##### Events
Behrang Noohi
King's college
Mon 4 Jan 2010, 3:10pm
Algebraic Geometry Seminar
Lie theory of 2-group
Mon 4 Jan 2010, 3:10pm-4:30pm

#### Abstract

In classical Lie theory a homomorphism of Lie groups f : H--> G, with H simply connected, is uniquely given by its effect on
the Lie algebras Lie(f) : Lie(H) --> Lie(G). When f : H --> G is a weak
morphism of Lie 2-groups, with H 2-connected (i.e., \pi_iH vanish
for i=0,1,2), we prove that f is uniquely given by Lie(f), where
Lie(f) : Lie(H) --> Lie(G) is the induced morphism in the derived
category of 2-terms diff. graded Lie algebras. We also exhibit a
functorial construction of the 2-connected cover H<2> of a Lie
2-group H.
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Mark Hamilton
Tokyo University
Wed 6 Jan 2010, 1:30pm
PIMS Seminars and PDF Colloquiums
WMAX 216
Geometric quantization of integrable systems
WMAX 216
Wed 6 Jan 2010, 1:30pm-2:30pm

#### Abstract

The theory of geometric quantization is one way of producing a "quantum system" from a "classical system," and has been studied a great deal over the past several decades. It also has surprising ties to representation theory. However, despite this, there still does not exist a satisfactory theory of quantization for systems with singularities.

Geometric quantization requires the choice of a polarization; when using a real polarization to quantize a regular enough manifold, a result of Sniatycki says that the quantization can be found by counting certain objects, called Bohr-Sommerfeld fibres. However, there are many types of systems to which this result does not apply. One such type is the class of completely integrable systems, which are examples coming from mechanics that have many nice properties, but which are nontheless too singular for Sniatycki's theorem to apply.

In this talk we will explore one approach to the quantization of integrable systems, and show a Sniatycki-type relationship to Bohr-Sommerfeld fibres. However, some surprising features appear, including infinite-dimensional contributions and strong dependence on the polarization.

I will give at least a brief explanation of both geometric quantization and integrable systems, and hope to make the talk accessible to a general differential geometric audience.

This is joint work with Eva Miranda.

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Sat 9 Jan 2010, 9:00am SPECIAL
Math 100
Qualifying Exams
Math 100
Sat 9 Jan 2010, 9:00am-4:00pm
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Petroleum Resources Division, Commonwealth Scientific and Industrial Research Organisation, Australia
Mon 11 Jan 2010, 3:00pm
Institute of Applied Mathematics
Klinck 301
Modelling the Growth of Large Mafic Sills and Laccoliths Using Hydraulic Fracturing Models
Klinck 301
Mon 11 Jan 2010, 3:00pm-4:00pm

#### Abstract

When molten rock rises from deep in the earth, invades the earth's crust and cools, this forms new rock structures called igneous intrusions. These widespread features are often associated with the formation of mineral deposits, and there is hope that understanding their emplacement mechanisms will benefit engineering applications by giving insight into how rock behaves at large scale. Particular attention is given here to so-called large mafic sills and laccoliths, which can be proposed as natural analogues to hydraulic fractures that grow relatively close to a free surface.

The use of elastic plate theory to model the growth of shallow igneous intrusions has been debated for over 40 years. Investigation has typically resulted in the elastic plate model being heavily questioned or abandoned because it fails to predict the characteristic flat-topped, steep-sided thickness profiles of laccoliths or the strikingly uniform thickness of large mafic sills. However, upon coupling elastic plate theory with a fracture mechanics based propagation criterion and, crucially, the driving force due to the weight of the magma, the predicted thickness profiles and thickness to length relationships for both laccoliths and large mafic sills are consistent with an extensive collection of field data. Furthermore, analysis of the large time asymptotics predict that large mafic sills will attain a thickness that is not only spatially uniform, but also constant in time, depending only on physical properties of the magma and host rock. While a number of questions remain open, it is an exciting prospect that a single, basic model could provide a unifying framework to understanding what controls the first-order behaviour of the growth of laccoliths and large mafic sills.

This talk will present work that results from collaboration with Professor Alexander Cruden of the University of Toronto, Department of Geology.

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Hsian-Hua Tseng
Ohio State University
Mon 11 Jan 2010, 3:00pm
Algebraic Geometry Seminar
PIMS 110
On the decomposition of etale gerbes
PIMS 110
Mon 11 Jan 2010, 3:00pm-4:00pm

#### Abstract

Let G be a finite group. A G-gerbe over a space X may be
intuitively thought of as a fiber bundle over X with fibers being the
classifying space (stack) BG. In particular BG itself is the G-gerbe
over a point. A more interesting class of examples consist of G-gerbes
over BQ, which are equivalent to extensions of the finite group Q by G.
Considerations from physics have led to conjectures asserting that
the geometry of a G-gerbe Y over X is equivalent to certain "twisted"
geometry of a "dual" space Y'. A lot of progresses have be made recently
towards proving these conjectures in general. In this talk we'll try to
explain these conjectures in the elementary concrete examples of G-gerbes
over a point or BQ.
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Brown University
Mon 11 Jan 2010, 4:00pm SPECIAL
Department Colloquium
MATX 1100
Analytic functions from hyperbolic manifolds
MATX 1100
Mon 11 Jan 2010, 4:00pm-5:00pm

#### Abstract

At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps."  These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known
about their behavior.  The ideas involved form a mix of geometry, algebra, and analysis.
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Mathematics UBC
Tue 12 Jan 2010, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 216
A hybrid asymptotic-Hermite Cubic scheme for solving Plane Strain Hydraulic Fracture Problems
WMAX 216
Tue 12 Jan 2010, 12:30pm-2:00pm

#### Abstract

In this talk I will describe the coupled integro-partial differential equations that model the evolution of a fluid-driven fracture propagating in a state of plain strain. I will discuss the use of the Mellin Transform and matched asymptotics to establish the asymptotic behavior of the solution in the vicinity of the fracture tip for a number of regimes of propagation. I also describe a novel cubic Hermite collocation scheme to solve these coupled equations. This algorithm involves special blended cubic Hermite-power law basis functions, with an arbitrary index 0<1, which are developed to treat the singular behavior of the solution that typically occurs at the tips of a hydraulic fracture. I also discuss the implementation of blended infinite elements to model semi-infinite crack problems. The cubic Hermite collocation algorithm is used to solve a number of different test problems and the results are compared to published similarity, asymptotic, and numerical solutions.
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Omer Dushek
Oxford University
Tue 12 Jan 2010, 2:00pm
Mathematical Biology Seminar
WMAX 110
TBA
WMAX 110
Tue 12 Jan 2010, 2:00pm-3:00pm

#### Abstract

TBA (see Mathematical Biology Seminar page for update).
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MIT
Tue 12 Jan 2010, 3:00pm SPECIAL
Topology and related seminars
MATX 1102
On the relationship between EO_n and TAF
MATX 1102
Tue 12 Jan 2010, 3:00pm-4:00pm

#### Abstract

It is well know that for p = 2, the K(1)-localization of KO is EO_1,
and for p = 2; 3, the K(2)-localization of TMF is
EO_2. When does the K(n)-localization of TAF contain a factor of EO_n?
We will provide a complete answer.  This is joint work with Mike
Hopkins.
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UBC
Tue 12 Jan 2010, 3:30pm
Algebraic Groups and Related Structures
MATH 125
Essential dimension of PGLn
MATH 125
Tue 12 Jan 2010, 3:30pm-4:30pm

#### Abstract

The essential dimension of the projective linear group PGLn is a measure of
complexity of PGLn-torsors or, alternatively, central simple algebras. It was first raised by Procesi in the 1960 and the exact value is still
mostly unknown. We will discuss some recent developments which have led to both new lower
and upper bounds. These are obtained in part by studying classes of algebras with additional
structure, e.g. crossed-products or simple algebras split by a distinguished field extension.

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Richard Kent
Brown University
Tue 12 Jan 2010, 4:00pm SPECIAL
Topology and related seminars
MATX 1102
Slicing, skinning, and grafting
MATX 1102
Tue 12 Jan 2010, 4:00pm-5:00pm

#### Abstract

Abstract:  A Bers slice is a naturally embedded copy of the Teichmuller
space in the SL(2,C) character variety of a surface.  We prove that Bers
slices are never algebraic.  A corollary is that Thurston's skinning map
is never constant.  The proof involves the theory of complex projective
structures and a little algebraic geometry.

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Wed 13 Jan 2010, 3:00pm SPECIAL
Department Colloquium
PIMS WMAX 110
Statistics of quadratic congruences and generalizations
PIMS WMAX 110
Wed 13 Jan 2010, 3:00pm-4:00pm

#### Abstract

We present the uniform distribution of roots of quadratic congruences on the unit circle. Several proofs have been rediscovered over the years. I will review some of the very different methods involved -- ergodic theory, exponential sums, automorphic forms. It constitutes an excellent introduction to the more delicate Linnik problems. I will then proceed to describe new generalizations. These have far reaching applications to arithmetic geometry and independence of Heegner points on rational elliptic curves.
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Seoul National University
Wed 13 Jan 2010, 4:00pm
Probability Seminar
WMAX 216
Behavior of Heat Kernel for Jump Process
WMAX 216
Wed 13 Jan 2010, 4:00pm-5:00pm

#### Abstract

In this talk, we discuss the behavior of heat kernel for symmetric jump-type process with jumping kernels comparable to radially symmetric function on the spaces. Parabolic Harnack principle and sharp two-sided heat kernel estimates for both small and large time will be discussed. This is a joint work with Zhen-Qing Chen and Takashi Kumagai.

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Alex Jakobsen
UBC
Thu 14 Jan 2010, 12:30pm
LSK 462
What is game theory?
LSK 462
Thu 14 Jan 2010, 12:30pm-1:00pm

#### Abstract

This talk will be a friendly introduction to the basic concepts of game theory, starting with the Nash solution concept (more appropriately, the “Cournot-Nash” concept – you’ll see why). My goal is to highlight some of the central results, illustrate some interesting examples, and to give an idea why game theory has become so important in economic analysis (and other disciplines, too). Technicalities will be kept to a minimum, so it should be easy for everyone to walk away with a good idea of what game theory is all about.
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David Kohler
UBC
Thu 14 Jan 2010, 1:00pm
LSK 462
What is an expander graph?
LSK 462
Thu 14 Jan 2010, 1:00pm-1:30pm

#### Abstract

This short talk aims at describing expander graphs and some of their fascinating applications to other fields of mathematics and computer science. Wether you are interested in coding theory, complexity theory, probability theory, number theory or group theory, (with or without a flavour of geometry and linear algebra on the side) there will be something for you. And if none of these really speak to you, at least you'll get a nice promenade in the mathematical landscape.
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Burt Simon
Thu 14 Jan 2010, 2:00pm
Mathematical Biology Seminar
WMAX (TBA)
Postponed
WMAX (TBA)
Thu 14 Jan 2010, 2:00pm-3:00pm

#### Abstract

TBA (see Mathematical Biology Seminar page for update).
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Thu 14 Jan 2010, 3:00pm
Number Theory Seminar
Room WMAX110 (PIMS - UBC Campus)
On the sup-norm of Maass forms of large level
Room WMAX110 (PIMS - UBC Campus)
Thu 14 Jan 2010, 3:00pm-3:50pm

#### Abstract

We discuss the question of quantitative bounds on the sup-norm of automorphic cusp forms. We present an improvement on a recent result by Blomer-Holowinski on Hecke-Maass forms on $X_0(N)$ with large level $N$. Analogous results are then established for all compact arithmetic surfaces by a geometric approach.

#### Note for Attendees

Cookies and tea will be served after the talk.
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UBC
Mon 18 Jan 2010, 3:00pm
Algebraic Geometry Seminar
WMAX 110
A smooth space of stable maps and a conjecture of Abramovich--Fantechi
WMAX 110
Mon 18 Jan 2010, 3:00pm-4:00pm

#### Abstract

The stack of stable maps parameterizes maps from a complete curves having at worst nodal singularities into a smooth scheme.  Generally this stack is not smooth, but we will explain how it can be made smooth by relaxing the condition that the source curves be complete.  Although the resulting stack is not fibered in groupoids, and therefore may not be easily accessible to geometric intuition, it is a natural setting in which to construct the virtual fundamental class.  We will discuss how this generalization can be used to prove a conjecture of Abramovich and Fantechi relating the virtual fundamental classes of two different moduli spaces parameterizing stable maps into mildly singular schemes.
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Susan Allen
Department of Earth and Ocean Sciences, UBC
Mon 18 Jan 2010, 3:00pm
Institute of Applied Mathematics
Klinck 301
Anomalously Strong Tides in the Gully, a Submarine Canyon on the Nova Scotia Shelf
Klinck 301
Mon 18 Jan 2010, 3:00pm-4:00pm

#### Abstract

Two major submarine canyons: Monterey Canyon off California
and Gaoping Canyon off Taiwan, have strongly enhanced ocean tides. A
very similar canyon, The Gully off Nova Scotia is also observed to
have these enhanced tides but with a significant difference. The
enhanced tides in Monterey and Gaoping Canyons are the 12 hr tides
whereas in The Gully the enhanced tides are those with a 24 hr
period. In this seminar I will show observations of the tides and
present two coupled theories that explain the enhanced sub-inertial
tides in the Gully. Comparisons between theoretical properties of the
amplified tides and observed properties support the applicability of
the theories.

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Northwestern University
Mon 18 Jan 2010, 4:00pm SPECIAL
Department Colloquium
MATX 1100
MATX 1100
Mon 18 Jan 2010, 4:00pm-5:00pm

#### Abstract

The Langlands program relates complex representations of GL_n(Q_p) to Galois representations. For n = 1 this is explained by class field theory and for n = 2 this is closely related to the theory of modular forms. For general n, this is now understood by the work of Harris-Taylor and Henniart. In the last decade, a mod-p (as well as a p-adic) version of the Langlands program have been emerging, and they have already played an important role in some recent progress in number theory. But so far understanding has been limited to n = 1 and 2. We survey some of the known story in the classical and in the mod p case, and then discuss some recent progress on the classification of mod p representations of GL_n(Q_p), as time permits.
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Mathematics, University of Washington
Tue 19 Jan 2010, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 216
L1-Laplace and Student's T Robust Kalman Smoothers
WMAX 216
Tue 19 Jan 2010, 12:30pm-2:00pm

#### Abstract

Kalman smoothing is an important topic in control theory, with a myriad of applications. We will discuss some of these applications, present the modeling framework amenable to solution by smoothing, and discuss two related approaches to making the smoother robust against errors in the measurement data. Specifically, we will consider two heavy tailed models for observation noise, discuss the merits of these models from a statistical point of view, show how in each case the statistical model gives rise to an optimization problem with special structure, and then solve these problems to find the a posteriori maximum likelihood (MAP) solution for each model. We will then compare the smoothers' performance on simulated data contaminated with different types of outliers and on real data in an underwater tracking experiment.
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Northwestern University
Tue 19 Jan 2010, 3:30pm
Algebraic Groups and Related Structures / Number Theory Seminar
MATH 125
The classification of irreducible mod p representations of a p-adic GL_n
MATH 125
Tue 19 Jan 2010, 3:30pm-4:30pm

#### Abstract

Let F be a finite extension of the p-adic numbers. We describe the classification of irreducible admissible smooth representations of GL_n(F) over an algebraically closed field of characteristic p, in terms of "supersingular" representations. This generalizes results of Barthel-Livne for n = 2. Our motivation is the hypothetical mod p Langlands correspondence for GL_n, which is supposed to relate smooth mod p representations to Galois representations.

#### Note for Attendees

This is a joint Number Theory/Algebraic Groups Seminar.

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Stephen Gustafson
UBC
Tue 19 Jan 2010, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110
Singularities and asymptotics for some dynamics of maps into the sphere
WMAX 110
Tue 19 Jan 2010, 3:30pm-4:30pm

#### Abstract

I will describe some background and recent results on singularity formation (and non-formation) for some simple, physical, and popular geometric PDE describing dynamics of maps into spheres -- the heat-flow, wave map, and Schroedinger map -- in the energy-critical 2D case. I'll try to keep it simple and accessible by illustrating the methods on a symmetric reduction of the heat-flow, leading to a single scalar PDE.
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MIT
Wed 20 Jan 2010, 3:00pm
Topology and related seminars
110 WMAX
An infinite loop space machine for symmetric monoidal 2-categories
110 WMAX
Wed 20 Jan 2010, 3:00pm-4:00pm

#### Abstract

Abstract:
In recent work of Baas-Dundas-Richter-Rognes, the authors prove that the classifying space of 2-vector bundles, K(Vect) is equivalent to the algebraic K-theory of the connective K-theory spectrum ku. In this talk we will show that K(Vect) is the group completion of the classifying space of the 2-category of 2-vector spaces, which is a symmetric monoidal 2-category. We will explain how to use the symmetric monoidal structure to produce a $\Gamma$-2-category, which will give an infinite loop space structure on K(Vect). Then we will show that the equivalence of BDRR is a map of infinite loop spaces.
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Brian Cook
UBC
Wed 20 Jan 2010, 3:00pm
Harmonic Analysis Seminar
TBA
Wed 20 Jan 2010, 3:00pm-4:00pm

#### Abstract

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UBC
Wed 20 Jan 2010, 3:00pm
MATH 105
Undergraduate Colloquium: Diophantine equations for fun (and profit?)
MATH 105
Wed 20 Jan 2010, 3:00pm-4:00pm

#### Abstract

The first talk this term for UBC/UMC, the undergraduate mathematics colloquium, will be given by Mike Bennett.

Title: Diophantine equations for fun (and profit?)

Diophantine equations are one of the oldest, frequently celebrated and most abstract objects in mathematics. In this talk, I'll attempt to show some of the roles these equations play in modern mathematics and maybe even reveal how they can be used to make a (not particularly) fast buck.

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Andy Wan
Mathematics, UBC
Wed 20 Jan 2010, 3:30pm
Symmetries and Differential Equations Seminar
Math Annex 1102
Applications of Symmetry Methods to Partial Differential Equations Part V:
Math Annex 1102
Wed 20 Jan 2010, 3:30pm-4:30pm

#### Abstract

Continuing from where Part IV of this series, we show how one
can use symmetries to  find new conservation laws from known
conservation laws and give a new short proof for the
conservation law formula which derives from using symmetries and a known
conservation law. We then discuss and compare the known methods for
finding fluxes, given a known set of CL multipliers. In particular, we
show that all known methods can be unified by a new method which reduces
the problem of finding fluxes to at most solving a decoupled linear PDE
system known as the â€œflux equationsâ€. We will highlight the utility and
efficiency of this new method for finding fluxes with old and new examples.
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Arizona
Wed 20 Jan 2010, 4:00pm
Probability Seminar
WMAX 216
The distributive law
WMAX 216
Wed 20 Jan 2010, 4:00pm-5:00pm

#### Abstract

This is an expository talk about the distributive law of algebra and its role in combinatorics, probability, and physics. The main idea is that one can run the distributive law either way, a process sometimes called re-summation. This extraordinarily simple idea underlies a fair amount of current research in probability and mathematical physics.

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Charles Samuels
PIMS/SFU/UBC
Thu 21 Jan 2010, 3:00pm
Number Theory Seminar
Room WMAX110 (PIMS - UBC Campus)
The parametrized family of metric Mahler measures
Room WMAX110 (PIMS - UBC Campus)
Thu 21 Jan 2010, 3:00pm-3:50pm

#### Abstract

Let $M(\alpha)$ denote the Mahler measure of the algebraic number $\alpha$. Dubickas and Smyth constructed a modified version $M_1$ of $M$ having the triangle inequality. $M_1$ is called the metric Mahler measure. We produce an entire parametrized family $\{M_t\}$ of metric Mahler measures which gives rise to a new reformulation of Lehmer's problem. We further examine the functions $t\mapsto M_t(\alpha)$, for fixed $\alpha$, showing that they are constructed piecewise from certain simpler functions.

#### Note for Attendees

Cookies and tea will be served between the two talks.
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UBC
Thu 21 Jan 2010, 3:30pm
MATH 225
Engaging students in the classroom: what is all this 'clicker' nonsense?
MATH 225
Thu 21 Jan 2010, 3:30pm-4:30pm

#### Details

This is the first talk in the teaching seminar associated with the TA Accreditation Program. (All are welcome!)

Title: Engaging students in the classroom: what is all this 'clicker' nonsense?

We will explore ways to engage students to think actively about course material in class using "clickers." We will make use of iClickers throughout this session.

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University of Lethbridge
Thu 21 Jan 2010, 4:10pm
Number Theory Seminar
Room WMAX110 (PIMS - UBC Campus)
Arithmetic dynamics
Room WMAX110 (PIMS - UBC Campus)
Thu 21 Jan 2010, 4:10pm-5:00pm

#### Abstract

Starting from a classical result of Skolem, Mahler and Lech for linear recurrence sequences, we present an algebraic geometric generalization of it. Then we interpret our result from the point of view of dynamics, linking it with the Mordell-Lang conjecture from Diophantine Geometry. We conclude by studying another dynamical question which generalizes the Manin-Mumford conjecture.
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University of Lethbridge
Fri 22 Jan 2010, 3:00pm
Department Colloquium
MATX 1100
The Dynamical Mordell-Lang Conjecture
MATX 1100
Fri 22 Jan 2010, 3:00pm-4:00pm

#### Abstract

Motivated by the classical Mordell-Lang problem we formulate a dynamical generalization, which we show that it doesn't always hold. Then we discuss the cyclic case of our question, which we call the Dynamical Mordell-Lang Conjecture. We present several positive results which support our conjecture, and discuss the difficulties one has for proving the full conjecture. In particular, our work answers a basic question from complex dynamics.
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Stanford University
Mon 25 Jan 2010, 3:00pm
Algebraic Geometry Seminar
WMAX 110
Stability Conditions and the Moduli of PT-Stable Objects
WMAX 110
Mon 25 Jan 2010, 3:00pm-4:00pm

#### Abstract

In the first half of the talk, I will explain the notion of PT stability, as defined by Bayer.  I will also explain how it is related to classical stability conditions on sheaves, and other Bridgeland-type stability conditions.  In the second half of the talk, I will discuss results on the moduli space of PT-stable objects from my thesis.  In particular, I will explain how to use semistable reduction to obtain the valuative criterion of completeness for PT-stable objects.
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Mathematics, UBC
Mon 25 Jan 2010, 3:00pm
Institute of Applied Mathematics
Klinck 301
Patterns Behind Invasions
Klinck 301
Mon 25 Jan 2010, 3:00pm-4:00am

#### Abstract

Temporal cycles in natural populations have long been observed. More recent field studies have shown that in some situations, the population cycles have different phases in different locations, consistent with the existence of a travelling wavetrain of population density, passing through the region. Numerical simulations of predator-prey models with spatial dependence show that travelling wavetrains and other patterns can form behind invading fronts of predators. For reaction-diffusion and similar models, mathematical analysis can be used to predict in some cases what spatiotemporal patterns will form behind an invading front. In this talk I will describe some of the analysis that is possible using dynamical systems methods, especially for predicting the properties of wavetrains that form behind an invading front.

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Leo Tzou
Stanford University
Mon 25 Jan 2010, 4:00pm SPECIAL
Department Colloquium
MATX 1100
The Calderon Problem - from the past to the present
MATX 1100
Mon 25 Jan 2010, 4:00pm-5:00pm

#### Abstract

The problem of determining the electrical conductivity of a body by making voltage and current measurements on the object's surface has various applications in fields such as oil exploration and early detection of malignant breast tumour. This classical problem posed by Calder\'on remained open until the late '80s when it was finally solved in a breakthrough paper by Sylvester-Uhlmann. In the recent years, geometry has played an important role in this problem. We will look at the connection between this analysis problem with seemingly unrelated fields such as symplectic geometry and differential topology as well as geometric scattering theory.

The speaker is partially supported by NSF Grant No. DMS-0807502}

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Roger Donaldson
Mathematics, SFU
Tue 26 Jan 2010, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 216
The Finite Element Method by Example: A Tutorial
WMAX 216
Tue 26 Jan 2010, 12:30pm-2:00pm

#### Abstract

This SCAIM lecture is more of a tutorial than a talk. I will present a simple Finite Element Method (FEM) code as a model for the more complex codes in common modern use. Code components include: mesh generation, matrix assembly, a linear solver, and a post-processor. I will discuss these components with reference to their object-oriented (C++) implementations. This tutorial is aimed at those needing a framework for modifying and using existing codes. As a model, the example computes a piecewise-linear approximation of the solution to the Poisson problem on a circular domain with Neumann or Dirichlet boundary conditions. Focus is on implementation issues rather than on issues of accuracy and convergence. The example C++ code will be provided on-line following the talk for use as a teaching and reference tool.
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UBC
Tue 26 Jan 2010, 3:00pm SPECIAL
MATX 1100 (CRM-Fields-PIMS prize colloquium talk)
MATX 1100 (CRM-Fields-PIMS prize colloquium talk)
Tue 26 Jan 2010, 3:00pm-4:00pm

#### Details

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UBC
Tue 26 Jan 2010, 3:30pm
Algebraic Groups and Related Structures
MATH 125
What is motivic integration?
MATH 125
Tue 26 Jan 2010, 3:30pm-4:30pm

#### Abstract

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Leo Tzou
Stanford University
Tue 26 Jan 2010, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
WMAX110
The Inverse Calderon Problem for Schoedinger Operator on Riemann Surfaces
WMAX110
Tue 26 Jan 2010, 3:30pm-4:30am

#### Abstract

We show that on a smooth compact Riemann surface with boundary (M_0, g) the Dirichlet-to-Neumann map of the Schr\"odinger operator \Delta_g + V determines uniquely the potential V. This seemingly analytical problem turns out to have connections with ideas in symplectic geometry and differential topology. We will discuss how these geometrical features arise and the techniques we use to treat them.

This is joint work with Colin Guillarmou of CNRS Nice.

The speaker is partially supported by NSF Grant No. DMS-0807502 during this work.
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Miguel Raggi
UBC
Tue 26 Jan 2010, 4:00pm
Discrete Math Seminar
WMAX 216
WMAX 216
Tue 26 Jan 2010, 4:00pm-5:00pm

#### Abstract

We wish to understand the boundary between forbidden configurations on
4 rows that yield a quadratic bound and those that have cubic
constructions. The result is joint with my supervisor and Attila Sali.
The bounds we are concerned with are the following: For a (0,1)-matrix
F, we define forb(m,F) to be the maximum number of columns in an
m-rowed (0,1)-matrix which has no repeated columns and has no
submatrix which is a row and column permutation of F. The asymptotics
of forb(m,F) for arbitrary F have been conjectured by Anstee and Sali.
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Wed 27 Jan 2010, 3:00pm
Topology and related seminars
110 WMAX
Optimal bounds for the colored Tverberg problem
110 WMAX
Wed 27 Jan 2010, 3:00pm-4:00pm

#### Abstract

Abstract
The "colored Tverberg problem" asks for a smallest size of the color
classes in a (d+1)-colored point set C in R^d that forces
the existence of an intersecting family of r "rainbow" simplices with
disjoint, multicolored vertex sets from C. Using equivariant topology
applied to a modified problem, we prove the optimal lower bound
conjectured by Barany and Larman (1992) for the case of partition into
r parts, if r+1 is a prime.
The modified problem has a "unifying" Tverberg-Vrecica type
generalization, which implies Tverberg's theorem as well as the ham
sandwich theorem.
This is joint work with Pavle V. Blagojevic and Gunter M. Ziegler.
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Akos Magyar
UBC
Wed 27 Jan 2010, 3:00pm
Harmonic Analysis Seminar
MATHX 125
Working seminar: The U^3 inverse Gowers theorem in finite fields
MATHX 125
Wed 27 Jan 2010, 3:00pm-4:00pm

#### Abstract

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University of Toronto
Wed 27 Jan 2010, 4:00pm
Probability Seminar
WMAX 216
Bridge Decomposition of Restriction Measures
WMAX 216
Wed 27 Jan 2010, 4:00pm-5:00pm

#### Abstract

In the early 60s Kesten showed that self-avoiding walk in the upper half plane has a decomposition into an i.i.d. sequence of "irreducible bridges". Loosely defined, a bridge is a self-avoiding path that achieves its minimum and maximum heights at the start and end of the path (respectively), and it is irreducible if it contains no smaller bridges. Considering only the 2-dimensional case, one can ask if the (likely) scaling limit of self-avoiding walk, the SLE(8/3) process, also has such a decomposition. I will talk about recent work with Hugo Duminil from Ecole Normale Superieure that provides a positive answer, using only the restriction property of SLE(8/3). In the end we are able to decompose the SLE(8/3) path as a Poisson Point Process on the space of irreducible bridges, in a way that is similar to Ito's excursion decomposition of a Brownian motion according to its zeros. Our decomposition can actually be generalized beyond SLE(8/3) and applied to an entire family of "restriction measures", hence the title of the talk. If time permits I will also talk about the natural time parameterization for SLE(8/3), which has immediate applications towards the bridge decomposition.
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David Steinberg
UBC
Thu 28 Jan 2010, 12:30pm
LSK 462
What is a vector bundle?
LSK 462
Thu 28 Jan 2010, 12:30pm-1:00pm

#### Abstract

A vector bundle is a continuously varying family of vector spaces; for example, the set of lines that are tangent to a smooth curve is a vector bundle. In this talk, we will draw pictures, give examples, state applications, and (time permitting) learn how vector bundles can mend a heart broken by Liouville's theorem. Our emphasis will be on intuition, and all technical details will be suppressed.
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Dennis Timmers
UBC
Thu 28 Jan 2010, 1:00pm
LSK 462
What is statistical physics?
LSK 462
Thu 28 Jan 2010, 1:00pm-1:30pm

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In statistical physics we study models for interacting particles. One of the main open questions is to find models which exhibit a phase transition (think about water turning into gas at 100 Celcius). First I will introduce all the big words people use in statistical physics. Then I will show a result of Lebowitz and Penrose on the existence of a phase transition for a certain class of models. If there is some time left I can talk about some extensions of the Lebowitz and Penrose result.
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Cherif Nouar
LEMTA, Nancy, France
Thu 28 Jan 2010, 1:00pm SPECIAL
Complex Fluids Seminar
MATX 1118
Transitional flow of a non-Newtonian fluid in a pipe: Experimental evidence of weak turbulence induced by shear-thinning behaviour
MATX 1118
Thu 28 Jan 2010, 1:00pm-2:00pm

#### Abstract


Dissipative nonlinear systems such as fluid dynamical systems can reach a chaotic state when the parameter measuring the nonlinearity is large. For instance, parallel shear flows of Newtonian fluids are turbulent when the ratio of the nonlinear inertial term and the viscous dissipation term, defined by the Reynolds number is sufficiently important. In non-Newtonian fluid flows, an additional nonlinearity is introduced via the constitutive equation. For viscoelastic fluids, this nonlinearity can give rise to turbulent flow at low Reynolds number (Larson Nature 2000 and Groisman and Steinberg Nature 2000). The degree of nonlinearity is expressed by the Weissenberg number which is a product of a characteristic rate of deformation and the relaxation time of the polymer. The shear-thinning behaviour, non linear decrease of the effective viscosity with the shear rate, is the most common property of non Newtonian fluids. It is reasonable to inquire, whether an interplay between this nonlinearity and inertia can lead to a chaotic flow. This point has been addressed in (Ashrafi and Khayat PRE 2000) using low order dynamical system (generalized Lorenz system) in the Taylor-Couette flow of weakly-thinning fluid. It is shown that the additional nonlinearity gives rise to a Hopf bifurcation otherwise non existent for Newtonian fluid. In the previous talk dealing with the transition to turbulence for a yield-stress shear-thinning fluid in a pipe, a new state with a robust coherent structure characterized by two weakly modulated counter-rotating longitudinal vortices was described. In this nonlinear asyrnmetric state, time-averaged axial velocity profiles exhibited increasing asymmetry with increasing Reynolds number. In the present talk, velocity fluctuations are analysed, and it is shown that this state displays the salient feature of chaos, namely, randomly fluctuating motion excited in a broad range of spatial and temporal scales. Beside the experimental part, a spectral Petrov-Galerkin method is used to study the nonlinear stability of Hagen-Poiseuille flow of shear-thinning fluid. In the first step and as suggest the experimental results, the perturbation is assumed homogeneous in the axial direction. In this situation, the numerical results show that travelling waves with an azimuthal wave number m=1, are not sustained.

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University of Chicago
Thu 28 Jan 2010, 3:30pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
WMAX110
Traveling Fronts in Combustible Media
WMAX110
Thu 28 Jan 2010, 3:30pm-4:30am

#### Abstract

Traveling fronts are special solutions of reaction-diffusion equations which model phenomena such as propagation of species in an environment or spreading of flames in combustible media. In this talk we will address questions of existence, uniqueness, and stability of traveling fronts in general inhomogeneous media. We will show that in certain circumstances a unique front exists and it is a global attractor of the corresponding parabolic evolution, thus describing long time dynamics for very general solutions of the PDE. In contrast to this, we will also present examples of media where no traveling front solutions exist.
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University of Chicago
Fri 29 Jan 2010, 3:00pm
Department Colloquium
MATX 1100
Reaction and Diffusion in Fluid Flow
MATX 1100
Fri 29 Jan 2010, 3:00pm-4:00pm

#### Abstract

Reaction-diffusion equations are parabolic partial differential equations used in the modeling of phenomena such as propagation of species in an environment or spreading of flames in combustible media. Their general solutions exhibit two basic behaviors, extinction (quenching) and spreading. In this talk we will review recent progress in our understanding of how the motion of the underlying medium, modelled by a fluid flow, affects both the occurence of quenching and the speed of spreading of reaction. The problem turns out to have fruitful connections to questions about mixing effixiency of flows and homogenization of advection-diffusion operators.
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