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 Events
University of Michigan
Mon 6 Jan 2014, 4:00pm SPECIAL
Department Colloquium
MATX 1100
Low-dimensionality in mathematical signal processing
MATX 1100
Mon 6 Jan 2014, 4:00pm-5:00pm

Abstract

Natural images tend to be compressible, i.e., the amount of information needed to encode an image is small. This conciseness of information -- in other words, low dimensionality  of the signal -- is found throughout a plethora of applications ranging from MRI to quantum state tomography. It is natural to ask: can the number of measurements needed to determine a signal be comparable with the information content?  We explore this question under modern models of low-dimensionality and measurement acquisition.
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University of Michigan
Tue 7 Jan 2014, 3:00pm SPECIAL
One Time Event
MATH 126 Seminar Room
Data Science Seminar: 1-bit compressed sensing, sparse binary regression, and random hyperplane tessellations
MATH 126 Seminar Room
Tue 7 Jan 2014, 3:00pm-4:00pm

Details

Abstract: 1-bit compressed sensing combines the dimension reduction of compressed sensing with extreme quantization -- only the sign of each linear measurement is retained and thus the signal is truly compressed. Is this sufficient information to reconstruct the signal?

Behind this question lies a geometric question about random hyperplane tessellations. Picture a subset K of the unit sphere, as in the continents on our planet. Now slice the sphere in half with a hyperplane, and then slice it several times more, thus cutting the set K into a number of sections. How many random hyperplanes are needed to ensure that all sections have small diameter? How is the geodesic distance between two points in K related to the number of hyperplanes separating them? We show that a single geometric parameter, the mean width of K, governs the answers to these questions. This approach to binary data gives a new perspective on related statistical models such as logistic regression.
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Ehsan Behzadfar
PhD student, Chemical and Biological Engineering Department, UBC
Wed 8 Jan 2014, 4:00pm
Fluids Lab Meeting
LSK 203
Flow properties of reservoir oils in the presence of Carbon dioxide
LSK 203
Wed 8 Jan 2014, 4:00pm-5:00pm

Abstract

Global warming is one of the serious issues facing mankind today. In order to resolve the issue, numerous options have been proposed among which carbon dioxide (CO2) storage underground is the most promising method in hand. However, this method does not sound appealing to industry because of its non-profit nature. CO2 Enhanced Oil Recovery (CO2-EOR) is an oil extraction technique which can be combined with CO2 storage to not only increase the amount of recovered oil, but also store a huge amount of CO2 deep underground. In CO2-EOR, carbon dioxide acts as a solvent to reduce the oil viscosity and hence increase the oil production. However, the accurate impact of CO2 on the oil flow behavior needs to be investigated more thoroughly. In this presentation, the experimental and theoretical study of the reservoir oils flow properties in the absence and presence of CO2 will be discussed. Moreover, a novel methodology in measuring the diffusion coefficient in the gas-oil systems is presented.
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University of Cambridge
Thu 9 Jan 2014, 3:30pm
Probability Seminar
MATH 203
Conformal invariance of isoradial dimers
MATH 203
Thu 9 Jan 2014, 3:30pm-4:30pm

Abstract

 An isoradial graph is a planar graph in which each face is inscribable into a circle of the same radius. We study perfect matchings on a bipartite isoradial graph, obtained from the union of an isoradial graph and its interior dual graph. Using the isoradial graph to approximate a simply-connected domain bounded by a simple closed curve, by letting the mesh size go to zero, we prove that in the scaling limit, the distribution of height is conformally invariant and converges to a Gaussian free field.
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SISSA
Fri 10 Jan 2014, 2:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
Framed sheaves on root stacks and gauge theory on ALE spaces
ESB 4127 (host: UAlberta)
Fri 10 Jan 2014, 2:00pm-3:00pm

Abstract

Abstract: We use stacky compactifications of ALE spaces and a theory of framed sheaves on them to give rigorous definitions of partition functions for supersymmetric gauge theories on ALE spaces. We use the notion of root stack to be able to incorporate instantons on the ALE spaces that have nontrivial holonomy at infinity. Joint work with F. Sala, and M. Pedrini and R. Szabo.
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U. of Cambridge
Fri 10 Jan 2014, 3:00pm
Department Colloquium
MATX 1100
Critical parameters of lattice models
MATX 1100
Fri 10 Jan 2014, 3:00pm-4:00pm

Abstract

A lattice model is a probability measure on configurations of a graph parametrized by a continuous variable. The critical parameter is the parameter where the phase transition occurs, i.e., when the macroscopic properties of a lattice model change sharply with respect to the parameter. I will talk about three different lattice models including percolation, Ising model and self-avoiding walk, as well as recent progress on identifying the exact values of their critical parameters or bounding their critical parameters. Part of the talk is based on joint work with Geoffrey Grimmett.
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Sat 11 Jan 2014, 9:00am SPECIAL
One Time Event
Math 100
Qualifying Exams - Analysis
Math 100
Sat 11 Jan 2014, 9:00am-12:00pm

Details

Lunch provided for those writing the Analysis exam only, in Math 125.
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Sat 11 Jan 2014, 1:00pm SPECIAL
One Time Event
Math 100
Qualifying Exams - Algebra
Math 100
Sat 11 Jan 2014, 1:00pm-4:00pm

Details


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Sat 11 Jan 2014, 1:00pm SPECIAL
One Time Event
Math 100
Qualifying Exams - Differential Equations
Math 100
Sat 11 Jan 2014, 1:00pm-4:00pm

Details


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Northwestern University
Sun 12 Jan 2014, 3:10pm
CRG Geometry and Physics Seminar
ESB4127
TBA
ESB4127
Sun 12 Jan 2014, 3:10pm-4:10pm

Abstract

 
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UBC
Mon 13 Jan 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Topics on algebraic cobordism
ESB 4127 (host: UBC)
Mon 13 Jan 2014, 3:00pm-4:00pm

Abstract

We will discuss some topics on the theory of algebraic cobordism from joint work with Kalle Karu. We will explain the computation via envelopes and the descent exact sequence. We review the relation of algebraic cobordism with Chow and K-theory. We will also discuss an extension of the cobordism rings of smooth varieties to the singular setting via a well-behaved operational bivariant theory. As an example, we describe the operational equivariant cobordism of toric varieties.
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Courant Institute
Mon 13 Jan 2014, 3:00pm
Institute of Applied Mathematics
LSK 460
Kinetics of particles with short-range interactions
LSK 460
Mon 13 Jan 2014, 3:00pm-4:00pm

Abstract

Nature has solved the problem, and now engineers would like to -- how can we design small components to spontaneously form more complicated structures? To answer this question theoretically requires a way to describe the configuration space and assembly pathways of components with given interactions. For many systems of interest (e.g. colloids) these interactions are very short-ranged compared to the size of the components, so traditional approaches to energy landscapes struggle to capture the relevant dynamics. We propose a new framework to look at particles with short-ranged interactions and illustrate with several applications, such as computing the free energy landscape and transition rates for clusters of spheres, experimentally measuring the hydrodynamic interactions between colloids, and enumerating rigid packings of hard spheres.

Note for Attendees

Refreshments will be served before the colloquium in the IAM Lounge.
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UC Berkeley
Mon 13 Jan 2014, 4:00pm
Department Colloquium
Math Annex (MATX) 1100
Intertwinings, wave equations and growth models
Math Annex (MATX) 1100
Mon 13 Jan 2014, 4:00pm-5:00pm

Abstract

We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal.

Note for Attendees

Refreshments will be served at 3:45 pm in the MATH 125 Lounge.
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Departments of Mathematics and Earth and Ocean Sciences, UBC
Tue 14 Jan 2014, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133
On Programming Languages for Scientific Computing
ESB 4133
Tue 14 Jan 2014, 12:30pm-2:00pm

Abstract

 Advances in programming languages have changed the field of scientific computing in the past decades. Especially Mathworks' Matlab with its easy-to-use interface and huge potential for simulation, linear algebra, optimization, and visualization have dramatically changed the way we explore and teach numerical methods. While Mathworks has been dominating the market for scientific computing software almost unrivaled for quite a while, different open-source projects provide increasingly attractive alternatives today. 

In a non-technical fashion, this talk will review Mathworks' contributions, discuss some of its limitations, and summarize first experiences with the open source software Python and Julia. 
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Wes Maciejewski
Tue 14 Jan 2014, 2:00pm
Mathematical Education
Math 126
The Aims of Education
Math 126
Tue 14 Jan 2014, 2:00pm-3:00pm

Abstract

We begin this semester with Alfred North Whitehead's The Aims of Education. Though it was written in 1929, it is no less relevant today as it was then. The essay may be found here: http://ayman980.com/class/Readings/The%20Aims%20of%20Education%20Alfred%20Whitehead.pdf
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Berkeley
Tue 14 Jan 2014, 3:30pm
Probability Seminar
ESB 2012
Large deviations for diffusions interacting through their ranks
ESB 2012
Tue 14 Jan 2014, 3:30pm-4:30pm

Abstract

Systems of diffusion processes (particles) with rank-based interactions have been studied heavily due to their importance in stochastic portfolio theory and the intriguing relations with particle systems appearing in statistical physics. We study the behavior of this particle system as the number of particles gets large. By obtaining a large deviations principle (LDP), we will show that the limiting dynamics can be described by a porous medium equation with convection, whereas paths of finite rate are given by solutions of appropriately tilted versions of this equation. This is the first instance of an LDP for diffusions interacting both through the drift and the diffusion coefficients. Based on joint work with Amir Dembo, S. R. Srinivasa Varadhan and Ofer Zeitouni.
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Dr. Egor Dontsov
Postdoctoral fellow, Mathematics Department, UBC
Wed 15 Jan 2014, 4:00pm
Fluids Lab Meeting
LSK 203
Numerical simulations of proppant transport in hydraulic fractures
LSK 203
Wed 15 Jan 2014, 4:00pm-5:00pm

Abstract

Hydraulic fracturing (HF) is a process where the material, such as rock, is cracked by a pressurized fluid. Among many applications of HF, the most common use is the stimulation of production from oil and gas wells. To prevent fracture from closing after the pressure is reduced, the propping agents, such as sand, are pumped together with the fracturing fluid. The problems of fluid-driven fracture propagation and flow of the suspensions have been studied extensively, but not many works combine both and address the fracturing caused by a slurry. To fill the gap, the aim of this study is to develop a computational model for calculating the propagation of a fracture induced by the mixture of the viscous fluid mixed with the spherical particles. First, the empirical constitutive law for the slurry is used to obtain the solution for the steady flow of the viscous fluid mixed with spherical particles in a channel. This solution is then used to formulate the conservation laws for the slurry and the particles, which govern the propagation of hydraulic fractures and the proppant transport inside them. The developments are applied to two fracture geometries -- Khristianovich-Zheltov-Geertsma-De Klerk (KGD) and pseudo-3D (P3D). Numerical simulations show that the proposed method allows to capture the proppant plug formation and growth, as well as the gravitational settling for both geometries. Dimensionless parameter, whose magnitude reflects the intensity of the settling, is introduced for the P3D fracture. Arising counterintuitive consequence, stating that the viscosity of the fluid can not directly affect the settling extent, is verified through the numerical examples.



Dr. Dontsov received his undergraduate degree in Physics from Novosibirsk State University in Russia, 2008. Then, in 2012, he graduated with PhD degree in Civil Engineering (and minor in Math) from the University of Minnesota, USA. During his PhD studies, he was doing nonlinear acoustic wave propagation from both theoretical and computational points of view with applications to medical imaging. After a short postdoc at the University of Minnesota, he joined Professor Anthony Peirce (Dept. of Math, UBC) in April 2013 and started to work on hydraulic fracturing.
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Imperial College
Thu 16 Jan 2014, 3:00pm SPECIAL
Mathematical Biology Seminar
ESB 2012
Pathogen phylogenies reveal ecological competition
ESB 2012
Thu 16 Jan 2014, 3:00pm-4:00pm

Abstract

 Ecological competition between strains of a pathogen occurs when strains compete for hosts -- either for susceptible hosts, host resources during co-infection, or the ability to re-infect hosts. Competition is important because when strains compete with each other, intervening against only some of them can pave the way for rises in others. This has happened, for example, with the introduction of polyvalent vaccines against Streptococcus pneumoniae. However, detecting ecological competition between strains of an infection is very challenging, because competition is by its nature revealed over relatively long periods of time and is a population-level phenomenon which we would not expect to observe in small-scale studies. Even population-level dynamical (ODE) models, which are frequently used in such situations, are hard to formulate and calibrate. Indeed, such models often make hidden assumptions about competition, rather than aiding in its estimation. I have therefore been motivated to ask: can sequence data for pathogens allow us to detect ecological competition? Large and rich datasets of pathogen gene sequences are now available, due to the development of next-generation sequencing; perhaps they can be of assistance if appropriately linked to models with and without competition. Here, I present a dynamical model in which there is a competition parameter which ranges continuously from 0 (where pathogen strains are independent of each other) to 1 (where competition is complete, and strain dynamics show competitive exclusion). It predicts that the branching rates in phylogenies for competing strains should be anti-correlated. A stochastic implementation of the model gives rise to pathogen phylogenies that are quantitatively different, both in their structures and their branch lengths, from phylogenies without competition. This leads to a distinct profile for a phylogeny under ecological competition: such trees have high imbalance early in the tree, greater topological distances from the root to the tips, lower widths and a characteristic skew in inter-branch distances, among other properties. I analyse a phylogeny of within-host HIV sequences and show that it fits the profile of ecological competition. I conclude with a discussion of other organisms and future directions for this work. 

Note for Attendees

 Refreshments at PIMS (ESB 4th floor) from 2.40 or so.
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UBC
Thu 16 Jan 2014, 3:30pm
Number Theory Seminar
room MATH 126
A stronger reformulation of Schmidt's strong subspace theorem in dimension two
room MATH 126
Thu 16 Jan 2014, 3:30pm-4:30pm

Abstract

Wolfgang Schmidt's Strong Subspace Theorem is a less well-known generalisation of his Subspace Theorem, and has not been studied much since its formulation in 1980. It is a result about integer points in parallelepipeds whose successive minima satisfy a certain condition. Thus, unlike the Subspace Theorem and its other generalisations, it falls within the field of the geometry of numbers.
 
This self-contained talk reintroduces the Strong Subspace Theorem and describes some new preliminary results, including a stronger reformulation of the theorem in dimension two.
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Imperial College
Fri 17 Jan 2014, 3:00pm
Department Colloquium
MATX 1100
Sequence data and the ecology of pathogens: new data, new methods and new mathematics
MATX 1100
Fri 17 Jan 2014, 3:00pm-4:00pm

Abstract

Infections are an increasingly important challenge worldwide: new pathogens are emerging, and old ones are adapting to evade our control strategies. Recent dramatic improvements in sequencing technology have made many large and rich datasets of pathogen gene sequences available. In principle, these data can shed light on how pathogens are spreading, evolving, and interacting with each other -- information that is crucial for controlling infections. Such genomic data are usually interpreted with the aid of phylogenetic trees. Inferring a phylogeny from data is a mature field with decades of mathematics behind it. But comparing phylogenies from different sets of data, and linking the properties of phylogenies (and the associated data) to how pathogens spread, evolve and interact is a field in its infancy. In this talk I will briefly introduce the field, describing the data and the need for novel mathematical approaches.  I will outline two recent contributions. In the first, we developed a new Bayesian method to infer a who-infected-whom tree from sequence data from an outbreak, and we applied it to whole-genome sequence data of  tuberculosis. The method uses a novel mapping from lineages to hosts to find a nice decomposition of the key likelihood term into rapidly-computable simple parts, and is thus flexible and quick. In the second contribution, we develop  novel summaries of phylogenetic trees and use them to classify trees according to the kind of transmission dynamics taking place.  I will describe my research program in this emerging field, whose advancement calls for the engagement of several areas of mathematics including applied probability, discrete mathematics, geometry and topology.

Note for Attendees

Refreshments will be served at 2:45 pm in the MATH 125 Lounge.
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Arizona State University
Mon 20 Jan 2014, 3:00pm
Institute of Applied Mathematics
LSK 460
Computational and Theoretical Epidemiology: Challenges and Opportunities
LSK 460
Mon 20 Jan 2014, 3:00pm-4:00pm

Abstract

The marriage of mathematics and epidemics has a long and distinguished history with a plethora of successes that go back to the work of Daniel Bernoulli (1700 – 1782) and Nobel Laureate and physician Sir Ronald Ross (1911) and associates. These individuals, mostly physicians, created the field of theoretical/mathematical epidemiology in their efforts to meet their commitment to diminish health disparities; the consequences of poverty and the lack of access to health services. The last four decades have seen deep and extensive computational and theoretical advances in the fields of computational, mathematical and theoretical epidemiology and the connections of this theoretical research to public health policy and security have had significant impact. These advances have been driven by the dynamics of specific emergent or re-emergent diseases including HIV, influenza, SARS and Tuberculosis as well as by bioterrorism concerns.  Challenges and opportunities arise from the demands generated by the study of disease dynamics over multiple time scales and levels of organization and by the search for response to questions of importance to the fields of public health, homeland security and evolutionary biology. In this lecture, I will revisit some of the history of the field and discuss selected applications in the context of slow and fast diseases; highlight the differences between single and recurrent outbreaks and related issues.
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University of Oxford
Mon 20 Jan 2014, 4:00pm
Department Colloquium
MATX 1100
Self-avoiding walks, phase separation and KPZ universality.
MATX 1100
Mon 20 Jan 2014, 4:00pm-5:00pm

Abstract

A fundamental notion in statistical mechanics is phase transition: a microscopic system composed of a huge number of random particles depends on a thermodynamic parameter, and the system undergoes sudden changes in its large-scale structure as this parameter varies across a critical point.

Self-avoiding walk was introduced in the 1940s as a model in chemistry of a long chain of molecules, and is now viewed as a fundamental model in the rigorous theory of statistical mechancs. By introducing a positive parameter which provides a penalty to self-avoiding walk which is exponential in the walk's length, we obtain an example of phase transition. Recent work with Hugo Duminil-Copin shows that uniformly chosen self-avoiding walks of given high length move sub-ballistically, and this is related to the nature of this phase transition at the critical point. I will give an overview of the main elements of the proof.   

Considering instead subcritical self-avoiding walk, and focussing on the planar case, we obtain a natural model for the problem of phase separation: when one substance is suspended in another, such as oil in water, a droplet forms, whose boundary approximates a smooth profile predicted by Wulff. Modelling the problem using a planar model such as subcritical self-avoiding walk, the fluctuation of the droplet boundary from its typical profile exhibits characteristic scaling exponents - 2/3 longitudinally and 1/3 latitudinally - which I derived a couple of years ago. The behaviour arises from a competition of local Gaussian randomness and global curvature constraints.

Phase separation in this guise is a static model. However,  the Gaussian competition with curvature, and the two exponents, are shared by many dynamic models, of interfaces growing at random and subject to forces of surface tension. These models form the Kardar-Parisi-Zhang universality class. Resampling techniques from the phase separation papers find counterparts in more recent work, joint with Ivan Corwin, in which a natural Gibbs property is proved for the multi-line Airy process, which is a fundamental scaling limit encountered in KPZ universality. This Brownian-Gibbs property is valuable in, for example, improving regularity assertions about the Airy process. These ideas form the subject of the final part of the talk..

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University of Oxford
Tue 21 Jan 2014, 3:30pm
Probability Seminar
CEME 1204
KPZ Line Ensemble: a marriage of integrability and probability
CEME 1204
Tue 21 Jan 2014, 3:30pm-4:30pm

Abstract

 The KPZ equation, introduced by Kardar, Parisi and Zhang, is a stochastic PDE that models randomly evolving interfaces that are subject to constraining forces such as surface tension. It is anticipated to be a universal object, in the sense that many microscopic models will share the KPZ equation as an accurate asymptotic description of their late time behavior. This view is supported by extensive numerical evidence, recent experimental evidence involving liquid crystal instabilities, and a limited but growing body of mathematically rigorous work. 

In recent work arXiv:1312.2600 with Ivan Corwin, we present a new technique for the analysis of the KPZ equation. The solution to the equation is represented as the lowest indexed curve in an N-indexed ensemble of curves, which we call a KPZ line ensemble. Curves within the ensemble enjoy a natural invariance under resampling, the H-Brownian Gibbs property, which property has the effect of energetically penalizing, but not absolutely forbidding, the crossing of adjacently indexed curves. This property is inherited from the O'Connell Yor semi-discrete continuum random polymer ensemble after a limiting procedure is applied.

The H-Brownian Gibbs property is an integrable one, in the sense that the precursor O'Connell-Yor ensemble is known to enjoy it by virtue of this ensemble's algebraic structure. However, it also offers a powerful probabilistic tool for the analysis of the KPZ equation. Since the solution of this equation is embedded in a KPZ line ensemble, we may analyse it using the H-Brownian Gibbs property, and in this way derive significant new estimates regarding the regularity and local structure of the KPZ solution. As I will aim to explain, these new estimates are valid uniformly in the time parameter for the KPZ equation, even after a natural rescaling of the equation is undertaken which accesses the fluctuation behavior of the KPZ evolution.    
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Hassan Jaber
Universite de Lorraine
Tue 21 Jan 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Hardy-Sobolev equations and related inequalities on compact Riemannian manifolds
ESB 2012
Tue 21 Jan 2014, 3:30pm-4:30pm

Abstract

Let (M,g) be a compact Riemannian Manifold without boundry of dimension n \geq 3, x_0 \in M, and s \in (0,2). We let \crit: = \frac{2(n-s)}{n-2} be the critical Hardy-Sobolev exponent. I investigate the influence of geometry on the existence of positive distributional solutions u \in C^0(M) for the critical equation

 

\Delta_g u+a(x) u=\frac{u^{\crit-1}}{d_g(x,x_0)^s}  \;\; \hbox{ in} \ M.

 

Via a minimization method, I prove existence in dimension n\geq 4 when the potential a is sufficiently below the scalar curvature at x_0. In dimension n=3, using a global argument, i prove existence when the mass of the linear operator \Delta_g + a is positive at x_0. On the other hand, by using a Blow-up around x_0, i prove that the sharp constant of the related Hardy-Sobolev inequalities on (M,g), which is equal to the one of the Euclidean Hardy-Sobolev inequalities, is achieved for all compact Riemannian Manifold of dimension n \geq 3 with or without boundary.


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Northeastern University
Wed 22 Jan 2014, 3:00pm
Department Colloquium
ESB 2012 (PIMS building)
Random lozenge tilings and other integrable probabilistic models
ESB 2012 (PIMS building)
Wed 22 Jan 2014, 3:00pm-4:00pm

Abstract

I will survey the general phenomenon of "integrable" probabilistic models, in which the presence of explicit formulas describing their distributions allow for an analysis by essentially algebraic methods.

Then I will discuss in detail an integrable probabilistic model of randomly tiling a hexagon drawn on the regular triangular lattice by lozenges of three types (equivalent formulations: dimer models on the honeycomb lattice, or random 3D stepped surfaces glued out of 1x1x1 boxes). This model has received a significant attention over the past 20 years (first results - the computation of the partition function - date back to P. MacMahon, 100+ years ago). Kenyon, Okounkov, and their co-authors (1998-2007) proved the law of large numbers: when the polygon is fixed and the mesh of the lattice goes to zero, the random 3D surface concentrates around a deterministic limit shape, which is algebraic. I will discuss finer asymptotics: local geometry, behavior of interfaces between phases (which manifests the Kardar-Parisi-Zhang universality), and global fluctuations of random surfaces (described by the Gaussian Free Field), as well as dynamical models associated with random tilings.

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UvA
Wed 22 Jan 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
Constraining higher derivative corrections with T-duality
ESB 4127 (host: UAlberta)
Wed 22 Jan 2014, 3:00pm-4:00pm

Abstract

From a target space perspective, T-duality relates certain pairs of string theory backgrounds with a U(1) isometry. If we perform a Kaluza-Klein reduction on the corresponding circle, T-duality then acts as a symmetry of the reduced theory, and this symmetry can be argued to constrain the higher derivative couplings, which in turn constrains the couplings of the higher dimensional theory. I will explain an unsophisticated brute force implementation of this procedure and show how it can be used to completely fix the four-derivative action of type II O-planes coupling to NS-NS sector bulk fields.
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UBC
Wed 22 Jan 2014, 4:00pm SPECIAL
Topology and related seminars
ESB 2012
Period & Index in Locally Ringed Topoi
ESB 2012
Wed 22 Jan 2014, 4:00pm-5:00pm

Abstract

In an Exposé published in 1968, Alexander Grothendieck generalized the notion of a central simple algebra over a field by defining Azumaya algebras in locally ringed topoi. Specific examples of Azumaya algebras in locally ringed topoi include (up to isomorphism) principal PUn or POn bundles on CW complexes, as well as Azumaya algebras over commutative rings. If the topos is connected, it is possible to define two invariants of an Azumaya algebra, the period & the index, which measure the nontriviality of the algebra. It is a classical theorem that the period & index have the same prime divisors in the case of central simple algebras over a field, and this is also known in the case of PUn bundles over CW complexes. In this talk, I will show that in the case of any locally ringed topos, the period & index have the same prime divisors.
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Dr. Sepideh Jankhah
UBC
Wed 22 Jan 2014, 4:00pm
Fluids Lab Meeting
LSK 203
Investigating the effect of size and frequency of sparged bubbles on the hydrodynamic conditions in submerged membrane systems
LSK 203
Wed 22 Jan 2014, 4:00pm-5:00pm

Abstract

Fouling control through air sparging in membrane systems is governed by the hydrodynamic conditions in the system and the resulting shear stress induced onto membranes. However, the relationship between hydrodynamic conditions and the extent of fouling control is not well understood. As a result, sparging approaches are designed using a capital and time intensive empirical trial-and-error approach that does not guarantee that optimal conditions are identified. To address this knowledge gap, the present research focused on characterizing the hydrodynamic conditions in a membrane system under different sparging conditions (bubble size and frequency) and on finding a correlation between the induced hydrodynamic conditions and fouling control efficiency.

New concepts of "zone of influence" of bubbles and "power transferred" were defined to characterize the hydrodynamic conditions in membrane  systems. A non-homogenous fouling distribution was observed in the zone of influence of bubbles due to a non-homogenous distribution of velocity and shear stress in this zone.  Fouling rates generally decreased with an increase in the area of the zone of influence, the root mean square of shear stress induced onto membranes and the rise velocity of bubbles. However, none of these parameters on their own could accurately describe the effect of the hydrodynamic conditions on fouling rate. On the other hand, power transferred onto fibers, which incorporates the effect of all the three parameters, could more effectively describe the effect of the hydrodynamic conditions on the rate of fouling.  Power transfer efficiency into the system, defined as the ratio of power transferred onto membranes to the power input in the system, was used to identify optimal sparging approaches. For all cases investigated, the power transfer efficiency to the system was consistently much higher for pulse bubble than for coarse bubble sparging. The results from the present research are currently being used by the industry partners, GE Water and Processes Technologies, for the design of the air sparged membrane systems.

Sepideh Jankhah has a PhD in Civil and Environmental Engineering, She did her BSc and MSc in Chemical Engineering. She worked on developing a new catalyst for fuel cells during her MSc degree. Her PhD project focused on characterizing the hydrodynamic conditions in membrane filtration systems using high speed-high resolution camera/Particle Image Velocimetry (PIV) and Electrochemcial Diffusion (EDM) Shear probes.

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École Fédérale Polytechnique de Lausanne
Thu 23 Jan 2014, 3:30pm
Number Theory Seminar
room MATH 126
Weak arithmetic equivalence of number fields
room MATH 126
Thu 23 Jan 2014, 3:30pm-4:30pm

Abstract

Inspired by the invariant of a number field given by its Dedekind zeta function we define the notion of weak arithmetic equivalence, and we show that under certain ramification hypothesis this equivalence determines the local root numbers of the number field. This is analogous to a result Rohrlich on the local root numbers of a rational elliptic curve. Additionally we prove that for tame non-totally real number fields the integral trace form is invariant under weak arithmetic equivalence.
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Northeastern University
Thu 23 Jan 2014, 3:30pm
Probability Seminar
MATH 203
Markov dynamics on interlacing arrays
MATH 203
Thu 23 Jan 2014, 3:30pm-4:30pm

Abstract


Since the end of 1990's there has been a significant progress in understanding the long time nonequilibrium behavior of certain integrable (1+1)-dimensional interacting particle systems and random growth models in the Kardar-Parisi-Zhang (KPZ) universality class. The miracle of integrability in most cases (with the notable exception of the partially asymmetric simple exclusion process) can be traced to an extension of the Markovian evolution to a suitable (2+1)-dimensional random growth model whose remarkable properties yield the solvability. So far, there have been two sources of such extensions. The first one originated from a classical combinatorial bijection known as the Robinson-Schensted-Knuth correspondence (RSK, for short) in the works of Johansson, O'Connell and their co-authors. The second approach introduced by Borodin-Ferrari was based on an idea of Diaconis-Fill of extending intertwined "univariate" Markov chains to a "bivariate" Markov chain that projects to either of the initial ones.
 
In a recent joint work with A. Borodin, we presented a way to unify these two approaches using a fairly general framework of Macdonald processes. This also provides new examples of integrable KPZ particle systems. 

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UBC
Mon 27 Jan 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
The fibre bundle structure of smooth and rationally smooth Schubert varieties
ESB 4127 (host: UBC)
Mon 27 Jan 2014, 3:00pm-4:00pm

Abstract

A theorem of Ryan and Wolper states that a type A Schubert variety is smooth if and only if it is an iterated fi bre bundle of Grassmannians. We extend this theorem to arbitrary finite type, showing that a Schubert variety in a generalized flag variety is rationally smooth if and only if it is an iterated fi bre bundle of rationally smooth Grassmannian Schubert varieties. The proof depends on deep combinatorial results in Coxeter groups. This is joint work with William Slofstra.
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University of Victoria
Mon 27 Jan 2014, 4:00pm
Department Colloquium
MATX 1100
Algebraic invariants for hyperbolic dynamical systems
MATX 1100
Mon 27 Jan 2014, 4:00pm-5:00pm

Abstract

I will describe a certain class of hyperbolic dynamical systems called Smale spaces, which arose from Smale's program of smooth dynamics. I will give a number of different examples. The goal of the talk is to provide algebraic invariants for these systems, whose existence was first conjectured in the 1970's by Rufus Bowen. I will try to describe the motivation for these invariants and also how their construction parallels others in algebraic topology.
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Lawrence Berkeley Lab
Tue 28 Jan 2014, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133
Towards an optimal-order approximate sparse factorization exploiting data-sparseness in separators
ESB 4133
Tue 28 Jan 2014, 12:30pm-2:00pm

Abstract

Nested dissection ordering and its graph partitioning generalization give rise to an ordered sequence of separators of (roughly) geometrically decreasing size. The fill-ins in the LU factors are confined in the parts of the matrix associated with the separators. In particular, the diagonal blocks associated with the separators are fully dense in the factors and they contribute to the dominant terms in the costs of the storage for the factors and the flops for computing the factors. Employing the data-sparse representations or compressions, such as low-rank approximation, for these separator blocks can drastically lower the overall factorization costs both in memory and flops. The low rankness can appear in many matrices from discretized PDEs.

Recently, we have been investigating fast and stable algorithms for one type of data-sparse representation called hierarchically semi-separable (HSS) structure, and using them in the sparse LU factorization. In this talk, we will show that both in theory and in practice, the HSS-embedded sparse LU factorization has much lower complexity than the traditional factorization algorithm. The complexity of  this class of algorithms is closely related to the numerical ranks of the separator blocks which vary with the PDEs. For elliptic problems, we can achieve large amount of compression and the resulting factorization can be used as a nearly optimal-order direct solver.  For wider classes of problems, the approximate factorization can be used as a preconditioner. We will show performance results from direct solvers as well as preconditioners for a wide range of problems. We will also illustrate the potential of such solvers/preconditioners being used for the extreme-scale computers and problem size.

This is joint work with A. Napov, F.-H. Rouet, S. Wang, and J. Xia.

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Sandra Merchant
UBC, Dept of Mathematics
Tue 28 Jan 2014, 2:00pm
Math Education Research Reading
MATH 126
The Moore Method of Teaching Mathematics
MATH 126
Tue 28 Jan 2014, 2:00pm-3:00pm

Abstract

This week's reading group will focus on the famous "Moore Method" of teaching mathematics, introduced by Robert Lee Moore.  The discussion will centre around the following two (very short) articles:

Jones, F. Burton, 1977, "The Moore method," American Mathematical Monthly 84: 273-77.

Cohen, David W., 1982, "A modified Moore method for teaching undergraduate mathematics", American Mathematical Monthly 89(7): 473-474, 487-490.

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Universidad de Chile
Tue 28 Jan 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Entire stable solutions of a 4rth order elliptic equation and a monotonicity formula
ESB 2012
Tue 28 Jan 2014, 3:30pm-4:30pm

Abstract

We consider the nonlinear fourth-order problem  \Delta^2 u=|u|^{p-1}u\ \ \mbox{in} \ \mathbb R^n, where p>1 and n\ge1.  We give a complete classification of stable and finite Morse index solutions in the full exponent range.  We also compute an upper bound of the Hausdorff dimension of the singular set of extremal solutions. A key tool is a new monotonicity formula.
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University of Victoria
Tue 28 Jan 2014, 4:00pm SPECIAL
One Time Event
MATH 126
Symbolic Dynamical Systems Seminar: Minimal dynamics on the Cantor set: orbit equivalence and applications in group theory.
MATH 126
Tue 28 Jan 2014, 4:00pm-5:00pm

Details

Abstract: I will discuss homeomorphisms of the Cantor set with dense orbits. I  will describe a simple algebraic invariant for such systems which leads to a complete classification of the systems up to orbit equivalence. The  key ingredient for this result is a model, called the Bratteli-Vershik model. Finally, I will briefly described how these dynamical systems have been used to provide new examples in group theory.
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Wed 29 Jan 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
TBA
ESB 4127 (host: UAlberta)
Wed 29 Jan 2014, 3:00pm-4:00pm

Abstract

 TBA
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Microsoft Research
Wed 29 Jan 2014, 3:00pm
Probability Seminar
ESB 2012
A Two-Sided Estimate for the Gaussian Noise Stability Deficit
ESB 2012
Wed 29 Jan 2014, 3:00pm-4:00pm

Abstract

     The Gaussian Noise Stability of a set A in Euclidean space is the
    probability that for a Gaussian vector X conditioned to be in A, a
    small Gaussian perturbation of X will also be in A. Borel's
    celebrated Isoperimetric inequality states that a half-space
    maximizes noise stability among sets with the same Gaussian measure.
    We will present a novel short proof of this inequality, based on
    stochastic calculus. Moreover, we prove an almost tight, two-sided,
    dimension-free robustness estimate for this inequality: We show that
    the deficit between the noise stability of a set A and an equally
    probable half-space H can be controlled by a function of the
    distance between the corresponding centroids. As a consequence, we
    prove a conjecture by Mossel and Neeman, who used the
    total-variation distance.
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UBC
Wed 29 Jan 2014, 3:15pm
Topology and related seminars
ESB 4133
Period & Index in Locally Ringed Topoi II
ESB 4133
Wed 29 Jan 2014, 3:15pm-4:15pm

Abstract

In an Exposé published in 1968, Alexander Grothendieck generalized the notion of a central simple algebra over a field by defining Azumaya algebras in locally ringed topoi. Specific examples of Azumaya algebras in locally ringed topoi include (up to isomorphism) principal PUn or POn bundles on CW complexes, as well as Azumaya algebras over commutative rings. If the topos is connected, it is possible to define two invariants of an Azumaya algebra, the period & the index, which measure the nontriviality of the algebra. It is a classical theorem that the period & index have the same prime divisors in the case of central simple algebras over a field, and this is also known in the case of PUn bundles over CW complexes. In this talk, I will show that in the case of any locally ringed topos, the period & index have the same prime divisors.
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Mathematics, McGill
Thu 30 Jan 2014, 3:00pm SPECIAL
Discrete Math Seminar
ESB 4133
Designing a Network for Uncertain Demand
ESB 4133
Thu 30 Jan 2014, 3:00pm-4:00pm

Abstract

Robust optimization is a paradigm for dealing with optimization problems whose input is uncertain. For instance, consider building a system (bridge, network, etc.) whose future demand (or stress) is unknown but bounded. Say we know that the set of possible demands will come from a given convex region called the "universe''. A solution/design is called robust if it supports any demand from the universe. Robust optimization asks for a minimum cost robust solution.  We consider this model for the design of communication (data) networks where future demand can be both unknown and varying over time. We will discuss in detail one variant of robust network design known as the Virtual Private Network (VPN) problem. We will also mention several open (theoretical and practical) questions.
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McGill University
Fri 31 Jan 2014, 3:00pm
Department Colloquium
MATX 1100
Disjoint path problems in graphs
MATX 1100
Fri 31 Jan 2014, 3:00pm-4:00pm

Abstract

An instance of the edge-disjoint paths problem (EDP) consists of a graph G  and some demand node pairs s_i,t_i, i=1,2, \ldots k.  A subset I \subseteq [k] of the demand pairs is called routable if there exists edge-disjoint paths in G which satisfy (connect) each pair s_i,t_i with i \in I.

We consider two optimization problems associated with EDP. The maximum edge-disjoint paths problem (MEDP) asks one to find a maximum size routable subset.  The minimum congestion problem asks for the minimum integer \alpha such that if we make \alpha copies of each edge, we can route all demands. We discuss the associated streams of work on approximating these problems, highlighting some recent advances and outstanding open problems. We will emphasize  both the parallels and the key distinctions between the two streams.

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