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 Events
Princeton University
Fri 1 Nov 2013, 3:00pm
Department Colloquium
Earth Sciences Building Room 2012
PIMS Hugh Morris Lecture: Can We Choose Optimally? The Neural Dynamics of Decisions.
Earth Sciences Building Room 2012
Fri 1 Nov 2013, 3:00pm-4:00pm

Abstract

Each day we make many choices, often under time pressure and with poor information. How do we do this? The basic electro-chemistry of individual neurons and synapses in our brains is fairly well understood. The key problem is one of scale: how do almost a trillion neurons and many more synapses interact to sift noisy evidence and weigh it against prior knowledge?  I will describe how mathematical models, coupled with human and animal experiments, illuminate the neural mechanisms responsible for some simple decisions and actions.

The talk will draw on joint work with Fuat Balci, Rafal Bogacz, Jonathan Cohen, Philip Eckhoff, Eric Shea-Brown, Patrick Simen, Marieke van Vugt, Kong Fatt Wong-Lin and Miriam Zacksenhouse.  Research supported by NIMH and AFOSR.

Note for Attendees

There will be a reception at PIMS at 2:30pm
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Carmen Bruni
UBC
Mon 4 Nov 2013, 2:00pm
Math Education Research Reading
Math 126
Where Learning Starts? A Framework for Thinking About Lectures in University Mathematics
Math 126
Mon 4 Nov 2013, 2:00pm-3:00pm

Abstract

Carmen will present "Where learning starts? A framework for thinking about lectures in university mathematics," which can be found here.
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Mathematical Sciences, SDSU
Mon 4 Nov 2013, 3:00pm
Institute of Applied Mathematics
LSK 460
Increased Regions of Stability for a Two-Delay Differential Equation
LSK 460
Mon 4 Nov 2013, 3:00pm-4:00pm

Abstract

Delay differential equations (DDEs) are used in a number of applications. Stability analysis of DDEs can be quite complex, particularly when multiple delays occur. We examine the scalar two-delay differential equation:
 
y'(t) = Ay(t) + B y(t - 1) + C y(t - R):
 
The stability region for this DDE has some very interesting features that this talk will explore. There are four parameters, A, B, C, and R, which can be varied. The stability region can be disconnected in the BC-space though for fixed R the 3D stability surface in the ABC-parameter space is connected. One of the most intriguing features is that when R is rational, this stability surface becomes larger. We demonstrate how certain rational values of R significantly increase the stability region, then show this significance in a nonlinear application. Understanding the details of this analysis can help mathematical modelers appreciate sensitivity in their stability analysis and the complexity of numerical solutions as delays vary in a model with multiple delays.
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Colorado State
Mon 4 Nov 2013, 3:10pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Topology and combinatorics of Hilbert schemes of points on orbifolds
ESB 4127 (host: UBC)
Mon 4 Nov 2013, 3:10pm-4:10pm

Abstract

The Hilbert scheme of n points on C^2 is a smooth manifold of dimension 2n. The topology and geometry of Hilbert schemes have important connections to physics, representation theory, and combinatorics. Hilbert schemes of points on C^2/G, for G a finite group, are also smooth, and their topology is encoded in the combinatorics of partitions. When G is a subgroup of SL_2, the topology and combinatorics of the situation are well understood, but much less is known for general G. After outlining the well-understood situation, I will discuss some conjectures in the general case, and a combinatorial proof that their homology stabilizes.
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Emily Walsh
Department of Mathematics, Simon Fraser University
Tue 5 Nov 2013, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133
Alignment of optimally transported meshes
ESB 4133
Tue 5 Nov 2013, 12:30pm-2:00pm

Abstract

Solutions of partial differential equations are often highly anisotropic and have strongly directional features. Examples include PDES which have shocks and interfaces in the solution. When calculating the solutions to these PDEs it is important to use computational meshes which align themselves with features in the solution. Many adaptive mesh methods explicitly and implicitly use equidistribution and alignment, and a metric tensor M is typically used to define the desired level of anisotropy. In this talk I will describe a mesh method which combines equidistribution with optimal transport that does not require the explicit construction of a metric tensor M, although such an M always exists. I will show that this method is very effective at aligning elements along solution features including linear shocks and radially symmetric structures. Furthermore, I will provide numerical results to show this method is cheap and robust to implement, and allows solutions to be very well approximated.
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Antoine Julien
Trondheim
Tue 5 Nov 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Homeomorphisms between aperiodic tiling spaces
ESB 2012
Tue 5 Nov 2013, 3:30pm-4:30pm

Abstract

In this talk, I will give an introduction to aperiodic tilings. Usually, one studies a topological dynamical system associated to these tilings rather than one specific tiling (this is the analogue to studying a subshift rather that one single word in symbolic dynamics).
It is a natural question to ask what happens to the underlying tilings when there is a homeomorphism between tiling spaces.
The result I will present is the following: whenever two tiling spaces are homeomorphic, the complexity function is preserved up to some multiplicative constants and rescaling.
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CNRS / U. Bordeaux
Tue 5 Nov 2013, 4:00pm
Discrete Math Seminar
ESB 4133
On computing Baker and Norine's rank parameter on complete graphs
ESB 4133
Tue 5 Nov 2013, 4:00pm-5:00pm

Abstract

In 2007, Baker and Norine stated a theorem which they called a version for graphs of a Riemann-Roch theorem. In this theorem,the rank is an integer parameter defined by an optimisation among some compositions on labeling of vertices by integers. In the case of complete graphs, we provide a greedy algorithm to compute the rank in linear time. Then we study the joint distribution of the rank and the other parameter in Baker and Norine theorem. This involves objects like parking functions, numbers like the Catalan numbers, and bijections, in a framework close to the sandpile model studied by Dhar. The interest in these classical notions is renewed by the addition of seemingly new parameters (orappearing in other contexts) deduced from the analysis of our greedy algorithm.
Joint work with Robert Cori.
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UBC
Wed 6 Nov 2013, 3:00pm
Probability Seminar
ESB 2012
Self-Interacting Walk and the Gaussian field (III)
ESB 2012
Wed 6 Nov 2013, 3:00pm-4:00pm

Abstract

In the second lecture I reviewed differential forms and then related the square of a differential form to the local time of random walk.  In this lecture I will prove this result in more detail and illustrate the idea by explaining why certain integrals  concentrate on critical points even before any large deviation limit is taken.  These are cases of a theorem called the Duistermaat Heckman theorem.
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Toronto/Fields
Wed 6 Nov 2013, 3:10pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
Families of lattice polarized K3 surfaces with monodromy
ESB 4127 (host: UAlberta)
Wed 6 Nov 2013, 3:10pm-4:10pm

Abstract

The concept of lattice polarization for a K3 surface was first introduced by Nikulin. I will discuss ways in which his definition can be extended to families of K3 surfaces over a (not necessarily simply connected) base curve, with the aim of gaining control over the action of monodromy upon the Néron-Severi lattice of a general fibre. I will then present an application of this to the study of Calabi-Yau threefolds that admit fibrations by Kummer surfaces.
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Maziar Jalal
PhD Student, Mechanical Engineering Department, UBC
Wed 6 Nov 2013, 4:00pm
Fluids Lab Meeting
LSK 203
Deformation of a Liquid Drop in a Gas Stream
LSK 203
Wed 6 Nov 2013, 4:00pm-5:00pm

Abstract

The fragmentation of droplets is an essential stage of several natural and industrial applications such as fuel atomization and rain phenomena. In spite of its relatively long history, the mechanism of fragmentation is not clear yet. This is mainly due to small length and time scales as well as the non-linearity of the process. In the present study, two and three-dimensional numerical simulations have been performed to understand the early stages of the fragmentation of an initially spherical droplet. Simulations are performed in high Reynolds and a range of relatively high Weber numbers (shear breakup). To resolve the small-scale instabilities generated over the droplet, a second-order adaptive finite volume/volume of fluids (FV/VOF) method is employed, where the grid resolution is increased with the curvature of the gas-liquid interface as well as the vorticity magnitude. The study is focused on the onset and growth of interfacial instabilities. The role of Kelvin-Helmholtz instability (in surface wave formation) and Rayleigh-Taylor instability (in azimuthal transverse modulation) are shown and the obtained results are compared with the linear instability theories for zero and non-zero vorticity layers. Moreover, the analogy between the fragmentation of a single drop and a co-axial liquid jet is discussed. The current results can be used for the further development of the current secondary atomization models.
 
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SFU
Thu 7 Nov 2013, 3:30pm
Number Theory Seminar
room ASB 10908 (IRMACS - SFU)*
Darmon's program for x^p + y^p = z^r and first case solutions
room ASB 10908 (IRMACS - SFU)*
Thu 7 Nov 2013, 3:30pm-4:30pm

Abstract

Darmon has developed a program to resolve the generalized Fermat equation xp + yp = zr using Galois representations and abelian varieties of GL2 type over a totally real field. I will survey some parts of his program and point out the key difficulties which remain. Recently, numerous irreducibility criteria for the mod p representations attached to elliptic curves over totally real fields have been developed (David, Billerey, Freitas-Dieulefait, Freitas-Siksek). These are based on a technique which first appeared in Serre's 1972 Inventiones paper. I will explain how this method can be adapted to Darmon's Frey abelian varieties of GL2 type over a totally real field and thereby show that the above equation does not have any non-trivial first case solutions for p large enough compared to r a regular prime ≥ 5.

Note for Attendees

* People can attend the talk via videoconferencing in room MATH 126 at UBC.
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Yannick Sire
University of Marseille
Tue 12 Nov 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
The fractional Yamabe problem
ESB 2012
Tue 12 Nov 2013, 3:30pm-4:30pm

Abstract

A great amount of work has been dedicated in the last years to understand
problems with integral diffusion for elliptic, parabolic or hyperbolic
equations and systems. In this talk, I will describe a new Yamabe problem
based on conformally covariant elliptic operators of fractional order. I
will describe some new results on existence of metrics for the regular and
singular problems.

 

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SFU
Tue 12 Nov 2013, 4:00pm
Discrete Math Seminar
ESB 4133
Dyson-Schwinger equations and chord diagrams
ESB 4133
Tue 12 Nov 2013, 4:00pm-5:00pm

Abstract

Dyson-Schwinger equations are certain integral equations in quantum field theory which mirror the combinatorial decompositions of trees by subtrees, or of graphs by subgraphs.  At the analytic level, many cases can still be interpreted combinatorially, as expansions indexed by rooted connected chord diagrams.  I will explain this construction, talk about which cases we know and where we are going next.
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University of Warwick
Wed 13 Nov 2013, 3:00pm
Probability Seminar
ESB 2012
Random field of gradients and elasticity
ESB 2012
Wed 13 Nov 2013, 3:00pm-4:00pm

Abstract

 Random fields of gradients are a class of model systems arising in
the studies of random interfaces, random geometry, field theory, and elasticity
theory. These random objects pose challenging problems for probabilists as even
an a priori distribution involves strong correlations. Gradient fields are
likely to be an universal class of models combining probability, analysis and
physics in the study of critical phenomena. They emerge in the following three
areas, effective models for random interfaces, Gaussian Free Fields (scaling
limits), and mathematical models for the Cauchy-Born rule of materials, i.e., a
microscopic approach to nonlinear elasticity. We will outline recent results
and will discuss possible applications in nonlinear elasticity theory. If time
permits we outline the scaling to the Gaussian Free Field for non-convex
interactions.
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Ashkan Babaie, PhD Candidate
Mechanical Engineering Department, UBC
Wed 13 Nov 2013, 4:00pm
Fluids Lab Meeting
LSK 203
Evaporation-driven low Reynolds number vortices in a cavity
LSK 203
Wed 13 Nov 2013, 4:00pm-5:00pm

Abstract

The solvent casting process is a cost-effective technique with potential applications to the fabrication of microstructures such as microneedles. It involves the evaporation of a solvent from a polymer solution inside a micron scale cavity, and results in a polymeric coating on the walls of the cavity. This drying process represents a complex fluid mechanics problem that is generally associated with several flow phenomena contributing to complex flow patterns inside the fluid film. In addition to evaporation-driven flow and Marangoni flow, the velocity field also reveals single and multiple vortices generated by the creeping flow induced by evaporation. An experimental study including laser scanning microscopy and particle image velocimetry (PIV) are used to introduce and characterize the low Reynolds corner vortices that can occur during the evaporation of thin films inside microliter cavities. The observed corner vortices all show a similar unsteady behavior, in that they continuously shrink over time and finally disappear. The initial viscosity of the fluid leads to different vortex behavior during the evaporation process, as larger and more persistent vortices are generated in initially less viscous films. The presence, size and endurance of the corner vortex are highly affected by the geometry, in particular the depth of the cavity. These vortices exist at Reynolds numbers as low as Re<1e-5 indicating the absence of inertia forces; they are therefore driven by the viscous flow. However, high shear stresses caused by increasing viscosity finally destroy these vortices. Viscous flow therefore plays a curious role in this flow problem where it is necessary to generate these vortices, while it also makes them disappear.

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Connor Behan (UBC Physics) and Nishant Chandgotia (UBC Math)
Thu 14 Nov 2013, 12:30pm
Graduate Student Seminar
Math 204
Quantum Field Theory (Feynman Diagrams) // Nearest Neighbour Shifts of Finite Type
Math 204
Thu 14 Nov 2013, 12:30pm-2:00pm

Abstract

Connor:

The discovery of quanta began a revolution on how we think about the
physical world and the mathematics we use to describe it. According to
quantum mechanics, a particle that appears to have three co-ordinates (x,
y, z) will in fact have a position described by a vector in an
infinite-dimensional Hilbert space such as L^2(R^3). Quantum field theory
is an attempt to apply the same principles to a system where the number of
classical degrees of freedom is already infinite. We will see that this
allows the description to be compatible with many phenomena from special
relativity. Because of the need for a much larger Hilbert space,
calculations in quantum field theory can be difficult to carry out, even
numerically. This talk will work toward a derivation of the method of
Feynman diagrams including a discussion of what these famous diagrams can, and cannot do.

Nishant:

Nearest neighbour shifts of Finite Type are system of constrained configurations on the $\Z^d$ lattice which arise in numerous contexts,
e.g. probability, data storage, smooth dynamics and statistical mechanics.
After providing some motivation, we shall try to explore how things change when we move up in dimensions. 



Note for Attendees

Pizza and pop will be provided during the break between the talks.





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UBC
Thu 14 Nov 2013, 3:00pm
Topology and related seminars
ESB 4133
Homotopy Colimits of Classifying Spaces of Abelian Groups
ESB 4133
Thu 14 Nov 2013, 3:00pm-4:00pm

Abstract

Given a finite group G, homotopy colimit of the classifying spaces of its abelian subgroups capture information about the commutativity in the group. For the class of extraspecial 2-groups of rank greater than 2 these colimits are not of the homotopy type of a K(\pi,1) space. The main ingreadient in the proof is the calculation of the fundamental group. Another natural question is the complex K-theory of these homotopy colimits, which can be computed modulo torsion.
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SFU
Thu 14 Nov 2013, 3:30pm
Number Theory Seminar
room ASB 10908 (IRMACS - SFU)*
Invisible Sha[4]
room ASB 10908 (IRMACS - SFU)*
Thu 14 Nov 2013, 3:30pm-4:30pm

Abstract

Mazur observed that for a lot of elliptic curves E with non-trivial elements in Sha(E/Q)[n], one can find another elliptic curve E' that is n-congruent to E and for which the corresponding element in H^1(Q,E'[n]) lies in the image of the Mordell-Weil group of E'. Such an element in Sha is said to be made visible by E'.
 
It was since proved that for n=2,3, one can always find such an E', both when the n-congruence preserves Weil-pairing and when it inverts it. For given E and n=4, the question boils down to deciding if a certain K3 surface has a rational point. In joint work with Tom Fisher, we have been able to finally find equations for these K3 surfaces, which allows us to determine visibility computationally in specific cases.

Note for Attendees

* People can attend the talk via videoconferencing in room MATH 126 at UBC.
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Bernd Milkereit, 2013-14 CSEG Distinguished Lecturer
University of Toronto
Thu 14 Nov 2013, 4:00pm SPECIAL
One Time Event
Earth Sciences Bldg. (ESB) Room 5104
UBC-Seismic Laboratory for Imaging & Modeling, EOAS Colloquium: Seismic Imaging in the Presence of Strong Contrasts: How Forgetful are Seismic Waves?
Earth Sciences Bldg. (ESB) Room 5104
Thu 14 Nov 2013, 4:00pm-5:00pm

Details

This seminar may be of interest to mathematicians and is included in the Mathematics listing of events on behalf of the Earth & Ocean Sciences Department.

Seismic imaging is an important geophysical tool for delineating and monitoring the earth’s subsurface structure and its oil, gas and mineral resources. Owing to the earth’s heterogeneity, such subsurface structures exist at different scales (sizes) with lateral and vertical variations in physical properties such as contrasts in bulk and shear moduli, and densities. Over the past decade, seismology entered a new era. Solving elastic and visco-elastic wave equations on large supercomputers, accurate and complete simulations for heterogeneous 3D earth models became a reality – replacing exact solutions for layered earth models. Seismic methods illuminate subsurface structures using compressional and shear waves. Recorded signal at surface and borehole seismic sensor locations arise from reflection, refraction, transmission, scattering and attenuation of elastic waves at lithological contacts, structural boundaries and the Earth's free surface, where abrupt and


Bernd Milkereit is the Teck Chair of Exploration Geophysics at the Department of Earth Sciences of the University of Toronto (since 2001). For more than 30 years, Bernd has worked at the intersection between mineral resources and exploration seismology. He carried out research projects on coal and groundwater before moving into hardrock seismic imaging and exploration for deep mineral deposits in the crystalline crust. He maintains a strong interest in international scientific drilling projects. Previous to his current position Bernd was a research scientist the Geological Survey of Canada (1985-1996) and professor of geophysics at Kiel University, Germany (1996-2001).

 
 
 

Note for Attendees

Anyone who wishes to meet with Dr. Milkereit during his visit here, please contact Miranda Joyce (mjoyce@eos.ubc.ca) or Brendan Smithyman (bsmithyman@eos.ubc.ca).
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Laurent Charette
UBC
Mon 18 Nov 2013, 2:00pm
Math Education Research Reading
Math 126
Twenty Terrible Reasons for Lecturing
Math 126
Mon 18 Nov 2013, 2:00pm-3:00pm

Abstract

Laurent will lead a discussion on Twenty Terrible Reasons for Lecturing: http://www.brookes.ac.uk/services/ocsld/resources/20reasons.html
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School of Earth and Ocean Sciences, University of Victoria
Mon 18 Nov 2013, 3:00pm
Institute of Applied Mathematics
LSK 460
Pipelines, Politics and Climate Science (IAM Distinguished Alumni Lectures)
LSK 460
Mon 18 Nov 2013, 3:00pm-4:00pm

Abstract

The reality of global warming has long been accepted within the scientific community, yet it remains a hotly debated topic at the political and social level.  Why? Is it because the ultimate effects of global warming will not be felt within our lifetime? Do we feel little responsibility for future generations?
 
This talk will present historical foundations of the science of global warming.  The range of projections of climate change over the next century will be summarized and the public confusion arising from the media portrayal of the science and its entry into the political arena will be discussed.  A review will also be given as to how potential Canadian oil and gas production as well as international policy options fit within the framework of necessary actions required to reduce greenhouse gas emissions.
 
The technological solutions to mitigate global warming exist, although price and behavioural barriers to their introduction are present.  As such, there has been a tendency in Canada, and more recently in BC, to entrench ourselves in the idea that our long-term economic prosperity lies within our continued export on fossil fuel extraction. I conclude the presentation with the suggestion that should society chose to deal with global warming, there is the potential to enter an age of creativity and innovation unlike any it has experienced before.

Note for Attendees

Refreshments start 15 minutes before the talk in the IAM Lounge, Room 306 of the LSK building.
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San Diego
Mon 18 Nov 2013, 3:10pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
The Chern classes of the Verlinde bundle
ESB 4127 (host: UBC)
Mon 18 Nov 2013, 3:10pm-4:10pm

Abstract

The Verlinde bundles over the moduli space M_g of smooth curves have as fibers spaces of generalized theta functions i.e., spaces of global sections of determinant line bundles over moduli of parabolic bundles. I will discuss a formula for the Chern classes of the Verlinde bundles, as well as extensions over the compactification \overline M_g.
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Stefan Mendez-Diez
UAlberta
Mon 18 Nov 2013, 3:10pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
Geometrization of N-Extended 1-Dimensional Supersymmetry Algebras
ESB 4127 (host: UAlberta)
Mon 18 Nov 2013, 3:10pm-4:10pm

Abstract

The problem of classifying off-shell representations of the $N$-extended one-dimensional super Poincar\'{e} algebra is closely related to the study of a class of decorated graphs known as Adinkras. We will discuss how these combinatorial objects possess a form of emergent supergeometry: Adinkras are equivalent to very special super Riemann surfaces with divisors. The method of proof critically involves Grothendieck's theory of "dessins d'enfants'', work of Cimasoni-Reshetikhin expressing spin structures on Riemann surfaces via dimer models, and an observation of Donagi-Witten on parabolic structure from ramified coverings of super Riemann surfaces.
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Fred Roosta
Department of Computer Science, UBC
Tue 19 Nov 2013, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133
Implicit matrix trace estimators: improved theory with application to PDE inverse problems with many measurements
ESB 4133
Tue 19 Nov 2013, 12:30pm-1:30pm

Abstract

This talk is concerned with Monte-Carlo methods for the estimation of the trace of an implicitly given matrix A, where the matrix information is only available through matrix-vector products. The need to estimate the trace of implicit matrices arises in many applications, where often A is symmetric positive semi-definite (SPSD). Thus, theoretical studies of accuracy and efficiency of these methods are very important. In order to set the scene, we initially present an application of such trace estimators which involves efficient stochastic methods for solving PDE-constrained inverse problems with many measurements.

The standard approach for estimating the trace of an implicit matrix involves averaging the quadratic forms of A with random vector realizations from a suitable probability distribution. We demonstrate the success of such stochastic methods in reducing the computational complexity of large scale inverse problems. We then derive new and improved theoretical results bounding the number of matrix-vector products required in order to guarantee a probabilistic bound on the relative error of the trace estimation. Bounds are derived for Rademacher (Hutchinson), Gaussian and uniform unit vector (with and without replacement) probability distributions. They provide some guidance in deciding which distribution to employ for a given application.


Note for Attendees

Pizza and pop will be served.
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Dong Li
UBC
Tue 19 Nov 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
On the norm inflation of Incompressible Euler in borderline spaces
ESB 2012
Tue 19 Nov 2013, 3:30pm-4:30pm

Abstract

 
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University of Vermont
Tue 19 Nov 2013, 4:00pm
Discrete Math Seminar
ESB 4133
Embedding complete graphs with every triangle a face
ESB 4133
Tue 19 Nov 2013, 4:00pm-5:00pm

Abstract

A common problem is to embed the complete graph on a surface so that every face is a triangle. To be perverse, suppose that we require that every triangle is a face. Let K^{(n-2)/2} denote the complete graph of order n where every pair of vertices are joined by (n-2)/2 parallel edges. For every even n at least 6 we construct a triangular embedding of this multigraph into both orientable and non-orientable surfaces such that any three vertices form a face. We give many other related results.
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University of Warwick
Wed 20 Nov 2013, 3:00pm
Probability Seminar
ESB 2012
Helffer-Sjoestrand random walk representation
ESB 2012
Wed 20 Nov 2013, 3:00pm-4:00pm

Abstract

 In the talk we discuss a recent common field in analysis and probability, the so-called Ginzburg-Landau interface models. In particular we
outline standard techniques as the Helffer-Sjoestrand PDE representation and relate them to the random field of gradients. An application of the
Helffer-Sjoestrand representation to non-convex energy functions leads to random walks having sparsely distributed negative conductances. The latter
problem is currently under intensive study and analysis and we will discuss different strategies. If time permits we will present a large deviation result
for random walks weights.
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University of Victoria
Thu 21 Nov 2013, 3:00pm
Topology and related seminars
ESB 4133
A colored operad for string link infection
ESB 4133
Thu 21 Nov 2013, 3:00pm-4:00pm

Abstract

Budney recently constructed an operad which encodes splicing of knots and proved a theorem decomposing the space of (long) knots over this operad. Infection of knots (or links) by string links is a generalization of splicing from knots to links and is useful for studying concordance of knots. In joint work with John Burke, we have constructed a colored operad that encodes this infection operation. This operad captures all the relations in the 2-string link monoid. We can also show that a certain subspace of 2-string links is freely generated over a suboperad of our infection colored operad by its subspace of prime links.
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University of Wisconsin, Madison
Thu 21 Nov 2013, 3:30pm
Number Theory Seminar
room MATH 126
Borcherds products and their CM values
room MATH 126
Thu 21 Nov 2013, 3:30pm-4:30pm

Abstract

In 1990s, in the process of proving the famous Moonshine conjecture, Borcherds discovered a new way to produce modular forms on a Shimura varieties of orthogonal type. Modular curves, Hilbert modular surfaces, Siegel 3-folds are all low dimensional Shimura varieties of this type. His modular form, typically called Borcherds product, has a very distinguished feature—its divisor is known. He later gave a more natural construction of these modular forms using "regularized theta lifting". This construction makes the computation of its values at CM points interesting, and gives some cool factorization formula for some very big integers. It can also be extended to prove high dimensional analogue of Gross–Zagier formula. In this talk, I will explain this story.
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Vanessa Radzimski
UBC
Mon 25 Nov 2013, 2:00pm
Math Education Research Reading
Math 126
Lesson Plays: Planning Teaching versus Teaching Planning
Math 126
Mon 25 Nov 2013, 2:00pm-3:00pm

Abstract

Vanessa will lead a discussion on "Lesson Plays: Planning Teaching versus Teaching Planning" by our colleagues at SFU: http://www.peterliljedahl.com/wp-content/uploads/JA-FLM-2009.pdf
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Research Institute for Technical Physics and Materials Science, Hungarian Academy of Sciences, Budapest, Hungary
Mon 25 Nov 2013, 3:00pm SPECIAL
Institute of Applied Mathematics
LSK 460
Evolutionary Potential Games (IAM-PIMS Distinguished Colloquium)
LSK 460
Mon 25 Nov 2013, 3:00pm-4:00pm

Abstract

For the potential games there exists a potential function derived from the payoff variation of those players who modify their strategies. First we survey the general features of these games and discuss the evaluation of potential for some cases.  Multi-agent spatial models will be constructed from pair interactions and studied for a specific evolutionary rule when these systems evolve into the Boltzmann statistics and become equivalent to the Ising type models used widely in solid state and statistical physics.  Finally we briefly discuss the spatial version of a counter-example (matching pennies on chessboard).

Note for Attendees

Refreshments start 15 minutes before the talk in the IAM Lounge, Room 306 of the LSK building.
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Carnegie Mellon
Tue 26 Nov 2013, 3:00pm SPECIAL
Discrete Math Seminar
ESB 4133
A Proof of the Manickam-Miklos-Singhi Conjecture for Vector Spaces
ESB 4133
Tue 26 Nov 2013, 3:00pm-4:00pm

Abstract

 Title: A Proof of the Manickam-Miklos-Singhi Conjecture for Vector Spaces

Abstract: Let V be an n-dimensional vector space over a finite field.
Assign a real-valued weight to each 1-dimensional subspace in V so that
the sum of all weights is zero. Define the weight of a subspace S of V to
be the sum of the weights of all the 1-dimensional subspaces it contains.
We prove that if n >= 3k, then the number of k-dimensional subspaces in V
with nonnegative weight is at least the number of k-dimensional subspaces
in V that contain a fixed 1-dimensional subspace. This result verifies a
conjecture of Manickam and Singhi from 1988.

Joint work with Ghassan Sarkis (Pomona College) and Shahriar Shahriari
(Pomona College).
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University of Alberta
Tue 26 Nov 2013, 4:00pm
Algebraic Groups and Related Structures
MATH 126
Lower bounds on the essential dimension for adjoint groups in characteristic 2
MATH 126
Tue 26 Nov 2013, 4:00pm-5:00pm
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Matt Folz, Mathematics Graduate Alumni
Yammer
Tue 26 Nov 2013, 4:00pm SPECIAL
One Time Event
AERL 120
Data Science Seminar: Data and Decision-Making at Yammer
AERL 120
Tue 26 Nov 2013, 4:00pm-5:00pm

Details

The Harvard Business Review recently called data scientist the 'sexiest job of the 21st century'.  As a data scientist at Yammer, I'll give a brief overview of what data science is and what the day-to-day life of a data scientist looks like.  I'll talk about some of the challenges present in our data, and try to give some insight into how we use data to better understand our users and make decisions at Yammer.

About the speaker:
Matthew is currently a data scientist at Yammer.  Previously, he completed a Ph.D in mathematics at UBC, studying probability theory, and was a Fellow in the Insight Data Science Fellows Program.

About Yammer:
Yammer is an Enterprise Social Network that brings together people, conversations, content, and business data in a single location.  Founded in 2008, Yammer was acquired by Microsoft Corporation in 2012 and is now part of the Microsoft Office Division.

There won't be any statistical background required, and Matthew will stay after the talk to answer any questions that people might have about data science/Yammer. 
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UBC
Wed 27 Nov 2013, 3:00pm
Probability Seminar
ESB 2012
Random walks on planar graphs via circle packings
ESB 2012
Wed 27 Nov 2013, 3:00pm-4:00pm

Abstract

 I will describe two results concerning random walks on planar graphs and
the connections with Koebe's circle packing theorem (which I will not
assume any knowledge of):
1. A bounded degree planar triangulation is recurrent if and only if the set
of accumulation points of its circle packing is a polar set (that is, has
zero logarithmic capacity). This extends a result of He and Schramm who
proved recurrence (transience) when the set of accumulation points is empty
(a closed Jordan curve). Joint work with Ori Gurel-Gurevich and Juan Souto.
2. The Poisson boundary (the space of bounded harmonic functions) of a
transient bounded degree triangulation of the plane is characterized by the
topological boundary obtained by circle packing the graph in the unit disk.
In other words, any bounded harmonic function on the graph is the harmonic
extension of some measurable function on the boundary of the unit disc.
Joint work with Omer Angel, Martin Barlow and Ori Gurel-Gurevich.
 
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Fields
Wed 27 Nov 2013, 3:10pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
Integrality of relative BPS state counts of toric Del Pezzo surfaces
ESB 4127 (host: UAlberta)
Wed 27 Nov 2013, 3:10pm-4:10pm

Abstract

This is joint work with Tony Wong and Gjergji Zaimi. Relative BPS state counts for log Calabi-Yau surface pairs were introduced by Gross-Pandharipande-Siebert and conjectured to be integers. For toric Del Pezzo surfaces, a proof of this conjecture will be presented.
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Nader Noroozi
Mech. Eng. Dep. UBC
Wed 27 Nov 2013, 4:00pm
Fluids Lab Meeting
LSK 203
Numerical Simulation and Flow Analysis of Structured Fluids: Nematic Liquid Crystals
LSK 203
Wed 27 Nov 2013, 4:00pm-5:00pm

Abstract

 Liquid crystals are known for their anisotropic characteristics, which lead to a preferred orientation of their molecules in the vicinity of solid surfaces. The ability of liquid crystalline materials to form ordered boundary layers with good load-carrying capacity and outstanding lubricating properties has been widely demonstrated. In order to study the advantages of implementing liquid crystals as lubricants, the steady state / time transient isothermal flow of nematic liquid crystals between two concentric / eccentric cylinders and in planar Couette geometries were studied numerically. To consider the influence of the microstructure formation / evolution on the macro-scale attributes of the flow; the Leslie-Ericksen and Landau-de Gennes theories were employed.
 
The simplicity of Leslie-Ericksen theory in capturing the orientational alignment angle of the molecules makes it a viable candidate for modelling the flow of flow-aligning nematic liquid crystals. On the other hand, the Landau-de Gennes nematodynamics equations are well suited for predicting texture formation since defects and disclinations are non-singular solutions of the governing equations. The Landau-de Gennes theory for the liquid crystalline microstructure along with continuity and momentum equations were solved simultaneously using General PDE and Laminar Flow modules of COMSOL Multiphysics. The investigation of flow characteristics and orientation of liquid crystalline molecules for different rotational shear rates and anchoring angles at the boundaries were presented. Furthermore, nucleation and evolution of singularities in texture of the liquid crystalline materials were tracked over the simulation time. Moreover, alterations in the macro-scale attributes of the flow such as velocity profile, pressure distribution and the first normal stress difference along with the evolution of defects were studied inside the liquid crystalline domain.
 
The implementation of Landau-de Gennes nematodynamic governing equations for LCs’ flow simulations offered an insight in application of these materials as lubricants. It was shown the LCs could provide protection against the wearing mechanism by forming a shielding layer in the vicinity of solid surfaces. Three-dimensional simulations of a simplified prosthetic hip joint suggested that liquid crystalline materials should be considered as potential bio-lubricants.
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IAM, UBC
Thu 28 Nov 2013, 12:30pm
Graduate Student Seminar
Math 204
Modelling of a Magnetized Target Fusion Reactor
Math 204
Thu 28 Nov 2013, 12:30pm-1:30pm

Abstract

 Nuclear fusion is a promising source of clean energy for the future, but designing an apparatus capable of fusing plasma and yielding a net energy gain has yet to be accomplished. This talk is aimed at providing an introduction to the basic physics of fusion, and outlining the methods and results obtained in analyzing the fusion reactor design of a local Canadian fusion research company.

Note for Attendees

 Pizza and pop will be provided.
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Sandra Merchant
Thu 28 Nov 2013, 12:30pm
Lunch Series on Teaching & Learning
MATH 126
Effective Use of WeBWorK in our Courses
MATH 126
Thu 28 Nov 2013, 12:30pm-1:30pm

Abstract

This lunch series session will begin with a brief overview of the online homework system WeBWorK, and presentation and discussion of the large quantity of student feedback we have collected about WeBWorK through student surveys.  This will be followed by an open discussion on the most effective ways to implement WeBWorK, and the benefits and challenges involved in using this system.  We particularly encourage instructors who have past experience with WeBWorK to join us, so you can share your wisdom with your colleagues, as well as future instructors who are considering using this system next term. 

As usual, pizza and pop will be provided.

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University of Michigan
Thu 28 Nov 2013, 3:00pm
Topology and related seminars
ESB 4133
Mirror symmetry and modular forms
ESB 4133
Thu 28 Nov 2013, 3:00pm-4:00pm

Abstract

Traditionally, we use mirror symmetry to map a difficult problem (A-model) to an easier problem (B-model). Recently, there is a great deal of activities in mathematics to understand the modularity properties of Gromov-Witten theory, a phenomenon suggested by BCOV almost twenty years ago. Mirror symmetry is again used in a crucial way. However, the new usage of mirror does not map a difficult problem to easy problem. Instead, we make both side of mirror symmetry to work together in a deep way. I will explain this interesting phenomenon in the talk. First we will give an overview of the entire story and then we will focus on the appearance of quasi-modularity.
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Pierre Youssef
U. Alberta
Thu 28 Nov 2013, 3:00pm SPECIAL
PIMS Seminars and PDF Colloquiums
Math Annex Bldg., Room 1118
PIMS-Math Analysis Seminar: Extracting a large well-conditioned block inside a matrix
Math Annex Bldg., Room 1118
Thu 28 Nov 2013, 3:00pm-4:00pm

Abstract

Given U an n×m matrix, the aim is to extract a large number of linearly independent columns of U and estimate the smallest and the largest singular value of the restricted matrix. For that, we give two deterministic algorithms: one for a normalized version of the restricted invertibility principle of Bourgain-Tzafriri, and one for the norm of coordinate restriction problem due to Kashin-Tzafriri. Merging the two algorithms, we are able to extract a well-conditioned block inside U, improving a previous result due to Vershynin. We give some applications of this result to the study of contact points of a convex body.
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Myrto Mavraki
UBC
Thu 28 Nov 2013, 3:30pm
Number Theory Seminar
room MATH 126
Variation of the canonical height for a family of rational maps
room MATH 126
Thu 28 Nov 2013, 3:30pm-4:30pm

Abstract

Let ≥ 2 be an integer and let ft(z) := (zd+t)/z be a family of rational maps indexed by an algebraic number t. We study the variation of the canonical heights for this particular family. This is joint work with Dragos Ghioca.
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University of Michigan
Fri 29 Nov 2013, 3:00pm
Department Colloquium
MATX 1100
Searching for quantum symmetry
MATX 1100
Fri 29 Nov 2013, 3:00pm-4:00pm

Abstract

 During the last thirty years, there have been a great deal of interactions between mathematics and physics. During these interactions, mathematicians are often impressed by the magic formulas and conjectures physicists can come up with. At the same time, it is frustrating that we can not come up with similar formulas and conjectures on our own. In this talk, I will illustrate how to apply a simple physical principal (quantization principal) to discover several new areas of mathematics.

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