoted C(x), consists of those points which can be reached from x by a path of retained bonds. There is a critical value pc∈(0,1) such that if p < pc then all clusters are finite, while for p > pc there is an infinite cluster.

Random walks on percolation clusters were introduced by De Gennes in 1976: he called this the problem of 'the ant in the labyrinth'. If p = p(n,x,y) is the probability that a random walker ('the ant'), starting at x, is at y at time n, then p describes diffusion of heat on the cluster.

For the supercritical phase (p > pc) this problem is now quite well understood, and p(n,x,y) converges to a Gaussian distribution as n→∞. PDE techniques introduced by Nash in the 1950s, play an important role in some of the arguments.

The critical case p = pc is much harder, since the clusters have fractal properties. One expects that p(n,x,x) ∼ x- ds/2, where ds is called the spectral dimension of the cluster. Alexander and Orbach conjectured in 1982 that ds = 4/3 in all dimensions: this has recently been proved in some high dimensional cases.

Note for Attendees

There will be tea and cookies in the math lounge at approximately 2:45pm.
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Leah Keshet, Brian Marcus and Malabika Pramanik
Department of Mathematics, UBC
Tue 14 Apr 2009, 2:05pm SPECIAL
One Time Event
WMAX 110 (PIMS)
PIMS/UBC Info Session on Grant Opportunities: "Funding Possibilities"
WMAX 110 (PIMS)
Tue 14 Apr 2009, 2:05pm-3:00pm

Details

We will discuss funding opportunities in pure and applied mathematics, and strategies for obtaining grants, fellowships, and so on. We will focus on NSERC grants in Canada and National Science Foundation grants in the U.S.
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Christopher A. Del Negro
The College of William and Mary
Wed 15 Apr 2009, 2:00pm
Mathematical Biology Seminar
WMAX 216
Emergent network properties in the preBotzinger Complex: the cellular and synaptic mechanisms of respiratory rhythm generation
WMAX 216
Wed 15 Apr 2009, 2:00pm-3:00pm

Abstract

Breathing is an interesting and essential life-sustaining behavior for humans and all mammals. Like many rhythmic motor behaviors, breathing movements originate due to neural rhythms that emanate from a central pattern generator (CPG) network. CPGs produce neural-motor rhythms that often depend on specialized pacemaker neurons or alternating synaptic inhibition. But conventional models cannot explain rhythmogenesis in the respiratory preBotzinger Complex (preBotzC), the principal central pattern generator for inspiratory breathing movements, in which rhythms persist under experimental blockade of synaptic inhibition and of intrinsic pacemaker currents. Using mathematical models and experimental tests, here we demonstrate an unconventional mechanism in which metabotropic synapses and synaptic disfacilitation play key rhythmogenic roles: recurrent excitation triggers Ca2+-activated nonspecific cation current (ICAN), which initiates the inspiratory burst. Robust depolarization due to ICAN also causes voltage-dependent spike inactivation, which diminishes recurrent excitation, allowing outward currents such as Na/K ATPase pumps and K+ channels to terminate the burst and cause a transient quiescent state in the network. After a recovery period, sporadic spiking activity rekindles excitatory interactions and thus starts a new cycle. Because synaptic inputs gate postsynaptic burst-generating conductances, this rhythm-generating mechanism represents a new paradigm in which the basic rhythmogenic unit encompasses a fully inter-dependent ensemble of synaptic and intrinsic components.
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Shankar Bhamidi
Department of Mathematics, UBC
Wed 15 Apr 2009, 3:00pm
Probability Seminar
WMAX 216
Branching processes and real world networks
WMAX 216
Wed 15 Apr 2009, 3:00pm-4:00pm

Abstract

The aim of this talk is to highlight the usefulness of continuous time branching process theory in understanding refined asymptotics about various random network models. We shall exhibit their usefulness in two different contexts:

(1) First passage percolation: Consider a connected network and suppose each edge in the network has a random positive edge weight. Understanding the structure and weight of the shortest path between nodes in the network is one of the most fundamental problems studied in modern probability theory. In the modern context these problems take an additional significance with the minimal weight measuring the cost of sending information while the number of edges on the optimal path (hopcount) representing the actual time for messages to get between vertices in the network. In the context of the configuration model of random networks we shall show how branching processes allow us to find the limiting distribution of the minimal weight path as well as establishing a general central limit theorem for the hopcount with matching means and variances.

(2) Spectral distribution of random trees: Many models of random trees (including general models embedded in continuous time branching processes) satisfy a general form of convergence locally to limiting infinite objects. In this context we find via soft arguments, the convergence of the spectral distribution of the adjacency matrix to a limiting (model dependent) non random distribution. For any \gamma we also find a sufficient condition for there to be a positive mass at \gamma in the limit.

Joint work with Remco van der Hoftsad, Gerard Hooghiemstra, Steve Evans and Arnab Sen.

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Jose Manuel Gomez
Department of Mathematics, UBC
Wed 15 Apr 2009, 3:00pm
Topology and related seminars
WMAX 110 (PIMS)
Stable decompositions and almost commuting elements in Lie groups
WMAX 110 (PIMS)
Wed 15 Apr 2009, 3:00pm-4:00pm

Abstract

In this talk I show that the space of almost commuting elements in a compact Lie group G splits after one suspension.
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Joe Yuichiro Wakano
Meiji Institute for Advanced Study of Mathematical Sciences
Thu 16 Apr 2009, 2:00pm
Mathematical Biology Seminar
WMAX 216
Origin of culture: an evolutionary model of social learning
WMAX 216
Thu 16 Apr 2009, 2:00pm-3:00pm

Abstract

Social learning is an important ability seen in a wide range of animals. Especially, humans developed the advanced social learning ability such as language, which triggered rapid cultural evolution. On the other hand, many species, such as viruses, rely on genetic evolution to adapt to environmental fluctuations. Here we propose an evolutionary game model of competition among three strategies; social learning, individual learning, and genetic determination of behavior. We identify the condition for learning strategies to evolve.
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Jon Carlson
University of Georgia
Wed 22 Apr 2009, 3:00pm
Department Colloquium / Topology and related seminars
WMAX 1110 (PIMS)
Modules of constant Jordan type
WMAX 1110 (PIMS)
Wed 22 Apr 2009, 3:00pm-4:00pm

Abstract

This is joint work with Eric Friedlander, Julia Pevtsova and Andrei Suslin.  We consider modules over an elementary abelian group on which every element in the radical, but not the square of the radical, has the same Jordan canonical form.  Such modules can be used to define bundles on projective spaces and Grassmanians.  They have many interesting properties.  We can get them as submodules of any module of the group algebra.  In this talk I will discuss some of the constructions and their generalizations.

Note for Attendees

There will be tea and cookies in the PIMS 1st floor lounge at approximately 2:45pm.
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Bahman Davoudi Dehaghi
BC Centre for Disease Control
Thu 23 Apr 2009, 2:00pm
Mathematical Biology Seminar
WMAX 216
Early Real-time Estimation of the Basic Reproductive Number
WMAX 216
Thu 23 Apr 2009, 2:00pm-3:00pm

Abstract

The basic reproductive number, R_0, which is generally defined as the expected number of secondary infections per primary case in a totally susceptible population, is an important epidemiological quantity. It helps us to understand the possible outcome of an initial infection seeding in a social setting: whether it leads to a small outbreak, or it evolves into a large-scale epidemic. The basic reproductive number encapsulates the information about the biology of disease transmission as well as the structure of human social contacts. We use concepts from network theory to present a novel method for estimating the value of the basic reproductive number during the early stage of an outbreak. This approach will greatly enhance our ability to reliably estimate the level of threat caused by an emerging infectious disease.
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Daniel Conus
University of Utah
Thu 23 Apr 2009, 3:30pm
Probability Seminar
WMAX 216 (PIMS)
The non-linear wave equation in high dimensions: existence, Holder-continuity and Ito-Taylor expansion
WMAX 216 (PIMS)
Thu 23 Apr 2009, 3:30pm-4:30pm

Abstract


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Ronald Stern
UC Irvine
Fri 24 Apr 2009, 3:00pm
Department Colloquium
WMAX 110 (PIMS)
Getting to the heart of smooth 4-manifolds
WMAX 110 (PIMS)
Fri 24 Apr 2009, 3:00pm-4:00pm

Abstract

In this talk, designed for a broad mathematical audience, we will describe what is known (and unknown) about the classification of smooth 4-manifolds. In particular we will uncover a new mechanism that makes progress towards the conjecture that every simply-connected closed 4-manifold has either zero or infinitely many distinct smooth structures.

Note for Attendees

 

There will be tea and cookies in the PIMS 1st floor lounge at approximately 2:45pm.
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Djun Kim
Vancouver Island University
Mon 27 Apr 2009, 2:30pm SPECIAL
One Time Event
MATH 225
Skylight Candidate Interview -- Subject: TBA
MATH 225
Mon 27 Apr 2009, 2:30pm-4:00pm

Details

TBA

Note for Attendees

Coffee and cookies will be served at 2:30 p.m.  There will be a 30 minute talk at 3 p.m., followed by a 20 minute forum.  All members of the department are encouraged to meet the candidate for the joint Skylight/Mathematics position.
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Nikolai Dokuchaev
Trent University
Wed 29 Apr 2009, 3:00pm
Probability Seminar
WMAX 216 (PIMS)
Myopic strategies and impact of forecast errors
WMAX 216 (PIMS)
Wed 29 Apr 2009, 3:00pm-4:00pm

Abstract

We introduce and discuss some new stochastic models of optimal portfolio selection with reduced impact of forecast errors. In particular, we found some new examples of optimal myopic strategies, including some discrete time models with serial correlations. In addition, we found some new cases when the strategies that don't leave the efficient frontier even if there is an error in the forecast. It may happen for non-myopic strategies if the required information about the future is limited.
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