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 Events
Ian Wilson
University of Cambridge
Thu 3 Sep 2009, 3:00pm
Complex Fluids Seminar
CHBE 204
A truly complex fluid - the challenge of chocolate
CHBE 204
Thu 3 Sep 2009, 3:00pm-4:00pm

Abstract

Many foods are complex fluids and chocolate is a prime example.
We infer the quality of chocolate by taste, which is our body's response
to the chemical and rheological processes that occur when we  eat it.
Although we usually consume chocolate in the plastic state (plastic in
the engineering sense), it is usually - not always - processed in the
molten state, in which case it belongs to the rheological family
of 'granular suspensions' or 'pastes'. These materials inhabit the
rheological no-man's land between yield stress fluids and multiphase
flows.  Even there it exhibits non-standard rheological behaviour,
arising from the nature of the components and the processing routes
used to make the chocolate. This presentation will outline some of the
challenges inherent in characterising and modelling this familiar
foodstuff, with a liberal sprinkling of facts from the world of
chocolate.
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Barcelona
Fri 4 Sep 2009, 2:00pm SPECIAL
Probability Seminar
WMAX 216
Hitting probabilities for systems of stochastic partial differential equations
WMAX 216
Fri 4 Sep 2009, 2:00pm-3:00pm

Abstract

A basic question in probabilistic potential theory is the following: Consider a random subset $K\subset \mathbb{R}^d$, for what nonrandom sets $A$ is $P\{K\cap A\neq\emptyset\}>0$? In this lecture we will give some abstract results when $K$ is the range of a random field $\{v(x), x\in I\}$, $I\subset \mathbb{R}^k$. More specifically, we will establish upper and lower bounds of the hitting probabilities in terms of the Hausdorff measure and the Bessel-Riesz capacity of $A$, respectively, and highlight the role of the dimensions $d$ and $k$. Application to systems of stochastic wave equations will be discussed.
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Cambridge
Fri 4 Sep 2009, 3:30pm SPECIAL
Probability Seminar
WMAX 216
Mixing times and coagulation-fragmentation
WMAX 216
Fri 4 Sep 2009, 3:30pm-4:00pm

Abstract

I will first describe a result on the uniqueness of invariant distributions for a certain process of coagulation and fragmentation. This result was first proved by Diaconis, Mayer-Wolf, Zeitouni and Zerner (2004) using representation theory, but subsequently Oded Schramm (2005) found a completely different and probabilistic proof. I will then explain how ideas from this approach can be used to give a new and probabilistic proof of the famous Diaconis-Shahshahani (1981) result about mixing times of random transpositions. In fact, this readily extends to much more general random walks on the permutation group (for which the increment is at each step uniformly selected from a given conjugacy class). This proves a conjecture of Roichman (1996). Joint work with Oded Schramm and Ofer Zeitouni.
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Tel Aviv University
Tue 8 Sep 2009, 4:00pm
Algebraic Groups and Related Structures
Math 125
Homogeneous spaces over number fields with finitely many rational orbits
Math 125
Tue 8 Sep 2009, 4:00pm-5:00pm

Abstract

Let G be a connected linear algebraic group over a number field K,
let H be a connected K-subgroup of G, and set X=H\G. We give a
convenient criterion to check, whether the set of rational orbits
X(K)/G(K) is finite, in terms of the Galois actions on pi1(H) and
on pi1(G). Using this criterion, we classify symmetric homogeneous
spaces of absolutely simple K-groups with finitely many rational
orbits.

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Johannes Nicaise
University of Leuven, Belgium
Fri 11 Sep 2009, 3:00pm
Department Colloquium
MATX 1100
Rational points on varieties over a discretely valued field
MATX 1100
Fri 11 Sep 2009, 3:00pm-4:00pm

Abstract

The starting point of this talk is a theorem of Serre's on the
classification of compact p-adic manifolds. Every such manifold is a
disjoint union of n closed unit balls, for a unique value of n in
{0,...,p-1}. Using motivic integration, the ideas of Serre's proof can be
generalized to algebraic varieties X over a complete discretely valued
field K (for instance, the field of complex Laurent series). In this way,
one can define the motivic Serre invariant S(X) of X, which is an element
of a certain ring of virtual varieties over the residue field of K. We
will explain how one can consider S(X) as a measure for the set of
rational points on X, and how this measure admits a cohomological
interpretation by means of a trace formula.

 In the first part of the talk, we recall the definitions of p-adic
numbers and p-adic manifolds, and we explain the elementary but elegant
proof of Serre's theorem. In the second part, we develop the basic
notions of motivic integration, and we illustrate the construction of the
motivic Serre invariant by some examples. In the third part, we explain
the statement of the trace formula, and we give some applications to
complex singularity theory and to arithmetic geometry.
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Mon 14 Sep 2009, 3:00pm
Algebraic Geometry Seminar
Math 125
Algebraic geometry seminar organizational meeting
Math 125
Mon 14 Sep 2009, 3:00pm-4:00pm

Abstract


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Rodrigo Restrepo
University of British Columbia
Tue 15 Sep 2009, 2:00pm
Mathematical Biology Seminar
WMAX 110
On the Emergence, Replication and Abundance of some Early Cell Structures
WMAX 110
Tue 15 Sep 2009, 2:00pm-3:00pm

Abstract

This talk presents some coherent though incomplete conjectures for the emergence, replication and abundance of some chemical structures found in each prokaryote, with special emphasis on the tRNAs and the rRNA filaments that constitute a large part of the ribosomes.

In addition to the consideration of the data, two guiding principles for the formulation of these conjectures are Occam's razor, and the idea of uniformitarianism introduced with great success by the geologists of the 19th century. These ideas, aided by the empirical data, suggest that the abundance of the relevant cell structures should be regarded as a clue for their emergence. Also, in this talk, the distinction between the purines and the pyridines is emphasized, while distinguishing each purine (or each pyrimidine) from the others is often ignored; and the conjectures advanced in this talk also suggest some experiments that may justify or falsify their ideas.
 
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Johannes Nicaise
University of Leuven
Tue 15 Sep 2009, 4:00pm
Algebraic Groups and Related Structures
Math 125
A proof of the motivic monodromy conjecture for abelian varieties
Math 125
Tue 15 Sep 2009, 4:00pm-5:00pm

Abstract

 We formulate a global form of Denef and Loeser's motivic
monodromy conjecture for complex hypersurface singularities, and we prove
it for tamely ramified abelian varieties A over a discretely valued field.
More precisely, we show that the motivic zeta function of A has a unique
pole, which coincides with Chai's base change conductor c(A), and we show
that this pole corresponds to a monodromy eigenvalue on the tame ell-adic
cohomology of A of degree dim(A). This is joint work with Lars Halvard
Halle (Hannover).

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University of Bonn
Wed 16 Sep 2009, 3:00pm
Topology and related seminars
110 WMAX
Hilbert Uniformization I: moduli spaces of surfaces
110 WMAX
Wed 16 Sep 2009, 3:00pm-4:00pm

Abstract

Abstract: We give a model for the moduli space of Riemann surfaces with one or more boundary curves using harmonic functions and canonical tesselations. The resulting simplicial complex is homeomorphic
to a flat vector bundle over the moduli space.
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Richard Liang
UBC
Wed 16 Sep 2009, 3:00pm
Probability Seminar
WMAX 216
Models in population genetics with continuous geography
WMAX 216
Wed 16 Sep 2009, 3:00pm-4:00pm

Abstract

The simplest models of population genetics, useful as they are in analyzing data, often have obvious shortcomings. Such models might ignore the effects of natural selection, mutation, or, as we will be concerned with in this talk, geography and migration. We will briefly look at the Wright-Fisher model of evolution of a single population; then, we will look at a so-called stepping stone model, where instead of a single population living all in one place, we model several populations living on discrete islands, with migration between the islands. It is often useful to consider these models' associated dual processes, which correspond to tracing the lineages of a current-day sample backwards through history. We will discuss these dual processes as well.

We will then discuss two models of evolution with *continuous* geography. Unlike the previous models, which describe directly the dynamics of a population evolving as time moves forward, the continuous geography models are instead defined in terms of prescribed dual processes.  Time permitting, we will also discuss some properties of these models, such as continuity.

This is joint work with Steve Evans.
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UBC and Université Henri Poincaré Nancy I
Wed 16 Sep 2009, 3:00pm
Harmonic Analysis Seminar
MATH 125
Working seminar: 3-term arithmetic progressions in the primes
MATH 125
Wed 16 Sep 2009, 3:00pm-4:00pm

Abstract

 
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Walid Abou-Salem
UBC
Wed 16 Sep 2009, 4:00pm
Diff. Geom, Math. Phys., PDE Seminar
MATH 103
Dimensional reduction of the mean-field dynamics of bosons in strongly anisotropic harmonic potentials
MATH 103
Wed 16 Sep 2009, 4:00pm-5:00pm

Abstract

I discuss recent results on the spatial dimensional reduction of the effective mean-field dynamics of many-body bosonic systems in strongly anisotropic harmonic potentials. In particular, the dynamics in the limit of strong anisotropy is effectively described by the nonlinear Hartree equation that is restricted to a submanifold of the original configuration space. Time permitting, I will discuss open problems regrading the mean-field dynamics of many-body constraint quantum systems.
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Mohammad El Smaily
PIMS/UBC
Thu 17 Sep 2009, 2:00pm SPECIAL
Department Colloquium
WMAX 216
KPP pulsating traveling fronts within large drift
WMAX 216
Thu 17 Sep 2009, 2:00pm-3:00pm

Abstract

PIMS/WMAX Postdoctoral Colloquium Abstract:  This talk is based on a joint work with St\'ephane Kirsch. Pulsating traveling fronts are solutions of  heterogeneous reaction-advection-diffusion equations that model some population dynamics. Fixing a unitary direction e,  it is a well-known fact that for nonlinearities of KPP type (after Kolmogorov, Petrovsky and  Piskunov, f(u)=u(1-u) is a typical homogeneous KPP nonlinearity), there exists a minimal speed c* such that a pulsating traveling front with a speed c in the direction of e exists if and only if c\geq c^*. In a periodic heterogeneous framework we have the formula of Berestycki, Hamel and Nadirashvili (2005) for the minimal speed of propagation. This formula involves elliptic eigenvalue problems whose coefficients are expressed in terms of the geometry of the domain, the direction of propagation, and the coefficients of reaction, diffusion and advection of our equation. In this talk, I will describe the asymptotic behaviors of the minimal speed of propagation within either a large drift, a mixture of large drift and small reaction, or a mixture of large drift and large diffusion. These ``large drift limits'' are expressed as maxima of certain variational quantities over the family of ``first integrals'' of the advection field. I will give more details about the limit  and a necessary and sufficient condition for which the limit is equal to zero in the 2-d case.

Note for Attendees

Tea and cookies will be served afterwards.
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Charles Samuels
PIMS/SFU/UBC
Thu 17 Sep 2009, 3:00pm
Number Theory Seminar
Room ASB 10900 (IRMACS - SFU Campus)
Metric versions of Mahler's measure
Room ASB 10900 (IRMACS - SFU Campus)
Thu 17 Sep 2009, 3:00pm-3:50pm

Abstract

The metric Mahler measure $M_1:A\to[1,\infty)$ is a modification of the classical Mahler measure $M$ that satisfies the triangle inequality $M_1(\alpha\beta)\leq M_1(\alpha)M_1(\beta)$. This function was first studied by Dubickas and Smyth in 2001, where they suggested a certain weakened version of Lehmer's conjecture. We establish this conjecture as well as give some applications showing that the value of $M_1$ cannot be too mysterious. We further examine a collection of other metric Mahler measures that give rise to new problems.

Note for Attendees

Cookies and tea will be served between the two talks.
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Johannes Nicaise
University of Leuven, Belgium
Thu 17 Sep 2009, 4:10pm
Number Theory Seminar
Room ASB 10900 (IRMACS - SFU Campus)
Trace formula for varieties over a discretely valued field
Room ASB 10900 (IRMACS - SFU Campus)
Thu 17 Sep 2009, 4:10pm-5:00pm

Abstract

We prove a trace formula à la Grothendieck-Lefschetz-Verdier for varieties X over a henselian discretely valued field with algebraically closed residue field. To the variety X, one can associate a motivic Serre invariant S(X), which measures the set of rational points on X. The trace formula expresses this measure in terms of the Galois action on the ell-adic cohomology of X, if X satisfies a certain tameness condition. If X is a curve, we relate the trace formula to Saito's criterion for tame ramification of the cohomology of X. If X is an abelian variety, we show how the trace formula gives a cohomological expression for the number of components of the Néron model of X.
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Jonathan Wise
UBC
Mon 21 Sep 2009, 3:10pm
Algebraic Geometry Seminar
MATH 125
Deformation theory (without the cotangent complex)
MATH 125
Mon 21 Sep 2009, 3:10pm-4:30pm

Abstract


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University of British Columbia
Tue 22 Sep 2009, 2:00pm
Mathematical Biology Seminar
WMAX 110
The Min system in E.coli: A stochastic polymer model and new ideas for experiments
WMAX 110
Tue 22 Sep 2009, 2:00pm-3:00pm

Abstract

The Min system in E.coli -- a group of three interacting proteins playing a role in cell division -- has attracted a lot of attention by modellers, some claiming it to be the 'measurement stick' in the rod-shaped bacterium. Different models have been proposed to explain the observed dynamical patterns -- oscillations, standing and travelling waves. Here, we will focus on a simple polymerisation/depolymerisation model. The model provides an interesting example of a stochastic hybrid dynamical system and we use probabilistic maps to compute probability distributions of experimentally accessible quantities. As a step towards model discrimination I will report on experiments we conducted on GFP-labelled E.coli.
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Alexandre Munnier
UBC and Nancy 1
Tue 22 Sep 2009, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110
Controllability results for a fish-like swimming body
WMAX 110
Tue 22 Sep 2009, 3:30pm-4:30pm

Abstract

We study the controllability of a shape changing body immersed in a perfect fluid. The shape changes are prescribed as functions of time and satisfy constraints ensuring that they are due to the work of body's internal forces only. The net locomotion of the body results from the exchange of momentum between the shape changes and the fluid. We consider the control problem that associates to any given shape changes the trajectory of the body in the fluid and we will show how this non-standard control problem can be solved within the framework of geometric control theory.
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Paul Ottaway
UBC
Tue 22 Sep 2009, 4:00pm
Discrete Math Seminar
WMAX 216
An introduction to combinatorial game theory
WMAX 216
Tue 22 Sep 2009, 4:00pm-5:00pm

Abstract

 A combinatorial game is one played by two players, Left and Right, who

alternately make moves.  The game has perfect information and no

element of chance.  The winner is determined by which player makes the

final move.  We will examine the structure of games and how they can

be treated as mathematical objects.  We will explore numbers, nimbers

and other values which naturally arise.  The concepts of inequality,

equality, negation, addition and identity are discussed with respect

to the group of games.

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Johannes Nicaise
University of Leuven
Tue 22 Sep 2009, 4:00pm
Algebraic Groups and Related Structures
Math 125
A proof of the motivic monodromy conjecture for abelian varieties
Math 125
Tue 22 Sep 2009, 4:00pm-5:00pm

Abstract

We formulate a global form of Denef and Loeser's motivic
 monodromy conjecture for complex hypersurface singularities, and we prove
it for tamely ramified abelian varieties A over a discretely valued field.
More precisely, we show that the motivic zeta function of A has a unique
pole, which coincides with Chai's base change conductor c(A), and we show
that this pole corresponds to a monodromy eigenvalue on the tame ell-adic
cohomology of A of degree dim(A). This is joint work with Lars Halvard
Halle (Hannover).

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Diwen Zhou
Department of Chemical and Biological Engineering, UBC
Wed 23 Sep 2009, 12:00pm
Complex Fluids Seminar
CHBE 204
Interfacial dynamics in complex fluids: studies of drop and free-surface deformation in polymer solutions
CHBE 204
Wed 23 Sep 2009, 12:00pm-1:00pm

Abstract

In this presentation, I describe three projects aimed at exploring interfacial dynamics of viscoelastic polymeric liquids: drop deformation in converging pipe flow, experiment on selective withdrawal, and finally numerical simulation on selective withdrawal. The first project consists of finite-element simulations of drop deformation in converging flows in an axisymmetric conical geometry. The moving interface is captured using a diffuse-interface model and accurate interfacial resolution is ensured by adaptive refinement of the grid. The second and third projects concern the same process of selective withdrawal, in which stratified layers of immiscible fluids are withdrawn from a tube placed a certain distance from the interface. For experiment, we used video recording and imaging processing to analyze how the interfacial deformation is influenced by the non- Newtonian rheology of the liquid. For simulation, we used a sharp- interface, moving-grid method to explicitly track the moving interface. The work of this presentation has lead to two main outcomes. The first is a detailed understanding of how viscoelastic stress can lead to unusual and sometimes counter-intuitive effects on interfacial deformation. The second is a potentially important new method for measuring elongational viscosity of low-viscosity liquids. This is worth further investigation considering the poor performance of existing methods.
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University of Bonn
Wed 23 Sep 2009, 3:00pm
Topology and related seminars
110 WMAX
Hilbert Uniformization II: homology of moduli spaces
110 WMAX
Wed 23 Sep 2009, 3:00pm-4:00pm

Abstract

Abstract: The simpicial complex of talk I consists of pieces of the classifying spaces of symmetric groups. We use this to investigate the homology of moduli spaces. At the end, we discuss generalizations, where the symmetric groups are replaced by other families of Coxeter groups
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UBC
Wed 23 Sep 2009, 3:00pm
Harmonic Analysis Seminar
MATH 125
Maximal estimates and differentiation theorems for sparse sets (part 1)
MATH 125
Wed 23 Sep 2009, 3:00pm-4:00am

Abstract

 
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Sebastian Andres
UBC
Wed 23 Sep 2009, 3:00pm
Probability Seminar
WMAX 216
Particle Approximation of the Wasserstein Diffusion
WMAX 216
Wed 23 Sep 2009, 3:00pm-10:00am

Abstract

In this talk a finite dimensional approximation of the recently constructed Wasserstein diffusion on the unit interval is presented. More precisely, the empirical measure process associated to a system of interacting, two-sided Bessel processes with dimension $0 < \delta < 1$ converges in distribution to the Wasserstein diffusion under the equilibrium fluctuation scaling. The passage to the limit is based on Mosco convergence of the associated Dirichlet forms in the generalized sense of Kuwae/Shioya. This is joint work with Max von Renesse.
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UBC
Wed 23 Sep 2009, 3:00pm
Undergraduate Colloquium
GEOG 214
Undergraduate Mathematics Colloquium
GEOG 214
Wed 23 Sep 2009, 3:00pm-4:00pm

Abstract

This is the first talk of the new undergraduate mathematics colloquium
at UBC, or UBC/UMC. These biweekly talks will be centred on research
in math, and accessible to undergrads.

The first talk will be given by Adam Clay.

Title: Introduction to Knot Theory

Abstract:
I will begin by describing some of the basic tools used in knot theory,
namely knot diagrams and Reidemeister moves. Next, we'll talk about
knot invariants, and I will give examples of some of the classical knot
invariants which are founded on the notion of knot diagrams. A good
example of such an invariant is "knot tricolourability".  Time permitting, 
I will also touch on some of the more powerful knot invariants, such as
the Alexander polynomial.


For more information, check out the UBC/UMC page at
     http://www.math.ubc.ca/~fsl/UMC.html
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George Bluman
Mathematics, UBC
Wed 23 Sep 2009, 3:30pm
Symmetries and Differential Equations Seminar
Math Annex 1102
Applications of Symmetry Methods to Partial Differential Equations
Math Annex 1102
Wed 23 Sep 2009, 3:30pm-4:30pm

Abstract

This weekly seminar series (Wednesdays, 3:30-4:30pm, Math Annex 1102, except for October 7th will alternate between talks given by George Bluman and other speakers (to-date: Raouf Dridi, Zhengzheng Yang, Andy Wan, Mark Gotay, Alexandre Munnier). George Bluman will give a series of talks on the forthcoming Springer book (expected publication date: November 2009) "Applications of Symmetry Methods of Partial Differential Equations" by G. Bluman, A. Cheviakov and S. Anco.  Topics include: local conservation laws and externsions of Noether's theorem, local symmetries, higher order symmmetries, invertible and noninvertible local mappings (including linearizations through symmetries and CLs), nonlocally related PDE systems, nonlocal symmetries, nonlocal CLs, nonlocal mappings, and the
nonclassical method to obtain solutions of PDEs.  The new book is a sequel to the Springer book "Symmetry Methods for Differential Equations" by G. Bluman
Bluman and S. Anco. The main emphasis of Bluman's lectures will be on how to find systematically symmetries (local and nonlocal) of a given PDE system 
and how to use systematically symmetries and conservation laws for related applications.
    The first seminar will present an overview of the new book's topics.  Participants can request a pdf file of the manuscript for private use.
 
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Ulf Rehmann
University of Bielefeld
Wed 23 Sep 2009, 4:00pm SPECIAL
Algebraic Groups and Related Structures
Math 125
Anisotropic splitting of division algebras
Math 125
Wed 23 Sep 2009, 4:00pm-5:00pm

Abstract

A theorem of Hasse-Brauer-Noether states that every central simple
algebra over a number field is cyclic.

This does not hold for arbitrary fields. However, we have the
following result:

For any given field F there exists a regular field extension E/F such
that

i)   any central simple E-algebra is cyclic,
ii)  for any central simple F-algebra, index and exponent over
     E (after field extension) are the same as over F,
iii) the restriction homomorphism res Br(F) --> Br(E) is injective.

This will be discussed in the talk.

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UBC
Fri 25 Sep 2009, 3:00pm
Department Colloquium
MATX 1100
Lagrangian Mean Curvature flow for entire Lipschitz graphs
MATX 1100
Fri 25 Sep 2009, 3:00pm-4:00pm

Abstract

In this talk I will give a brief introduction to the mean curvature flow and review some classic theory and results in the area.  I will then introduce the Lagrangian mean curvature flow and discuss recent results which can be viewed as Lagrangian versions of classic results of Ecker-Huisken on the mean curvature flow of entire hypersurfaces.  In particular, we prove existence of longtime smooth solutions to mean curvature flow of entire Lipschitz Lagrangian graphs.  As an application of our estimates we classify all self-similar entire solutions to Lagrangian mean curvautre flow satisfying certain conditions. The results are from joint work with Jingyi Chen and Weiyong He.
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Yale University
Fri 25 Sep 2009, 4:00pm SPECIAL
Topology and related seminars
110 WMAX
Bilipschitz equivalence is not equivalent to quasi-isometric equivalence for finitely generated group
110 WMAX
Fri 25 Sep 2009, 4:00pm-5:00pm

Abstract

Abstract: We give an example of two finitely generated quasi-isometric
groups that are not bilipschitz equivalent. The proof involves
structure of quasi-isometries from rigidity theorems, analysis of
bilipschitz maps of the n-adics and uniformly finite homology
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Ben Young
McGill University
Mon 28 Sep 2009, 3:10pm
Algebraic Geometry Seminar
MATH 125
Computing Donaldson-Thomas invariants for brane tilings with vertex operators
MATH 125
Mon 28 Sep 2009, 3:10pm-4:30pm

Abstract

One particularly easy way to compute generating functions for 3D Young diagrams, and for "pyramid partitions", is to use the commutation properties of vertex operators.  In fact, the vertex operator method turns out to apply to a broader class of box-counting / dimer cover problems.

We will describe this more general class of problems, and explicitly give their generating functions.  All of these generating functions can be readily turned into Donaldson-Thomas partition functions for the associated quivers (modulo a superpotential) by introducing signs on certain variables.
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Wood Science, UBC
Tue 29 Sep 2009, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 216
Numerical Approaches to Solving the Problems of Utilising Wood
WMAX 216
Tue 29 Sep 2009, 12:30pm-2:00pm

Abstract

Abstract

Wood is nature’s solution to the structural and hydraulic problems faced by the World’s largest living organisms-trees. The solutions to these problems are both elegant and energy efficient and are starting to inspire new (biomimetic) approaches to the design of novel materials. Wood in its native form, however, is still a very important material and sustains numerous industries that are vital to the economies of many countries, including Canada’s. The utilization of wood by these industries is constantly throwing up complex and important problems whose solution often benefits from an interdisciplinary approach involving the collaboration of biologists, physicists, chemists and mathematicians. This seminar will describe a range of fundamental and applied problems involving the utilization of wood that were solved by an interdisciplinary approach involving material scientists and mathematicians at The Australian National University. I will also introduce a new problem on the quantification of penetration of coatings into the porous microstructure of wood that could benefit from a similar interdisciplinary approach.

 

Biography.

Professor Philip Evans is the BC Leadership Chair in Advanced Forest Products Manufacturing Technology in the Faculty of Forestry at UBC. He is also an Adjunct Professor at The Australian National University and a Visiting Fellow in the Department of Applied Mathematics at The ANU. His research focuses on the surface properties of wood and the development of new wood-based materials that can compete with plastics, metals and concrete. 

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U. Virginia
Tue 29 Sep 2009, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110
On an isoperimetric inequality for a Schroedinger operator depending on the curvature of a loop
WMAX 110
Tue 29 Sep 2009, 3:30pm-4:30am

Abstract

Let \gamma be a smooth closed curve of length 2\pi in R^3, and let \kappa(s) be its curvature regarded as a function of arc length s. We associate with this curve the one-dimensional Schroedinger operator H_\gamma = -d^2/ds^2 + \kappa^2(s) acting on the space of square integrable 2\pi-periodic functions. A natural conjecture is that the lowest eigenvalue e_0(\gamma) of H_\gamma is bounded below by 1 for any \gamma (this value is assumed when \gamma is a circle). We study a family of curves which includes the circle and for which e_0(\gamma)=1 as well, and show that the curves in this family are local minimizers; i.e., e_0(\gamma) does not decrease under small perturbations. A connection between the inequality and a dynamical elastica will be described. The conjecture remains open.
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UBC
Tue 29 Sep 2009, 4:00pm
Algebraic Groups and Related Structures
Math 125
Essential Dimension of A_7 and S_7
Math 125
Tue 29 Sep 2009, 4:00pm-5:00pm

Abstract

Recently, Y. Prokhorov classified all finite simple groups with faithful
actions on rationally connected threefolds. Using this classification,
I show that the essential dimensions of the alternating group, A7, and the
symmetric group, S7, are 4.  In particular, the essential dimension of S7
is a measure of how much one can simplify a ``general polynomial'' of degree
7 by Tschirnhaus transformations.  This was a long-standing open problem and
is related to algebraic forms of Hilbert's 13th problem.

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Richard Anstee
UBC
Tue 29 Sep 2009, 4:00pm
Discrete Math Seminar
WMAX 216
Forbidden Configurations: Critical Substructures
WMAX 216
Tue 29 Sep 2009, 4:00pm-5:00am

Abstract

Let F be a kxl (0,1)-matrix. We say that a (0,1)-matrix A has F as a
`configuration' if some row and column permutation of F is a
submatrix of A.

We are  interested in `simple' matrices, namely (0,1)-matrices with no
repeated columns. If A is a simple matrix and has no configuration F then
what can we deduce about A? Our extremal problem is given m,F to
determine the maximum number of columns forb(m,F) in an m-rowed simple matrix A
which has no configuration F.

A `critical substructure' of F is a configuration F’  which is
contained in F and such that forb(m,F’)=forb(m,F). We give some examples to
demonstrate how this idea often helps in determining forb(m,F).

This represents joint work with Steven Karp and also Miguel Raggi.
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Peng Gao
Department of Chemical and Biological Engineering, UBC
Wed 30 Sep 2009, 12:00pm
Complex Fluids Seminar
CHBE 204
Numerical simulation of biolocomotion on water
CHBE 204
Wed 30 Sep 2009, 12:00pm-1:00pm

Abstract

Water striders and fishing spiders are creatures living on water. The special structure of their legs renders them highly nonwetting or superhydrophobic so that these creatures can stand effortlessly and walk quickly over the free surface of water. While the hydrostatics has been well understood, the propulsion mechanism of water walkers is still not fully resolved. We have performed finite-element simulations of the interfacial flow induced by the stoke motion of a leg, which is modeled as a cylinder. The free interface and the moving contact line are handled by using a diffuse-interface method. Results show that it is primary the curvature force pushing the water walkers forward, while the pressure force is of secondary role and the viscous force can be neglected. The superhydrophobicity doesn’t play an important role in the driving force, but it can decrease the resistance during the recovery stroke and increase the safety margin to delay the surface penetration. The relative importance of resulted waves and vortices is also discussed.
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UBC
Wed 30 Sep 2009, 3:00pm
Harmonic Analysis Seminar
MATH 125
Maximal estimates and differentiation theorems for sparse sets (part 2)
MATH 125
Wed 30 Sep 2009, 3:00pm-4:00am

Abstract

 
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Technion
Wed 30 Sep 2009, 3:00pm
Probability Seminar
WMAX 216
The Infinite rate mutually catalytic branching model
WMAX 216
Wed 30 Sep 2009, 3:00pm-4:00pm

Abstract


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Raouf Dridi
Mathematics, UBC
Wed 30 Sep 2009, 3:30pm
Symmetries and Differential Equations Seminar
Math Annex 1102
New classification techniques for ordinary differential equations
Math Annex 1102
Wed 30 Sep 2009, 3:30pm-4:30pm

Abstract

In this talk I will present a new ordinary differential equation solver
based on the powerful equivalence method of Élie Cartan. This solver
returns a target equation equivalent to the equation to be solved and the
transformation realizing the equivalence. The target ODE is a member of a
dictionary of ODEs, that are regarded as well-known, or at least
well-studied. The dictionary considered here comprises the ODEs in a book
of Kamke. The major advantage of our solver is that the equivalence
transformation is obtained without integrating differential equations. We
provide also a theoretical contribution revealing the relationship between
the change of coordinates that maps two differential equations and their
symmetry pseudo-groups.
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