University of Washington

Mon 5 Oct 2015, 3:00pm
Algebraic Geometry Seminar
MATH 126

Projectivity of the moduli space of stable logvarieties

MATH 126
Mon 5 Oct 2015, 3:00pm4:00pm
Abstract
This is a report on joint work with Zsolt Patakfalvi. We prove a strengthening of Kollár's Ampleness Lemma and use it to prove that any proper coarse moduli space of stable logvarieties of general type is projective. We also confirm the IitakaViehweg conjecture on the subadditivity of logKodaira dimension for fiber spaces whose general fiber is of log general type.
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UBC/PIMS

Mon 5 Oct 2015, 3:00pm
Harmonic Analysis Seminar
Math Annex 1102

Discrete Analogues in Harmonic Analysis: Quadratic Carleson

Math Annex 1102
Mon 5 Oct 2015, 3:00pm4:30pm
Abstract
Since the late eighties, when Bourgain proved his celebrated pointwise ergodic theorems, discrete analogues in harmonic analysis have come into vogue. Indeed, much work has been devoted to studying maximal functions and (maximal truncations of) singular integrals. The Carleson operator  strictly more singular than either above operator  is a natural operator to try adapt to the discrete setting: Eli Stein has been successful in "transferring" the continuous result to the discrete setting. In particular, he has established the L^2(\Z) boundedness of the discrete Carleson operator
\[ \sup_{\lambda}  \sum_{m \neq 0} f(nm) e^{2\pi i \lambda m}/m .\]
The purpose of this talk will be to study a discrete analogue of the quadratically modulated Carleson operator:
\[ \sup_{\lambda}  \sum_{m \neq 0} f(nm) e^{2\pi i \lambda m^2}/m  \]
where \lambda ranges over certain subsets of (0,1].
This will be the first talk of the sequence, and very little background is required  though the argument will eventually combine elements from analytic number theory, probability theory, and harmonic analysis.
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Department of Mathematics, UBC

Tue 6 Oct 2015, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Relative Equilibria with a Dominant Vortex

ESB 4133 (PIMS Lounge)
Tue 6 Oct 2015, 12:30pm1:30pm
Abstract
In fluids, the presence of a dominant vortex has an organizing effect on the surrounding flow. We exploit this effect to simplify the stability problem for relative equilibria of (N+1) interacting point vortices, where N vortices have infinitesimal circulation and one vortex is strong in relation. Within this framework, existence and stability of equilibria reduces to characterizing critical points of a function defined on a circle. In the case that all vortices have circulation of the same sign, this function is potentiallike, with minima corresponding to stable configurations and maxima and saddle points corresponding to unstable solutions. Surprisingly, typical stable configurations exhibit asymmetry.
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University of Aveiro

Tue 6 Oct 2015, 2:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126

An Introduction to Convolutional codes

Math 126
Tue 6 Oct 2015, 2:00pm3:00pm
Abstract
A followup talk on multidimensional convolutional codes will be given on Thursday, October 8.
Coding theory  theory of error correcting codes  is one of the most interesting and applied parts of mathematics.Coding theory methods are often elegant applications of very basic concepts and methods of (abstract) algebra. IIn this talk we shall start by giving a brief general overview of this area before introducing the main topic of the talk, namely, convolutional codes.
These codes are mathematically more involved than the standard block codes as they posses a very rich algebraic structure. In this context the data is considered as a sequence. Even though the data is split into blocks of a fixed rate as in block codes, the relative position of each block in the sequence is taken into account. The blocks are not encoded independently and previous nodes in the sequence have an effect over the next encoded node. Because of this, convolutional codes have memory. From a mathematical point of view they can be seen as F[x]submodules of F[x]^n, where F is a finite field and F[x] is the ring of polynomials over F.
The aim of this talk is to introduce this powerful class of codes, their properties and their use in practice. We shall conclude by presenting some of the most fascinating open problems in the design of convolutional codes.
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UBC

Tue 6 Oct 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

On type II singularity formulation of harmonic map flows

ESB 2012
Tue 6 Oct 2015, 3:30pm4:30pm
Abstract
I will consider the following classical harmonic map flow from a general twodimensional domain D to S^2:
u_t=\Delta u +\nabla u^2 u, u: D \to S^2
We develop a parabolic gluing method to construct finite time blowup solutions of Type II in general domains. We show that type II blowup solutions with blowup rate
(Tt)/\log^2 (Tt)
is stable and generic in arbitrary domains (without any symmetry). I will also discuss the construction of multiple blowups, reverse bubbling, bubbling trees, bubbling at infinity. As a byproduct we can perform new geometric surgeries. (Joint work with Manuel del Pino and Juan Davila.)
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UBC and SFU

Tue 6 Oct 2015, 4:00pm
Discrete Math Seminar
ESB 4127

Bounds for randomized rumour spreading protocols

ESB 4127
Tue 6 Oct 2015, 4:00pm5:00pm
Abstract
Consider a social network modelled as a graph, with people and friendships represented by vertices and edges, respectively. Suppose that a person knows a piece of information, and as time passes, talks to other people and spreads it. How long it takes until everyone knows the rumour? The answer, which we call the "spread time", certainly depends on the graph's structure and how the rumour spreads. In this talk we discuss two well known randomized rumour spreading protocols (known as push&pull protocols) and survey the known results on their spread times on various graphs.
Based on joint work with H. Acan, A. Collevecchio, and N. Wormald.
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University of British Columbia and Pacific institute for the Mathematical Sciences

Wed 7 Oct 2015, 3:00pm
Probability Seminar
ESB 2012

Restrictions of Brownian motion

ESB 2012
Wed 7 Oct 2015, 3:00pm4:00pm
Abstract
It is classical that the zero set and the set of record times of a linear Brownian motion have Hausdorff dimension almost surely. Can we find a larger random subset on which a Brownian motion is monotone? Perhaps surprisingly, the answer is negative. We outline the short proof, which is an application of Kaufman's dimension doubling theorem for planar Brownian motion. This is a joint work with Yuval Peres.
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University of Utah

Wed 7 Oct 2015, 3:15pm
Topology and related seminars
ESB 4133

Subgroups of the automorphism group of a free product

ESB 4133
Wed 7 Oct 2015, 3:15pm4:15pm
Abstract
I will discuss classification results for subgroups of Out(Fn) (analogous to Ivanov's classification of subgroups of mapping class groups of surfaces), and more generally of automorphism groups of free products. In particular, I will present a version of the Tits alternative for the automorphism group of a free product. This is partly joint work with Vincent Guirardel.
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University of Aveiro

Thu 8 Oct 2015, 3:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math Annex 1102

Multidimensional Convolutional Codes

Math Annex 1102
Thu 8 Oct 2015, 3:00pm4:00pm
Abstract
An introductory talk on one dimensional convolutional codes will be given on Tuesday, October 6.
Multidimensional (nD) convolutional codes generalize one dimensional (1D) convolutional codes and correspond to multidimensional systems widely studied in the systems theory literature. These codes have a practical potential in applications as they are very suitable to encode data recorded in n dimensions, e.g., pictures, videos, storage media, wireless applications, etc. However, in comparison to 1D convolutional codes, little is known in the area of nD convolutional codes and much more needs to be done to make it attractive for practical applications. From a mathematical point of view, these codes can be viewed as F[x_1,...,x_n]submodules of F[x_1,...,x_n]^n, where F is a finite field and F[x_1,...,x_n] is the ring of polynomials in several variables over F. In this talk we present a construction of an nD convolutional code based on superregular matrices with excellent errorcorrecting capabilities.
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Thu 8 Oct 2015, 3:30pm
Number Theory Seminar
room MATH 126


room MATH 126
Thu 8 Oct 2015, 3:30pm4:30pm
Abstract
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University of Auckland

Fri 9 Oct 2015, 3:00pm
SPECIAL
Institute of Applied Mathematics
C680 HSBC Hall, Robson Square Campus (downtown)

The dynamics of aircraft as ground vehicles

C680 HSBC Hall, Robson Square Campus (downtown)
Fri 9 Oct 2015, 3:00pm4:00pm
Abstract
Aircraft are designed to fly but also need to operate efficiently and safely as vehicles on the ground. The tricycle configuration of commercial aircraft presents challenges for manoeuvres, such as highspeed turns off a runway. The talk will present results of a collaboration with Airbus into the stability of ground manoeuvres, whose central idea is to employ tools from bifurcation analysis to relevant industryvalidated aircraft models. Compared to standard extensive numerical simulations, this approach has been demonstrated to have potential efficiency benefits during the design stage. In particular, it allows for detailed studies of the nature of instabilities that need to be avoided in practice. As an example, we show that the sudden loss of lateral stability of a midsize passenger aircraft turning on the ground is due to a canard phenomenon that arises due to a nonobvious slowfast splitting.
This is joint work with Etienne Coetzee (Airbus), James Rankin (INRIA France), Mathieu Desroches (INRIA France) and Mark Lowenberg (University of Bristol).
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University of Auckland

Fri 9 Oct 2015, 4:00pm
SPECIAL
Institute of Applied Mathematics
C680 HSBC Hall, Robson Square Campus (downtown)

Shaken but not stirred: using mathematics in earthquakes

C680 HSBC Hall, Robson Square Campus (downtown)
Fri 9 Oct 2015, 4:00pm5:00pm
Abstract
Predicting the behaviour of a structure when subjected to an earthquake is an important problem from Civil Engineering. Here, we consider a planar posttensioned frame, which can be modelled as a twodegreeoffreedom system that is equivalent to the analytical model of a tied rocking block on an elastic foundation. The frame remains structurally sound as long as the tilt angle of the frame does not exceed a certain maximal angle. A standard approach to studying the dynamics would be to run simulations, where it is assumed that the earthquake is a pure sine wave with varying frequency and amplitude. Such a bruteforce approach establishes a region in the frequencyamplitude plane for which the structural stability of the frame eventually fails. We propose a novel approach that calculates the failure region in a much more efficient way by determining the failure boundary directly. Our method is based on continuation of a suitable twopoint boundary value problem. Our computations demonstrate that the failure boundary is only piecewise smooth and the results highlight further interesting details of how the dynamics is organised in the frequencyamplitude plane.
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Note for Attendees