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 Events
Jeff Smith
UBC
Wed 1 Feb 2012, 3:00pm
Topology and related seminars
WMAX 216 (PIMS)
The Adem HW problem and the moduli space of commuting endomorphisms.
WMAX 216 (PIMS)
Wed 1 Feb 2012, 3:00pm-4:00pm

Abstract

 
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UC Berkeley
Wed 1 Feb 2012, 3:00pm
Probability Seminar
MATH 126
Reconstruction for Colorings on Trees
MATH 126
Wed 1 Feb 2012, 3:00pm-4:00pm

Abstract

For spin systems on a tree, roughly, the reconstruction problem
is to determine whether correlations persist between vertices
deep inside the tree and the root. Reconstruction on trees plays
an important role in explaining threshold phenomena in random
constraint satisfaction problems on sparse random graphs as well
as the efficiency of finding and sampling solutions for these
problems.

In this talk, I will speak about the following results:

(1) Bounds on the reconstruction threshold for colorings and
rapid mixing of the block dynamics for sampling colorings. (with
Vera, Vigoda, and Weitz '11)

(2) An algorithm to compute the reconstruction threshold, with
an application showing bounds on the threshold for the Potts
model on small-degree trees. (with Maneva '11)

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UC Berkeley
Thu 2 Feb 2012, 1:00pm SPECIAL
Department Colloquium
MATH 100
Reconstruction for the Hardcore Model
MATH 100
Thu 2 Feb 2012, 1:00pm-2:00pm

Abstract

I will speak about the connections of the reconstruction problem on trees with constraint satisfaction on random graphs and efficiency of algorithms. I will describe our bounds on the reconstruction threshold for the hardcore model on trees. (with Sly and Tetali '11)

Time permitting, I will speak about some unrelated results on non-uniform models for random permutations and bounds on the length of the longest increasing subsequences. (with Peled, in progress)
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Zhengzheng Yang
UBC Math
Thu 2 Feb 2012, 2:30pm
Symmetries and Differential Equations Seminar
Math Annex 1118
Nonlocally related PDE systems III
Math Annex 1118
Thu 2 Feb 2012, 2:30pm-3:20pm

Abstract

It will be shown that each point symmetry of a given PDE system systematically yields a nonlocally related PDE system.  Examples will be exhibited that yield nonlocal symmetries for a given PDE system not obtainable systematically through previously known methods.
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University of Victoria
Thu 2 Feb 2012, 3:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 102
Alpern theorems for higher-dimensional flows
Math 102
Thu 2 Feb 2012, 3:00pm-4:00pm

Abstract


We discuss Alpern theorems (a generalization of Rokhlin's lemma) for R^d actions
in which the `towers' are rectangular boxes of prescribed sizes, proving both
sufficient and necessary conditions on the number of boxes. (joint work with
Bryna Kra and Ayşe Şahin).
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Greg Mayer
UBC
Thu 2 Feb 2012, 4:00pm
Mathematical Education
MATH 126
Teaching Seminar: Using definitions, examples and technology
MATH 126
Thu 2 Feb 2012, 4:00pm-5:00pm

Abstract

This week Greg Mayer will conduct the discussion. We will study the section title "Using definitions, examples and technology". This section is composed of three papers, our discussion will focus on the third one:
  • The role of mathematical definitions in mathematics and in undergraduate mathematics courses (pdf)
  • Compute-based technologies and plausible reasoning (pdf)
  • Worked examples and concept example usage in understanding mathematical concepts and proofs (pdf)

Please see the Seminar's wiki page available at: http://wiki.ubc.ca/Sandbox:Math_Teaching_Seminar
You will find access to the pdf version of these papers.
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Universitšt Wien
Fri 3 Feb 2012, 3:00pm
Department Colloquium
MATX 1100
The interaction of a gap with a free boundary in a two-dimensional dimer system
MATX 1100
Fri 3 Feb 2012, 3:00pm-4:00pm

Abstract

I shall consider a rhombus tiling model (equivalently, a dimer model on a hexagonal graph) with a free boundary. The correlation of a small triangular hole in this model will be determined. As I shall explain, this kind of problem features phenomena which are parallel to phenomena in electrostatics. This is joint work with Mihai Ciucu.
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MIT
Mon 6 Feb 2012, 3:00pm SPECIAL
Department Colloquium / Institute of Applied Mathematics
LSK 301, 6356 Agricultural Road, UBC
Seismic imaging with multiply scattered waves
LSK 301, 6356 Agricultural Road, UBC
Mon 6 Feb 2012, 3:00pm-4:00pm

Abstract

The acoustic wave equation is a mathematical model commonly used for the propagation of seismic waves through the Earth's subsurface, where the wavespeed is determined by the geological composition of the Earth.  The seismic imaging problem is to recover this geological composition based on surface data, and is typically formulated as an inverse problem to recover the wavespeed in the acoustic wave-equation model.  To linearize this inverse problem, it is typically assumed that waves reflect only once in the subsurface.  This assumption, combined with the data acquisition geometry which restricts sources and receivers to lie on the Earth's surface, makes these algorithms most effective at imaging structures that are nearly flat.  The inclusion of multiply scattered waves mitigates this to some extent, but at the cost that the inverse problem becomes nonlinear. I will describe a series framework for including multiply scattered waves in the seismic inverse problem allowing us to approach this nonlinear problem as a series of linear problems.  Within this approach, we use techniques of seismic interferometry, a method based on Green's theorem.  I will briefly describe how we use these techniques in other applications in particular for locating micro earthquakes relative to one another.
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Kansas State University
Mon 6 Feb 2012, 3:10pm
Algebraic Geometry Seminar
WMAX 110
Chern-Simons functional and Donaldson-Thomas theory
WMAX 110
Mon 6 Feb 2012, 3:10pm-4:10pm

Abstract

I will survey the constructions of holomorphic Chern-Simons functionals for the moduli spaces of sheaves on CY 3-folds and several applications to the theoretical and computational aspects of Donaldson-Thomas theory.

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MIT
Mon 6 Feb 2012, 4:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126
Correlation decay property and the problem of computing the partition function
Math 126
Mon 6 Feb 2012, 4:00pm-5:00pm

Abstract

 Loosely speaking, a stochastic system exhibits the correlation decay property if correlations between components of the system decay as a function of the distance between the components. The notion appears primarily in the context of uniqueness of Gibbs measures in statistical physics, but also appears to have interesting algorithmic applications.  We illustrate how the correlation decay property can be used for designing a polynomial time deterministic approximation algorithm, which we call the cavity expansion algorithm, for the problem of computing the partition function for Gibbs distributions on general graphs. Prior algorithms for this problem rely primarily on the Monte Carlo simulation technique and thus suffer from the sampling error. In contrast, the cavity expansion algorithm is deterministic and takes advantage of some structural property of Gibbs measures on graphs. We will illustrate our method on the problem of counting partial matchings in a graph - a well known #P hard algorithmic problem. Then we will demonstrate the practicality of our approach for the problem of computing the counting entropy for some lattice models. Specifically, we obtain an estimate of  the entropy of the monomer-dimer coverings of a lattice, improving earlier estimates by several orders of magnitude.

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UBC
Tue 7 Feb 2012, 3:30pm
Algebraic Groups and Related Structures
MATX 1102
Coxeter groups and palindromic Poincare polynomials
MATX 1102
Tue 7 Feb 2012, 3:30pm-4:30pm

Abstract

Let W be a Coxeter group. For any w in W, let P_w denote the Poincare polynomial of w (i.e. the generating function of the principle order ideal of w with respect to length). If W is the Weyl group of some Kac-Moody group G, then P_w is the usual Poincare polynomial of the corresponding Schubert varitey X_w.

In this talk, I will discuss work in progress with W. Slofstra on detecting when the sequence of coefficients of a Poincare polynomial are the same read forwards and backwards (i.e. palindromic). The polynomial P_w satisfies this property precisely when the Schubert variety X_w is rationally smooth. It turns out that for many Coxeter groups, this property is relatively easy to detect.

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MIT
Tue 7 Feb 2012, 4:00pm SPECIAL
One Time Event
WMAX 110 (PIMS)
Seminar: High order methods for high fidelity models of wave propagation
WMAX 110 (PIMS)
Tue 7 Feb 2012, 4:00pm-5:00pm

Details

High-order surface integral methods are powerful modeling tools for problems involving isolated variations in sound speed.  The challenge in these methods lies in designing discretizations that appropriately account for the singularities in the Green's functions.  I will discuss a method for doing this and will illustrate its applicability with two examples: (i) Modelling ultrasound vibro-acoustography, a nonlinear medical imaging technique that uses two different frequencies of ultrasound, combining the resolution of high-frequency ultrasound with the clean images possible when imaging at low frequencies.  (ii) Understanding wavefront healing, a phenomena observed in seismic tomography where traveltime delays are reduced as waves propagate further from an isolated anomaly.  I will also briefly discuss a related method for modeling seismic data near topography; our method allows us to quickly estimate a rough structure that can then be used as a starting model for full-waveform inversion techniques.
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Gergely Ambrus
UBC
Tue 7 Feb 2012, 4:00pm
One Time Event
Math 126
Longest convex chains
Math 126
Tue 7 Feb 2012, 4:00pm-5:00pm

Details

A classical problem in probability is to determine the length of the
longest increasing subsequence in a random permutation. Geometrically,
the question can be formulated as follows: given n independent,
uniform random points in the unit square, find the longest increasing
chain (polygonal path through the given points) connecting two
diagonally opposite corner of the square, where "length" means the
number of points on the chain. The variant of the problem I am going
to talk about asks for the length of the longest convex chain
connecting two vertices. We determine the asymptotic expectation up to
a constant factor, and derive strong concentration and limit shape
results. We also prove an ergodic result as well as giving a heuristic
argument for the exact asymptotics of the expectation. Some of these
results are joint with Imre Barany.
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Harvard University
Wed 8 Feb 2012, 3:00pm
Topology and related seminars
WMAX 216 (PIMS)
Mapping class groups and finite covers
WMAX 216 (PIMS)
Wed 8 Feb 2012, 3:00pm-4:00pm

Abstract

I will give a survey of results concerning the actions of a mapping class on the homology of various finite covers to which it lifts. I will draw connections to 3-manifold theory, especially largeness, growth of torsion homology and Alexander polynomials.
 
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UBC
Wed 8 Feb 2012, 3:00pm
Probability Seminar
WMAX 110
The critical points of lattice trees and lattice animals in high dimensions
WMAX 110
Wed 8 Feb 2012, 3:00pm-4:00pm

Abstract

Lattice trees and lattice animals are used to model branched polymers. They are of interest in combinatorics and in the study of critical phenomena in statistical mechanics. A lattice animal is a connected
subgraph of the d dimensional integer lattice. Lattice trees are lattice animals without cycles. We consider the number of lattice trees and animals with n bonds 
that contain the origin and form the corresponding generating functions. We are mainly interested in the radii of convergence of these functions, which are the 
critical points. In this talk we focus on the calculation of the first three terms of the critical points for both models as the dimension goes to infinity.

This is ongoing work with Gordon Slade.


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Tufts University
Thu 9 Feb 2012, 3:00pm SPECIAL
One Time Event
WMAX 110 (PIMS)
Seminar: Fast Solvers for Tuned Discretizations
WMAX 110 (PIMS)
Thu 9 Feb 2012, 3:00pm-4:00pm

Details

While the combination of standard finite-element discretizations and fast multigrid-based solvers is now well-established and well-understood for uniformly elliptic systems of PDEs, much work remains for problems that fall outside this class. This talk focuses on recent developments in the theory and practice of multigrid solvers for two important classes of non-uniformly elliptic systems: singular-perturbation and saddle-point problems.  For singular-perturbation problems, boundary and interior layers are generated as the perturbation parameter goes to zero, leading to the need for strongly locally refined meshes to efficiently resolve the solutions to these systems.  I will show how layer-aware multigrid methods can be developed to achieve optimal solver efficiency for these meshes. For saddle-point problems, difficulties arise due to the indefiniteness of the discretized linear systems, leading to many approaches based on block factorization treatment of two smaller but definite matrices. I will discuss an alternative monolithic approach, based on the constrained optimization viewpoint, to developing optimal multigrid solvers for these problems.
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Warren Code & David Kohler
UBC
Thu 9 Feb 2012, 4:00pm
Mathematical Education
MATH 126
TA Accreditation Program Seminar: Creating effective clicker questions
MATH 126
Thu 9 Feb 2012, 4:00pm-5:00pm

Abstract

 Whether you are an experienced clicker user or a pure novice who barely knows what clickers are, this session is for you! Clickers allow us to ask multiple-choice questions to a large crowd and gather global information about the state of your learners. Everyone will agree that creating effective clicker questions is a challenge. In this session we will offer some activities to allow everybody to improve their skills crafting such questions.

Note: Despite the fact that clickers themselves are mainly used in the classroom, this session isn't designed solely for instructors. Since designing effective questions which challenge the conceptual understanding of students is at the core of our activities, every TA will improve their skills of crafting effective questions, understand common misconceptions and reflect on what type of feedback informs you of the state of understanding of your learners.

Cookies and tea will be offered by our generous sponsors.
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UCLA
Fri 10 Feb 2012, 2:00pm SPECIAL
Topology and related seminars
WMAX 216 (PIMS)
A conjecture relating Heegaard Floer homology and the fundamental group
WMAX 216 (PIMS)
Fri 10 Feb 2012, 2:00pm-3:00pm

Abstract

L-spaces are 3-manifolds with simplest possible Heegaard Floer homology. These arise naturally in many applications of Heegaard Floer theory, and as a result it has been asked if there is an alternate characterization of this class of 3-manifolds. A recent conjecture suggests the following: A 3-manifold is an L-space if and only if its fundamental group is not left-orderable. This talk will attempt to put this conjecture in context and describe some of the evidence supporting it.
 
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Tufts University
Fri 10 Feb 2012, 3:00pm SPECIAL
Department Colloquium
MATX 1100
Algebraic multigrid in theory and practice
MATX 1100
Fri 10 Feb 2012, 3:00pm-4:00pm

Abstract

Computational simulation is an important tool in many fields of science and engineering, providing crucial insight into a wide range of real-world problems. At the core of many simulations lies the solution of large linear systems of equations that can, in principle, be solved using simple techniques, such as Gaussian elimination. The high computational cost of Gaussian elimination, however, often makes high-fidelity simulations intractable. The modelling of convective flows in the Earth's mantle, for example, are limited to simulations with a few hundred thousands of degrees of freedom using this approach. In this talk, I will discuss both the theory and practice of algebraic multigrid methods, which can be used to overcome this barrier in many cases. I will show both theoretical analysis, leading to a rigorous framework for motivating the choice of components within a multigrid algorithm, and practical results, enabling efficient simulations of mantle convection with up to 100 million degrees of freedom.
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UBC
Mon 13 Feb 2012, 1:00pm
Harmonic Analysis Seminar
Math 126
Corners in dense subsets of P^2
Math 126
Mon 13 Feb 2012, 1:00pm-1:55pm

Abstract

 We will discuss how to modify an approach of Solymosi and Tao, based on the so-called relative triangle removal lemma, to show that subsets of positive relative density of P^2 contain infinitely many corners, that is sets of the form {(a,b), (a+d,b),(a,b+d)}. This is ongoing joint work with T. Titichetrakun.
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University of Idaho
Mon 13 Feb 2012, 3:10pm
Algebraic Geometry Seminar
WMAX 110
Local complete intersection Schubert varieties
WMAX 110
Mon 13 Feb 2012, 3:10pm-4:10pm

Abstract

We characterize Schubert varieties (for GLn) which are local complete intersections (lci) by the combinatorial notion of pattern avoidance.  For the Schubert varieties which are local complete intersections, we give an explicit minimal set of equations cutting out their neighborhoods at the identity.  Although the statement only requires ordinary pattern avoidance, showing the other Schubert varieties are not lci appears to require more complicated combinatorial ideas which have their own geometric underpinnings.  The Schubert varieties defined by inclusions, originally introduced by Reiner and Gasharov, turn out to be an important subclass of lci Schubert varieties.  Using the explicit equations at the identity for the lci Schubert varieties, we can recover formulas for some of their local singularity invariants at the identity as well as explicit presentations for their cohomology rings.  

This is joint work with Henning Ulfarsson (Reykjavik U.).

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National Chiao Tung University, Taiwan
Tue 14 Feb 2012, 3:30pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar / Mathematical Biology Seminar
WMAX 110 (PIMS) (PDE-Math Biology Joint seminar)
Asymptotic Limit in a Cell Differentiation Model
WMAX 110 (PIMS) (PDE-Math Biology Joint seminar)
Tue 14 Feb 2012, 3:30pm-4:30pm

Abstract

T cells of the immune system, upon maturation, differentiate into either Th1 or Th2 cells that have different functions. The decision to which cell type to differentiate depends on the concentrations of transcription factors T-bet (x_1) and GATA-3 (x_2). These factors are translated by the mRNA whose levels of expression, y_1 and y_2, depend, respectively, on x_1 and x_2 in a nonlinear nonlocal way. The population density of T cells, \phi(t,x_1,x_2, y_1, y_2), satisfies a hyperbolic conservation law with coefficients depending nonlinearly and nonlocally on (t, x_1,x_2, y_1, y_2), while the x_i, y_i satisfy a system of ordinary differential equations. We study the long time behavior of \phi and show, under some conditions on the parameters of the system of differential equations, that the gene expressions in the T-cell population aggregate at one, two or four points, which connect to various cell differentiation scenarios.
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Jozsef Solymosi
UBC
Tue 14 Feb 2012, 4:00pm
Discrete Math Seminar
Math 126
Roth type theorems in finite groups
Math 126
Tue 14 Feb 2012, 4:00pm-5:00pm

Abstract

In this talk we prove Roth type theorems in finite groups. Our main
tool is the Triangle Removal Lemma of Ruzsa and Szemeredi. For example
we show that for every c>0 there is a bound n such that if a finite
group G has order at least n, then any set S which is at least c-dense
in GxG contains four elements (a, b), (a, c), (e,c), (e,f) such that
ab = ec and ac = ef.
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Technion
Wed 15 Feb 2012, 3:00pm
Probability Seminar / Topology and related seminars
WMAX 110
DRAT: Doing random algebraic topology
WMAX 110
Wed 15 Feb 2012, 3:00pm-4:00pm

Abstract

Over the past few years there has been considerable activity in exploiting the power of algebraic topology to investigate areas outside of mathematics. The phrase 'applied algebraic topology'
is no longer an oxymoron!

Even more recently the intrinsically random nature of the world is beginning to bring statistical and probabilistic tools to these problems, leading to the birth 
of a new area of 'random algebraic topology'.

In this talk I will discuss some of the few results in random algebraic topology, including the persistence homology of the sub-level sets of Gaussian processes 
over manifolds, and limit theorems for the Betti numbers of random complexes built over random point processes.

Since this is to be a joint Probability/Topology seminar, I shall assume no prior knowledge in either area.

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University of Alberta
Wed 15 Feb 2012, 4:00pm SPECIAL
Department Colloquium
WMAX 110 (PIMS)
"A great deal more is known than has been proved."
WMAX 110 (PIMS)
Wed 15 Feb 2012, 4:00pm-5:00pm

Abstract

Feynman's famous quote is of particular relevance for research at the interface of mathematics and physics in recent decades. A striking example is the impressive number of fascinating results (many of them still conjectural) in various areas of mathematics, such as geometry, topology and number theory, that have been obtained via string theory. In this vein, mirror symmetry and topological string theory have been particularly fruitful. In this talk I will focus on a number of mathematical conjectures and theorems that we have obtained through careful study of mirror symmetry. I will discuss what string theory tells us about (quasi-)modularity of the generating functions of Gromov-Witten invariants of Calabi-Yau threefolds, and what it implies for the crepant resolution conjecture relating Gromov-Witten invariants of an orbifold to the invariants of its crepant resolution. I will also talk about a new mysterious recursive structure conjecturally satisfied by the Gromov-Witten generating functions for toric Calabi-Yau threefolds, with far-reaching and still mostly unexplored consequences. By the end of the talk, you should hopefully be convinced of "the unreasonable effectiveness of string theory in mathematics"!
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Yonsei University
Thu 16 Feb 2012, 2:00pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
ANGU 235 (It is in *Sauder School*, the second floor)
Harnack inequality for second order elliptic operators on Riemannian manifolds.
ANGU 235 (It is in *Sauder School*, the second floor)
Thu 16 Feb 2012, 2:00pm-3:00pm

Abstract

In this talk, I will give a survey on Harnack inequalities for solutions of second-order elliptic equations on Riemannian manifolds.
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Michael Rempe
Whitworth University
Thu 16 Feb 2012, 2:00pm
Mathematical Biology Seminar
WMAX 110 (PIMS)
A mathematical model of human sleep and insomnia
WMAX 110 (PIMS)
Thu 16 Feb 2012, 2:00pm-3:00pm

Abstract

I will present a biologically-based mathematical model that accounts for several features of human sleep and demonstrate how particular features depend on  interactions between a circadian pacemaker and a sleep homeostat. The model is made up of regions of cells that interact with each other to cause transitions between sleep and wake as well as between REM and NREM sleep. Analysis of the mathematical mechanisms in the model yields insights into potential biological mechanisms underlying sleep and sleep disorders including stress-induced insomnia and fatal familial insomnia.
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University of Victoria
Thu 16 Feb 2012, 3:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 102
Weak mixing suspension flows over shifts of finite type are universal
Math 102
Thu 16 Feb 2012, 3:00pm-4:00pm

Abstract

Let S be an ergodic measure-preserving automorphism on a non-atomic
probability space, and let T be the time-one map of a topologically weak
mixing suspension flow over an irreducible subshift of finite type under a
Holder ceiling function. We show that if the measure-theoretic entropy of
the S is strictly less than the topological entropy of T, then there
exists an embedding from the measure-preserving automorphism into the
suspension flow. As a corollary of this result and the symbolic dynamics
for geodesic flows on compact surfaces of negative curvature developed by
Bowen and Ratner, we also obtain an embedding from the measure-preserving
automorphism into a geodesic flow, whenever the measure-theoretic entropy
of S is strictly less than the topological entropy of the time-one map of
the geodesic flow.
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University of Alberta
Thu 16 Feb 2012, 3:00pm SPECIAL
One Time Event
PIMS, WMAX 110
Geometry and Physics Seminar: Topological recursion on elliptic curves
PIMS, WMAX 110
Thu 16 Feb 2012, 3:00pm-4:30pm

Details

In recent years, a unifying theme has been found for a surprising number of counting problems. It appears that in many seemingly unrelated contexts, generating functions for enumerative invariants satisfy a particular topological recursion, based on the geometry of a complex curve. As examples, Hurwitz theory,
Gromov-Witten theory of the complex line, and open/closed Gromov-Witten theory of the three-dimensional complex plane and other toric Calabi-Yau threefolds are all encoded by the same topological recursion on certain complex curves. In this talk, I will first review applications of the topological recursion on genus zero curves, and then report on work in progress on studying the topological recursion for families of elliptic curves. In this context, the recursion
produces an infinite tower of quasi-modular forms. The question is: to what counting problem should these quasi-modular forms be related?
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SFU
Thu 16 Feb 2012, 3:00pm
Number Theory Seminar
Room ASB 10900 (IRMACS - SFU Campus)
On the correlation of completely multiplicative functions
Room ASB 10900 (IRMACS - SFU Campus)
Thu 16 Feb 2012, 3:00pm-3:50pm

Abstract


Note for Attendees

Refreshments will be served between the two talks.
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Warren Code & David Kohler
UBC
Thu 16 Feb 2012, 4:00pm
Mathematical Education
MATH 126
Teaching Seminar: Foundations for beginning calculus
MATH 126
Thu 16 Feb 2012, 4:00pm-5:00pm

Abstract

This week we will study the section titled "Foundations for beginning calculus". This section is composed of four papers: 1) On developing a rich conception of variable 2) Rethinking change 3) Foundation reasoning abilities that promote coherence in students' function understanding and 4) The concept of accumulation in calculus. Please see the Seminar's wiki page available at: http://wiki.ubc.ca/Sandbox:Math_Teaching_Seminar

You will find access to the pdf version of these papers.
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Capilano University
Thu 16 Feb 2012, 4:10pm
Number Theory Seminar
Room ASB 10900 (IRMACS - SFU Campus)
Strong normality
Room ASB 10900 (IRMACS - SFU Campus)
Thu 16 Feb 2012, 4:10pm-5:00pm

Abstract

At a previous seminar, we proposed a "strong normality" test, to exclude numbers like Champernowne's number. Now we give a sharp version of this test. Almost all numbers are strongly normal, and every strongly normal number is normal. We use a method of Sierpinski to construct an absolutely normal number satisfying the new criterion. (This is joint work with Peter Borwein.)
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Stanford University
Fri 17 Feb 2012, 3:00pm
Department Colloquium
MATX 1100 (PIMS/UBC Distinguished Colloquium)
Exact Phase Retrieval via Convex Programming
MATX 1100 (PIMS/UBC Distinguished Colloquium)
Fri 17 Feb 2012, 3:00pm-4:00pm

Abstract

This talks introduces a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations together with ideas from convex programming to recover the phase from intensity measurements, typically from the modulus of the diffracted wave. We demonstrate empirically that any complex-valued object can be recovered from the knowledge of the magnitude of just a few diffracted patterns by solving a simple convex optimization problem inspired by the recent literature on matrix completion. More importantly, we also demonstrate that our noise-aware algorithms are stable in the sense that the reconstruction degrades gracefully as the signal-to-noise ratio decreases. Finally, we present some novel theory showing that our entire approach may be provably surprisingly effective.
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USC
Mon 20 Feb 2012, 3:10pm
Algebraic Geometry Seminar
WMAX 110
Classifying vector bundles on smooth affine varieties
WMAX 110
Mon 20 Feb 2012, 3:10pm-4:10pm

Abstract

If X is a finite CW complex of small dimension, information about the homotopy groups of unitary groups can be translated into cohomological classification results for complex vector bundles on X.  I will explain how A^1-homotopy theory can be used in an analogous fashion in the classification of vector bundles of on smooth affine varieties of small dimension.   In particular, I will explain some joint work (in progress) with J. Fasel which shows how to give a complete classification of vector bundles on smooth affine 3-folds over certain fields.  No knowledge of A^1-homotopy theory will be assumed.

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UBC
Mon 27 Feb 2012, 3:10pm
Algebraic Geometry Seminar
WMAX 110
Motivic invariants of quivers via dimensional reduction
WMAX 110
Mon 27 Feb 2012, 3:10pm-4:10pm

Abstract

We explain how the computation of motivic Donaldson-Thomas invariants associated to a quiver with potential reduces to the computation of the motivic classes of simpler quiver varieties.  This has led to the calculation of these invariants for some interesting Calabi-Yau geometries derived equivalent to a quiver with potential. Here we observe q-deformations of the classical generating series.

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Department of Physics, University of Texas at Austin
Mon 27 Feb 2012, 4:00pm SPECIAL
One Time Event
MATX 1100
Specialized Seminar: A Discontinuous Galerkin Method for Vlasov-Like Systems
MATX 1100
Mon 27 Feb 2012, 4:00pm-5:00pm

Details


pdf
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Aleksandr (Sasha) Aravkin
CS/EOS, UBC
Tue 28 Feb 2012, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 110
Robust Statistical Modeling for Geophysical Imaging and Kalman Smoothing
WMAX 110
Tue 28 Feb 2012, 12:30pm-1:30pm

Abstract

For many inverse problems, accuracy of data is required by standard methods, yet rarely achievable in practice. In many applications, data may contain large artifacts, such as outliers caused by measurement errors, or physical phenomena not explained by the predictive model. In this setting, robust methods, i.e. methods that find reasonable results even in the face of gross errors, are an appealing alternative to pre-processing, outlier removal, or very complex modeling.

In this talk, we will discuss two applications: geophysical imaging and inference for dynamical systems. In both cases, we will show how to design robust methods by modifying the statistical error models. We can then get robust solutions by finding the maximum likelihood estimates for parameters in these modified models. In order to solve these problems quickly, optimization techniques must exploit the underlying problem structure. We will highlight this structure for both classes of applications, and present numerical results to show how
the methods work in practice.

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Department of Physics, University of Texas at Austin
Tue 28 Feb 2012, 3:00pm SPECIAL
Department Colloquium
GEOG 101
Negative Energy Transitions to Instability in Continuum Models of Matter Dynamics
GEOG 101
Tue 28 Feb 2012, 3:00pm-4:00pm

Abstract

 
pdf
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UBC
Tue 28 Feb 2012, 3:30pm
Algebraic Groups and Related Structures
Math 1101
A few words on cohomological invariants
Math 1101
Tue 28 Feb 2012, 3:30pm-4:30pm

Abstract

We continue to introduce basic ideas in Cohomological invariant theory, with a particular focus on unramified cohomology and on invariants of étale algebras.
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