UBC

Mon 3 Oct 2011, 3:10pm
Algebraic Geometry Seminar
WMAX 110

Derived Moduli of Noncommutative Projective Schemes

WMAX 110
Mon 3 Oct 2011, 3:10pm4:10pm
Abstract
I will talk on joint work in progress with Behrang Noohi. We study the GIT problem given by the differential graded Lie algebra of Hochschild cochains of a finite graded algebra. This will lead to a definition of stability for noncommutative polarized projective schemes, and to the construction of quasiprojective moduli spaces for them. These moduli spaces are differential graded schemes. There may be new moduli spaces with symmetric obstruction theories coming out of this.
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UBC

Mon 3 Oct 2011, 4:00pm
Harmonic Analysis Seminar
MATX 1102

Buffon's needle probability for rational product Cantor sets, part 2

MATX 1102
Mon 3 Oct 2011, 4:00pm5:00pm
Abstract
This talk is a continuation of Matt Bond's talk from Sept 19: We investigate the probability that "Buffon's Needle" lands near a onedimensional selfsimilar product set in the complex plane, where the similarity maps have rational centers and identical scalings. If the factors A and B are defined by at most 6 similarities, then the likelihood that the needle intersects an e^{n}neighborhood of such a set is at most Cn^{p/\log\log n} for some p>0. (Joint work with M. Bond and A. Volberg.)
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UBC

Tue 4 Oct 2011, 12:30pm
SPECIAL
One Time Event
MATX 1102

Lunch Series for Teaching and Learning: The Course Archive Project, a Teaching Resource for Everyone

MATX 1102
Tue 4 Oct 2011, 12:30pm1:30pm
Details
Are you teaching a course for the first time and would like to see old midterm exams? Are you looking for old course materials from when you taught the same course a few years ago but can't find them? Would you like to have access to old homework assignments and worked solutions for the course you are teaching? Have you ever had to spend time collecting and compressing files to share course materials with your colleagues only to find out that your zip file is too big to send by email?
If any of these applies to you, then the Course Archive Project (CAP) is what you need. Now available on a secure department site, CAP allows you to store, search through, and easily access commonlyused course materials. We will give a short demo of the site and discuss effective ways to organize materials, including strategies to upload documents and enter information. Pizza and pops will be available.
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UBC

Tue 4 Oct 2011, 2:00pm
Stochastic Dynamics Working Group
IAM Lounge (LSK 306)

Noise driven synchronization of two conditional oscillators

IAM Lounge (LSK 306)
Tue 4 Oct 2011, 2:00pm3:00pm
Abstract
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UBC

Tue 4 Oct 2011, 2:00pm
Mathematical Education
MATX 1101

How to Prepare To Teach ?

MATX 1101
Tue 4 Oct 2011, 2:00pm3:00pm
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UBC

Tue 4 Oct 2011, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110 (PIMS)

Regularity for the optimal transport problem with Euclidean distance squared cost on the embedded sphere

WMAX 110 (PIMS)
Tue 4 Oct 2011, 3:30pm4:30pm
Abstract
We consider regularity for Monge solutions to the optimal transport problem when the initial and target measures are supported on the embedded sphere, and the cost function is the Euclidean distance squared. Gangbo and McCann have shown that when the initial and target measures are supported on boundaries of strictly convex domains in $\mathbb{R}^n$, there is a unique Kantorovich solution, but it can fail to be a Monge solution. By using PDE methods, in the case when we are dealing with the sphere with measures absolutely continuous with respect to surface measure, we present a condition on the densities of the measures to ensure that the solution given by Gangbo and McCann is indeed a Monge solution, and obtain higher regularity as well. This talk is based on joint work with Micah Warren.
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UBC

Tue 4 Oct 2011, 3:30pm
Algebraic Groups and Related Structures
MATX 1101

Galois Cohomology associated to Central Simple Algebras with Involution

MATX 1101
Tue 4 Oct 2011, 3:30pm4:30pm
Abstract
We present some of the Galois Cohomology set associated to central simple algebras with involutions.
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Eotvos University

Tue 4 Oct 2011, 4:00pm
Discrete Math Seminar
Matx 1102

Constant term identities for Laurent polynomials

Matx 1102
Tue 4 Oct 2011, 4:00pm5:00pm
Abstract
The computation of the joint probability distribution
of the eigenvalues of random matrices originating in
statistical mechanics often leads to the evaluation
of a Selbergtype integral which can be reduced to a
problem in algebraic combinatorics. Such a problem
was first identified by Dyson in 1962, leading to
far reaching generalizations. We present a simple
algebraic method which among others leads to a very
short proof of Andrews' qDyson conjecture as well as
to the solution of a longstanding open problem of
Forrester.
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UBC

Wed 5 Oct 2011, 2:00pm
Complex Fluids Seminar
Math Annex 1118

Vesicles and red blood cell clusters in Poiseuille flow

Math Annex 1118
Wed 5 Oct 2011, 2:00pm3:00pm
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Tokai University, Japan

Wed 5 Oct 2011, 3:00pm
Topology and related seminars
WMAX 216 (PIMS)

Minimal crossing diagram and Jones polynomial

WMAX 216 (PIMS)
Wed 5 Oct 2011, 3:00pm4:30pm
Abstract
It seemed quite difficult to determined crossing number of a link until Jones discovered a new polynomial invariant. Important results about crossing number of a link were shown after Kauffman gave a method for calculating Jones polynomial.
I will survey the relation between the reduced degree of Jones polynomial of a link and its crossing number and discuss Jones polynomial of a pretzel link. I will introduce an adequate diagram and discuss minimality of a diagram from the viewpoint of it. I will discuss the difference between the reduced degrees of Jones polynomials of pretzel links and their crossing numbers, and whether Jones polynomial is a complete invariant on alternating pretzel knots.
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Microsoft Research

Wed 5 Oct 2011, 3:00pm
Probability Seminar
MATH 126

Detection by Poisson Brownian motions

MATH 126
Wed 5 Oct 2011, 3:00pm4:00pm
Abstract
Consider a Poisson point process of intensity \lambda in R^d and let each
point move as an independent Brownian motion. Consider a target particle
that is initially placed at the origin at time 0 and can move according to
any continuous function. We say that the target is detected at time t if
there exists at least one point of the point process within distance 1 of
the target at time t. We show that if \lambda is sufficiently large, then
the target will eventually be detected even if its motion can depend on the
past, present and future positions of the points. In the proof we use
coupling and multiscale analysis to show that some good events percolate in
space and time.
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Bernhard Konrad and Robert Klinzmann
UBC

Thu 6 Oct 2011, 12:30pm
Graduate Student Seminar
LSK 460

Graduate Student Colloquium

LSK 460
Thu 6 Oct 2011, 12:30pm2:00pm
Abstract
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UBC

Thu 6 Oct 2011, 3:00pm
Number Theory Seminar
Room WMAX 216 (PIMS  UBC Campus)

Roots of unity, torsion on fibers, and preperiodic points for families of rational maps

Room WMAX 216 (PIMS  UBC Campus)
Thu 6 Oct 2011, 3:00pm3:50pm
Abstract
In early 1960's, Lang proved that if for a given polynomial G(X,Y) with complex coefficients, there exist infinitely many pairs (x,y) where both x and y are roots of unity such that G(x,y) = 0, then essentially G(X,Y) = X^mY^n  c, for some integers m and n, and a root of unity c. In 2009, Masser and Zannier proved a result (similar in the spirit of Lang's result) for torsion points on a family of elliptic curves. In our talk we explain how both results come from the same general principle in arithmetic geometry, and at the same time we present a partial result to a more general conjecture which subsumes both Lang and MasserZannier theorems.
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UBC

Thu 6 Oct 2011, 4:10pm
Number Theory Seminar
Room WMAX 216 (PIMS  UBC Campus)

Galois representations and deformations

Room WMAX 216 (PIMS  UBC Campus)
Thu 6 Oct 2011, 4:10pm5:00pm
Abstract
Representations of the Galois group of the rationals abound in nature and are important in understanding the structure of the Galois group of the rational numbers. Iwasawa theory studies certain arithmetic modules arising from such representations. Hida theory provides a technique to package some of these representations in a family and study them simultaneously. In this talk I will demonstrate the usefulness of this technique in obtaining information on certain fundamental invariants arising in Iwasawa theory for such families and studying their variation within a family.
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UBC

Fri 7 Oct 2011, 3:00pm
Department Colloquium
MATX 1100

Scattering and blowup of Schroedinger maps.

MATX 1100
Fri 7 Oct 2011, 3:00pm4:00pm
Abstract
The Schroedinger map PDE is a simple, natural, geometric (hence nonlinear) generalization of the classical (linear) Schroedinger equation of quantum mechanics. Remarkably, it is also a basic model in ferromagnetism.
Without assuming a PDE background, I will discuss the key questions one asks about the qualitative properties of solutions of such equations  which concern singularity (non)formation and asymptotic behaviour  leading up to results of mine (joint with Eva Koo, and with Kenji Nakanishi and TaiPeng Tsai) and others which address these questions, and along the way touching on recent developments in the field of nonlinear dispersive equations more generally.
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Fri 7 Oct 2011, 4:00pm
SPECIAL
One Time Event
Graduate Student Center, Room 200

Doctoral Exam

Graduate Student Center, Room 200
Fri 7 Oct 2011, 4:00pm7:00pm
Details
An algebraic view of discrete geometry
This thesis includes three papers and one expository chapter as background for one of the papers. They have in common that they combine algebra with discrete geometry, mostly by using algebraic tools to prove statements from discrete geometry. Algebraic curves and number theory also recur throughout the proofs and results.
In the first paper, we prove that an infinite set of points in the real plane such that all pairwise distances are rational cannot be contained in an algebraic curve, except if that curve is a line or a circle, in which case at most 4 resp. 3 points of the set can be outside the line or circle. In the proof we use the classication of curves by their genus, and Faltings' Theorem.
In the second paper, we prove a bound on the number of unit distances that can occur between points of a finite set in the real plane, under the restriction that the line segments corresponding to these distances make a rational angle with the horizontal axis. In the proof we use graph theory and an algebraic theorem of Mann.
In third paper, we give an upper bound on the length of a simultaneous arithmetic progression (a twodimensional generalization of an arithmetic progression) on an elliptic curve, as well as for more general curves. We give a simple proof using a theorem of Jarnik, and another proof using the Crossing Inequality and some bounds from elementary algebraic geometry, which gives better explicit bounds.
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Mathematics Department, University of Toronto

Tue 11 Oct 2011, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 110

Inverse Problems with (Minimal) Interior Measurements

WMAX 110
Tue 11 Oct 2011, 12:30pm1:30pm
Abstract
A new class of Inverse Problems seeks to significantly improve both the quantitative accuracy and the resolution of traditional inverse boundary value problems by using data which can be determined in the interior of the object. I will briefly explain how such measurements of current density can be obtained
using Magnetic Resonance Imaging in a nonstandard way. Imaging electric conductivity then leads to beautiful mathematics involving minimal surfaces in a conformal metric determined by the measured data, and a corresponding variable coefficient least gradient problem.
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UBC

Tue 11 Oct 2011, 2:00pm
Stochastic Dynamics Working Group
IAM Lounge (LSK 306)

Noiseinduced coherence and network oscillations in a reduced bursting model

IAM Lounge (LSK 306)
Tue 11 Oct 2011, 2:00pm3:00pm
Abstract
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UBC

Tue 11 Oct 2011, 2:30pm
Symmetries and Differential Equations Seminar
Math Annex 1118

Some recent developments in symmetries and conservation laws for PDEs. Part I

Math Annex 1118
Tue 11 Oct 2011, 2:30pm3:30pm
Abstract
This series of lectures will be concerned with some recent developments on how to find and use symmetries for PDEs; how to find and use conservation laws for PDEs; connections between symmetries and conservation laws for PDEs. Much of the material appears in Applications of Symmetry Methods to Partial Differential Equations (Bluman/Cheviakov/Anco), Springer (2010). Background material appears in Symmetry and Integration Methods for Differential Equations (Bluman/Cheviakov), Springer (2002) on Lie groups of transformations and their applications to solving ODEs, the construction of conservation laws (integrating factors) for ODEs, and finding invariant solutions of PDEs. Both of these books are available online through the UBC library.
No background beyond undergraduate mathematics is necessary as a prerequisite for this series. These lectures were presented at Moscow State University in June 2011 and will flow as follows.
 General introduction giving an extensive overview of topics to be covered.
 Review of Lie’s work on point symmetries and invariant solutions for PDEs.
 Local symmetries—point, contact, higherorder. How to find them for a given PDE system.
 Construction of conservation laws—direct method to find them, connections with Noether’s theorem.
 Use of symmetries to construct new conservation laws from known CLs.
 Invertible mappings of nonlinear PDEs to linear PDEs through symmetry analysis and through conservation law multiplier analysis.
 Invertible mappings of linear PDEs with variable coefficients to linear PDEs with constant coefficients.
 The nonclassical method to find solutions of PDEs.
 How to systematically find trees of equivalent but nonlocally related PDE systems for a given PDE system.
 How to systematically find nonlocal symmetries and nonlocal conservation laws for a given PDE system.
 The multidimensional situationgauge constraints.
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Cornell University

Tue 11 Oct 2011, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110 (PIMS)

Harnack Inequalities, Heat Kernel Estimates and the Ricci flow

WMAX 110 (PIMS)
Tue 11 Oct 2011, 3:30pm4:30pm
Abstract
In this talk, we will discuss about LiYauHamilton type differential Harnack inequalities, heat kernel estimates and their applications to study type I ancient solutions of the Ricci flow. Some of this is joint work with Q. S. Zhang.
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UBC

Tue 11 Oct 2011, 4:00pm
Algebraic Groups and Related Structures
Math 126

A Derived Equivalence for some Projective Homogeneous Varieties

Math 126
Tue 11 Oct 2011, 4:00pm5:00pm
Abstract
We produce a derived equivalence for some examples of Projective Homogeneous Varieties (SeveriBrauer Varieties, Quadrics, and Involution Varieties) by constructing a Tilting Bundle in each case.
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UBC

Tue 11 Oct 2011, 4:00pm
Discrete Math Seminar
Matx 1102

Decoding binary linear codes through linear programming

Matx 1102
Tue 11 Oct 2011, 4:00pm5:00am
Abstract
A fairly recent thesis by John Feldman (MIT 2002) presents
maximumlikelihood decoding of binary linear codes as an integer
linear program. For LDPC and turbolike codes, certain relaxations
allow for a good decoding algorithm. Since then, there have been a
number of results on improved versions of the LP decoder, suggesting
that it may become a more useful paradigm than more commonly used
messagepassing algorithms.
Following a 2008 by Navin Kashyap (Queen's), we discuss an old but
previously neglected connection between codes and matroids. We give a
survey of results obtained by matroid decomposition techniques, and
their implications for LP decoding.
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University of Michigan

Wed 12 Oct 2011, 3:00pm
Topology and related seminars
WMAX 216 (PIMS)

Bounds on eigenvalues of the Laplacian for certain hyperbolic 3manifolds

WMAX 216 (PIMS)
Wed 12 Oct 2011, 3:00pm4:00pm
Abstract
In this talk I will prove that in the presence of bounds for the rank of the fundamental group and the injectivity radius, the kth eigenvalue of the Laplacian of a closed hyperbolic 3manifold M is bounded from above and below by a multiple of vol(M)^{2}.
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ENS Paris

Wed 12 Oct 2011, 3:00pm
Probability Seminar
MATH 126

Strong convergence of partial match queries in random quadtrees

MATH 126
Wed 12 Oct 2011, 3:00pm4:00pm
Abstract
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UBC

Fri 14 Oct 2011, 3:00pm
Department Colloquium
MATX 1100

Stochastic dynamics and HIV infection

MATX 1100
Fri 14 Oct 2011, 3:00pm4:00pm
Abstract
I will present recent work on modelling treated HIV infection using branching process models. We use simulations and novel numerical methods to calculate probability distribution functions for virus and cell concentrations. An overview of relevant HIV biology will be included in the talk. Most of this work is joint with Jessica Conway (UBC).
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UC Berkeley

Mon 17 Oct 2011, 3:10pm
Algebraic Geometry Seminar
WMAX 110

Twisted strong Macdonald theorems

WMAX 110
Mon 17 Oct 2011, 3:10pm4:10pm
Abstract
Let L be a reductive Lie algebra. The strong Macdonald theorems of Fishel, Grojnowski, and Teleman state that the cohomology algebras of L[z]/z^N and L[z,s] (where s is an odd variable) are free skewcommutative algebras with generators in certain degrees. The theorems were originally conjectured by Hanlon and Feigin as Lie algebra cohomology extensions of Macdonald's constant term identity in algebraic combinatorics. The proof uses ideas from the Kahler geometry of the loop Grassmannian.
I will explain how to extend Fishel, Grojnowski, and Teleman's ideas to generalized flag varieties of (twisted) loop groups, and consequently get strong Macdonald theorems for p[s] and p/z^N p when p is a parahoric. When p has a nontrivial parabolic component the cohomology of p/z^N p is no longer free, as it contains a factor which is isomorphic to the cohomology algebra of the flag variety of the corresponding parabolic.
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Karlsruhe Institute of Technology, Germany

Tue 18 Oct 2011, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 110

A Fully Automatic hpAdaptive Refinement Strategy

WMAX 110
Tue 18 Oct 2011, 12:30pm1:30pm
Abstract
The finite element method is a widely accepted tool for the numerical solution of partial differential equations. Nowadays a posteriori error estimation is an expected and assessed feature in scientific computing. It is used for adaptively creating approximation spaces and to assess the accuracy of numerical solutions. The performance of the method can be improved by mesh refinement (hrefinement) or the use of higher oder ansatz spaces (prefinement). Taking a combination of both (hprefinement) can lead to exponentially fast convergence with respect to the number of degrees of freedom. Especially for hpFEM there have been proposed several strategies for adaptively creating problemdependent meshes, e.g. estimating the analyticity of the solution, solving local boundary value problems and minimize the global interpolation error can be minimized.
In this talk we present a fully automatic hpadaptive refinement strategy, which is based on the solution of local boundary value problems. We present the strategy for the Poisson and the Maxwell boundary value problem and show convergence of the algorithm. The talk is concluded by some numerical examples.
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UBC

Tue 18 Oct 2011, 2:00pm
Mathematical Education
MATX 1101

What to Expect from the Students ?

MATX 1101
Tue 18 Oct 2011, 2:00pm3:00pm
Abstract
In this talk, we present the 4th chapter of Bain's book. The problematic is to determine what college teachers should expect from their students. More info under : wiki.ubc.ca/Sandbox:MathTeachingSeminar
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UBC

Tue 18 Oct 2011, 2:00pm
Stochastic Dynamics Working Group
IAM Lounge (LSK 306)

Noiseinduced coherence and network oscillations in a reduced bursting model (continued).

IAM Lounge (LSK 306)
Tue 18 Oct 2011, 2:00pm3:00pm
Abstract
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UBC

Tue 18 Oct 2011, 2:30pm
Symmetries and Differential Equations Seminar
Math Annex 1118

Some recent developments in symmetries and conservation laws for PDEs. Part II: Local symmetries

Math Annex 1118
Tue 18 Oct 2011, 2:30pm3:30pm
Abstract
In the second part of this series, we will consider the following topics.
1. Review of Lie’s work on point symmetries and the construction of invariant solutions for PDEs.
2.Local symmetries—point, contact, higherorder. How to find them for a given PDE system.
It is not necessary to have attended the first part last week to follow along.
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UBC

Tue 18 Oct 2011, 3:00pm
One Time Event
MATH 103

TAAP Seminar: Effective Tutoring

MATH 103
Tue 18 Oct 2011, 3:00pm4:00pm
Details
Tutoring is one of the most common TA assignments for new graduate students, and is a skill all TAs can benefit from improving. But what makes a tutor effective? What are some good practices to use while tutoring, and do we follow them? In this session, we will examine questions such as these in a reflective process and discussion in an attempt to better our abilities as tutors.
This is the first talk in the TA Accreditation Program Seminar Series; more information can be found at
http://www.math.ubc.ca/~fsl/TAAP%20Seminar%20Series.html
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UBC

Tue 18 Oct 2011, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110 (PIMS)

Uniqueness of the compactly supported weak solutions of the relativistic VlasovDarwin system

WMAX 110 (PIMS)
Tue 18 Oct 2011, 3:30pm4:30pm
Abstract
The relativistic VlasovDarwin (RVD) system is a kinetic model that describes the evolution of a collisionless plasma whose particles interact through the selfinduced electromagnetic ﬁeld. In contrast with the VlasovMaxwell system, the particle interaction is assumed to be a loworder relativistic correction (i.e., the Darwin approximation) to the full Maxwell case. A consequence of this assumption is that instead of the less tractable hyperbolic Maxwell equations, the resulting system has elliptic features even though there is a fully coupled magnetic ﬁeld. We use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the RVD system. Our proof extends the method used by Loeper in [J. Math. Pures Appl., 86 (2006), pp. 6879 ] to obtain uniqueness results for the VlasovPoisson system. This is a joint work with Martial Agueh.
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Institut de Mathematiques de Jussieu

Tue 18 Oct 2011, 4:00pm
Algebraic Groups and Related Structures
Math 126

SK_1 and SK_2 of central simple algebras

Math 126
Tue 18 Oct 2011, 4:00pm5:00pm
Abstract
We discuss several constructions of homomorphisms from SK1 and SK2 of central simple algebras to subquotients of Galois cohomology groups.
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Wed 19 Oct 2011, 2:00pm
Complex Fluids Seminar
MATX 1118

From Displacement to Mixing in a Slightly Inclined Duct

MATX 1118
Wed 19 Oct 2011, 2:00pm3:00pm
Abstract
This work studies buoyant displacement flows with two miscible fluids in pipes and 2D channels that are inclined at angles close to horizontal. Detailed experimental, analytical and computational approaches are employed in an integrated fashion. The displacements are at low Atwood numbers and high Peclet numbers, so that miscibility effects are mostly observable after instability and via dispersive mixing. For isoviscous Newtonian displacements, studying the front velocity variation as a function of the imposed flow velocity allows us to identify 3 distinct flow regimes: an exchange flow dominated regime characterized by KelvinHelmholtzlike instabilities, a laminarised viscous displacement regime with the front velocity linearly increasing with the mean imposed flow rate, and a fully mixed displacement regime. The transition between the first and the second regimes is found to be marked by a stationary layer of displaced fluid. In the stationary layer the displaced fluid moves in countercurrent motion with zero net volumetric flux. Different lubrication/thinfilm models have been used to predict the flow behaviour. We also succeed in characterising displacements as viscous or inertial, according to the absence/presence of interfacial instability and mixing. This dual characterisation allows us to define 56 distinct flow regimes, which we show collapse onto regions in a twodimensional parameter plane. In each regime we have been able to offer a leading order approximation to the leading front velocity. A weighted residual method has also been used to include the effect of inertia within the lubrication modelling approach, which allows us to predict longwave instabilities.
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UBC

Wed 19 Oct 2011, 3:00pm
Topology and related seminars
WMAX 216 (PIMS)

Abstract Commensurators of the Johnson Filtration

WMAX 216 (PIMS)
Wed 19 Oct 2011, 3:00pm4:00pm
Abstract
The Torelli group is the subgroup of the mapping class group which acts trivially on the homology of the surface. It is the first term of the Johnson filtration, the sequence of subgroups which act trivially on the surface group modulo some term of its lower central series. We prove that the abstract commensurator of each of these subgroups is the full mapping class group. This is joint work with Martin Bridson and Juan Souto.
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UBC

Wed 19 Oct 2011, 3:00pm
Probability Seminar
MATH 126

Nonuniqueness for parabolic stochastic PDE

MATH 126
Wed 19 Oct 2011, 3:00pm4:00pm
Abstract
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Eugene Barsky (UBC Library) and Simon Rose
UBC

Thu 20 Oct 2011, 12:30pm
Graduate Student Seminar
LSK 460

Graduate Student Colloquium

LSK 460
Thu 20 Oct 2011, 12:30pm2:00pm
Abstract
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UBC

Thu 20 Oct 2011, 3:00pm
Number Theory Seminar
Room ASB 10900 (IRMACS  SFU Campus)

The iterated Carmichael lambda function

Room ASB 10900 (IRMACS  SFU Campus)
Thu 20 Oct 2011, 3:00pm3:50pm
Abstract
The Carmichael lambda function \lambda(n) is defined to be the smallest positive integer m such that a^m \equiv 1 \pmod{n} for all (a,n)=1. \lambda_k(n) is defined to be the k th iterate of \lambda(n). We will discuss some previous known results about k=1,2 as well as sketch a proof of a normal order for n/\lambda_k(n) for all k.
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UBC

Thu 20 Oct 2011, 4:10pm
Number Theory Seminar
Room ASB 10900 (IRMACS  SFU Campus)

The generalized Fermat equation

Room ASB 10900 (IRMACS  SFU Campus)
Thu 20 Oct 2011, 4:10pm5:00pm
Abstract
We will survey results on, and techniques for, the generalized Fermat equation x^p + y^q = z^r, where p, q, and r satisfy 1/p + 1/q + 1/r < 1. This is joint work with Imin Chen, Sander Dahmen, and Soroosh Yazdani.
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UBC

Fri 21 Oct 2011, 3:00pm
Department Colloquium
MATX 1100

hpAdaptive finite element methods

MATX 1100
Fri 21 Oct 2011, 3:00pm4:00pm
Abstract
We develop hpadaptive finite element schemes for the numerical approximation of linear secondorder elliptic boundaryvalue problems. We begin by reviewing some classical results from the late eighties. Then we show that on geometrically and anisotropically refined meshes in three dimensional polyhedral domains, hpmethods achieve exponential rates of convergence in the number of degrees of freedom, thereby proving a longstanding conjecture in the theory of hpfinite element methods. In the last part of the talk, we discuss some recent results related to fully automated hpadaptivity and illustrate numerically that our proposed adaptive refinement strategies lead to exponential rates of convergence. The talk includes work done with my former Ph.D. student Liang Zhu.
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University of Ottawa

Mon 24 Oct 2011, 3:10pm
Algebraic Geometry Seminar
WMAX 110

Equivariant pretheories and invariants of torsors

WMAX 110
Mon 24 Oct 2011, 3:10pm4:10pm
Abstract
We will introduce and study the notion of an equivariant pretheory. Basic examples include equivariant Chow groups, equivariant Ktheory and equivariant algebraic cobordism. As an application we generalize the theorem of KarpenkoMerkurjev on Gtorsors and rational cycles; to every Gtorsor E and a Gequivariant pretheory we associate a graded ring which serves as an invariant of E. In the case of Chow groups this ring encodes the information concerning the motivic Jinvariant of E and in the case of Grothendieck's K_0  indexes of the respective Tits algebras.
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UBC

Mon 24 Oct 2011, 4:00pm
Harmonic Analysis Seminar
MATX 1102

An exposition of the bilinear approach to the Falconer distance problem

MATX 1102
Mon 24 Oct 2011, 4:00pm5:00pm
Abstract
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Mathematics Department, UBC

Tue 25 Oct 2011, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 110

Modelling Hydraulic Fractures using a Boundary Element Method (BEM) and the Extended Finite Element Method (XFEM)

WMAX 110
Tue 25 Oct 2011, 12:30pm1:30pm
Abstract
This talk presents the development of BEM and XFEM frameworks for modelling hydraulic fractures, which arise in a wide range of geoengineering applications. The mathematical formulation of the problem involves a system of coupled nonlinear partial differential equations with a moving boundary, arising from the coupling between the fluid flow in the evolving fracture and the deformation of the parent material. Each of the discussed approaches has its own advantages: the BEM can efficiently simulate a propagating crack in linear homogeneous domains, while the XFEM is able to model complex settings such as multiple fractures in porous and layered rocks or plastic material deformation. The first part of the talk presents a BEM algorithm coupled with the finitevolume fluid flow model. An example of a nearsurface radial crack is investigated, for which the required Green’s functions, that represent the crack as a distribution of material discontinuities, are derived. A comparison of the numerical results generated by this numerical model with data from laboratory experiments identifies particular physical phenomena that have to be accounted for in the mathematical formulation for accurately capturing the complex fracture propagation process.
In the second part of the talk, an XFEM approach to this problem is discussed. The development includes derivation of shape functions that enrich the underlying finite element formulation by representing discontinuities and singularities associated with the hydraulically driven crack. An example is presented in which a coupled XFEM model simulates a crack driven by a viscous fluid through a layered material.
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UBC

Tue 25 Oct 2011, 2:30pm
Symmetries and Differential Equations Seminar
Math Annex 1118

Some recent developments in symmetries and conservation laws for PDEs: Part III: conservation laws

Math Annex 1118
Tue 25 Oct 2011, 2:30pm3:30pm
Abstract
It will be shown how to find directly all conservation laws for a given PDE system. A consequence is the extension of the classical Noether theorem to nonvariational systems. Connections to Noether's theorem and connections between symmetries and conservation laws will be discussed.
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Universite Libre de Bruxelles

Tue 25 Oct 2011, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
PIMS (WMAX 110)

A rough guide to reduction methods for strongly coupled elliptic systems

PIMS (WMAX 110)
Tue 25 Oct 2011, 3:30pm4:30pm
Abstract
In this talk, I will first recall the notions of superlinearity and subcriticality for strongly coupled elliptic systems. I will present various functional frameworks and their limitations. I will then discuss two reduction methods that allow to get rid of the indefiniteness of the energy functional. These reductions to a single equation are powerful to treat basic questions for superlinear systems. For instance, I will discuss the notion of ground states, in bounded domains and in R^N, show how to get the information on the symmetry and the sign of the ground states through the definition of a convenient Nehari manifold or constrained minimization problem. I will also discuss the classical question of existence of infinitely many critical points of perturbed indefinite symmetric functionals and how one of the reduction method allow to use the notion of Morse index. Finally, I will show how these reduction methods can help in proving partial symmetry and symmetry breaking. As a paradigm, I will illustrate the ideas on the LaneEmden system with Hénon weights.
References : B.Ramos ANIHP 2009  B.dos Santos JDE 2010  B.Ramosdos Santos Trans. AMS 2012 & preprint.
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University of Ottawa

Tue 25 Oct 2011, 4:00pm
Algebraic Groups and Related Structures
Math 126

Basic polynomial invariants, fundamental representations and the Chern class map

Math 126
Tue 25 Oct 2011, 4:00pm5:00pm
Abstract
Consider a crystallographic root system together with its Weyl group W acting on the weight lattice M. Let Z[M]^W and S^*(M)^W be the Winvariant subrings of the integral group ring Z[M] and the symmetric algebra S^*(M) respectively. A celebrated theorem of Chevalley says that Z[M]^W is a polynomial ring over Z in classes of fundamental representations w_1,...,w_n and S^*(M)^{W} over rational numbers is a polynomial ring in basic polynomial invariants q_1,...,q_n, where n is the rank. In this talk we will establish and investigate the relationship between w_i's and q_i's over the integers.
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Dartmouth

Wed 26 Oct 2011, 3:00pm
Probability Seminar
MATH 126

EdgeCover by Random Walk

MATH 126
Wed 26 Oct 2011, 3:00pm4:00pm
Abstract
We show that the time for a random walk to cover all
the edges of a graph with m edges is bounded by 2m^2;
if all edges must be covered in both directions, 3m^2.
These results generalize to graphs with edgelengths
(even with infinitely many vertices) and to Brownian
motion.
Joint work with Agelos Georgakopoulos.
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The University of Texas at Austin

Wed 26 Oct 2011, 3:00pm
Topology and related seminars
WMAX 216 (PIMS)

The density conjecture and a short survey on Kleinian groups

WMAX 216 (PIMS)
Wed 26 Oct 2011, 3:00pm4:00pm
Abstract
I will try to give a short survey of some of the major results in the study of Kleinian groups in recent years. We will concentrate on the proof of the Bers' Density Conjecture and I will try to give an outline of the proof based on a joint work with J. Souto.
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UBC

Wed 26 Oct 2011, 4:00pm
Undergraduate Colloquium
MATH 225

Deforming complicated plane curves to simple ones

MATH 225
Wed 26 Oct 2011, 4:00pm5:00pm
Abstract
The curve shortening flow has been much studied in differential geometry over the past 25 years. In this talk we will introduce the problem,
which involves the flow of a plane curve in the normal direction with speed equal to the curvature. It was shown by M. Grayson in 1987 that
the flow converts an arbitrary "nice" closed curve into a circle! Over the next 10 years Grayson's proof was clarified and simplified by
R. Hamilton and G. Huisken.
We will describe the main ingredient in these simplifications, which involves finding a geometric quantity that is "improved" under the flow
and prevents the formation of certain types of singularities. Although this is a hard theorem, its proof uses only two variable calculus
together with a lot of cleverness. The curve shortening flow is the simplest of several geometric flows whose study is a topic of current
research interest in differential geometry. These flows have certain features and methods in common, particularly with regard to the
formation of singularities.
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Dartmouth

Fri 28 Oct 2011, 3:00pm
Department Colloquium
MATX 1100

Scheduling, Percolation, and the Worm Order

MATX 1100
Fri 28 Oct 2011, 3:00pm4:00pm
Abstract
We show that in any submodular system there is a maximal chain that is minimal, in a very strong sense, among all paths from 0 to 1. The consequence is a set of general conditions under which optimal
scheduling can be done without backward steps. Among the applications are a fast algorithm for scheduling multiple processes without overusing a resource; a theorem about searching for a lost child in a forest; and a closedform expression for the probability of escaping from the origin in a form of coordinate percolation. Joint work in part with Graham Brightwell (LSE) and in part with Lizz Moseman (NIST).
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Institut de Mathematiques de Jussieu

Mon 31 Oct 2011, 3:10pm
Algebraic Geometry Seminar
WMAX 110

Somekawa's Kgroups and Voevodsky's Hom groups

WMAX 110
Mon 31 Oct 2011, 3:10pm4:10pm
Abstract
We construct an isomorphism from Somekawa's Kgroup associated to a finite collection of semiabelian varieties (or more general sheaves) over a perfect field to a corresponding Hom group in Voevodsky's triangulated category of effective motivic complexes.
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Note for Attendees
Refreshments will be served between the two talks.