Mathematics Dept.
  Events
Mathematics, Guelph
Mon 3 Nov 2014, 3:00pm SPECIAL
Institute of Applied Mathematics
LSK 460
The Good, the Bad, and the Ugly: From Biofilms to Mathematics and Back Again
LSK 460
Mon 3 Nov 2014, 3:00pm-4:00pm

Abstract

Bacterial biofilms are microbial depositions that form on immersed surfaces wherever environmental conditions sustain bacterial growth. They have been called the most successful life form on Earth and cities of microbes. Biofilms have important applications in environmental engineering, but are detrimental in a medical or industrial context. They have been characterised as both, spatially structured microbial populations, and as mechanical objects. Life in biofilm communities significantly differs from life in planktonic cultures. This is reflected in the complexity of mathematical models of biofilms that are essentially more involved than models of suspended microbial communities. In this talk I will focus on a class of highly degenerate diffusion-reaction biofilm models. In its simplest form this includes simultaneously two nonlinear diffusion effects: (i) a porous medium equation like degeneracy when the dependent variable biomass density vanishes, and (ii) a super-diffusion singularity when it attains its {\it a priori} known upper bound. I will summarize some analytical (well-posedness) results, and discuss applications of the model to answer questions about biofilms by numerical simulations. I will hereby focus on the contribution of mathematical models (this and others) to understand the formation of cluster-and-channel biofilm architectures, and I will illustrate how our model framework, extended by a model of bacterial communication by quorum sensing, can be used to shed light on the transition from an initial mode of biofilm colonization to a protected mode of biofilm growth.
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UBC
Mon 3 Nov 2014, 3:00pm
Harmonic Analysis Seminar
Math 204
Restriction theory and quadratic equations in dense variables
Math 204
Mon 3 Nov 2014, 3:00pm-4:00pm

Abstract

We are interested in the problem of solving a translation-invariant linear equation in a dense subset of the squares. We focus on the quality of density bounds, and we explain how the efficient energy increment method developed by Heath-Brown and Szemeredi for Roth's theorem can be adapted to this problem. A key tool in the process is a restriction estimate of Bourgain for lattice sets, and we discuss its role in our density increment strategy.
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Purang Abolmaesumi
Department of Electrical and Computer Engineering, UBC
Tue 4 Nov 2014, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Interventional Ultrasound for Spine Injections
ESB 4133 (PIMS Lounge)
Tue 4 Nov 2014, 12:30pm-1:30pm

Abstract

Our goal is to develop an innovative, robust, intuitive and affordable system for guiding needle insertion into the lumbar spine.
Ultrasound imaging will be the basis for guidance before and during needle insertion. The main application is facet joints and epidural/steroid injection for the relief of chronic back pain, and labour/analgesia. The anesthesiologist is expected to use the system to choose a suitable puncture location, insert the needle at an appropriate angle and stop when the needle reaches the desired depth. The goal is to increase the confidence level by enabling an accurate needle placement on the first attempt, and hence reduce complications and pain for the patient. In current practice, the needle insertion is either done blindly, using palpation to choose a puncture site, or under fluoroscopy/CT guidance, which carry a high radiation dose risk to both patient andanesthesiologist. We propose to add real-time ultrasound capability to these procedures and display the ultrasound, pre-procedure CT and needle trajectory to the anesthesiologist. We also propose to incorporate spine statistical atlas information for enhanced interpretation of ultrasound images. I will finish the talk by also overviewing some of our emerging works in cancer interventions using machine learning techniques.

Note for Attendees

Sushi will be provided.
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Kyoto University
Tue 4 Nov 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Global dynamics of nonlinear dispersive equations above the ground state energy
ESB 2012
Tue 4 Nov 2014, 3:30pm-4:30pm

Abstract

This is a survey on the joint works with Wilhelm Schlag,
Joachim Krieger and Tristan Roy. We classify global behavior of all
solutions with energy up to slightly more than the ground state for
the nonlinear Klein-Gordon, Schrodinger, and wave equations. The
dynamics include scatteing (to 0), blow-up, and scatttering to
solitons. The solutions scattering to solitons form threshold
hypersurfaces in the energy space, giving a complete classification
under the energy constraint. It also describes how a solution can
disperse in the past and blow up in the future.
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Justin Chan
SFU
Tue 4 Nov 2014, 4:00pm
Discrete Math Seminar
ESB 4127
An infinite family of inv-Wilf-equivalent permutation pairs
ESB 4127
Tue 4 Nov 2014, 4:00pm-5:00pm

Abstract

Wilf-equivalence is one of the central concepts of pattern-avoiding permutations, and has been studied for more than thirty years. The two known infi nite families of Wilf-equivalent permutation pairs, due to Stankova-West and Backelin-West-Xin, both satisfy the stronger condition of shape-Wilf-equivalence. Dokos et al. recently studied a di fferent strengthening of Wilf-equivalence called inv-Wilf-equivalence, which takes account of the inversion number of a permutation. They conjectured that all inv-Wilf-equivalent permutation pairs arise from trivial symmetries. We disprove this conjecture by constructing an infi nite family of counterexamples derived from the permutation pair (231) and (312). The key to this construction is to generalize simultaneously the concepts of shape-Wilf-equivalence and inv-Wilf-equivalence. A further consequence is a proof of the recent Baxter-Jaggard conjecture on even-shape-Wilf-equivalent permutation pairs.
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MIT
Wed 5 Nov 2014, 3:00pm SPECIAL
Discrete Math Seminar / Harmonic Analysis Seminar
MATX1118
On geometric incidences
MATX1118
Wed 5 Nov 2014, 3:00pm-4:00pm

Abstract

 
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York University
Wed 5 Nov 2014, 3:10pm
Probability Seminar
ESB 2012
Random walk in non-elliptic random environments
ESB 2012
Wed 5 Nov 2014, 3:10pm-4:10pm

Abstract

Much of the literature on random walk in random environment assumes uniformly ellipticity, i.e., that nearest neighbour steps have probabilities bounded away from zero. I’ll describe some work with Mark Holmes (Univ. of Auckland) in which we relax this assumption, and allow some such steps to be forbidden. This leads naturally to percolation models, using which one can in some cases prove ballisticity of the random walks (existence of non-zero asymptotic speeds).
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Mike Wakin
Colorado School of Mines
Thu 6 Nov 2014, 12:00pm
Mathematics of Information and Applications Seminar
4133 ESB (PIMS lounge)
The Sketched SVD and Applications in Structural Health Monitoring
4133 ESB (PIMS lounge)
Thu 6 Nov 2014, 12:00pm-1:00pm

Abstract

We present a simple technique for estimating parts of the Singular Value Decomposition (SVD) of a data matrix from a small randomly compressed "sketch" of that matrix. In sensor network settings--where each column of the data matrix comes from a separate sensor--the sketch can be assembled using operations local to each sensor. As an application of this work, we consider the problem of Structural Health Monitoring (SHM). SHM systems are critical for monitoring aging infrastructure (such as buildings or bridges) in a cost-effective manner. Such systems typically involve collections of battery-operated wireless sensors that sample vibration data over time. After the data is transmitted to a central node, modal analysis can be used to detect damage in the structure. We propose and study three frameworks for Compressive Sensing (CS) in SHM systems; these methods are intended to minimize power consumption by allowing the data to be sampled and/or transmitted more efficiently. At the central node, all of these frameworks involve a very simple technique for estimating the structure's mode shapes without requiring a traditional CS reconstruction of the vibration signals; all that is needed is to compute a simple SVD. We support our proposed techniques theoretically and using simulations based on synthetic and real data. This project is joint work with Anna Gilbert and Jae Young Park.
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UBC
Thu 6 Nov 2014, 12:30pm
Graduate Student Seminar
Math 225
Supersymmetric integration
Math 225
Thu 6 Nov 2014, 12:30pm-1:45pm

Abstract

We begin by defining the Grassmann integral of a function of both commuting ("bosonic") and anti-commuting ("fermionic") variables. An important example is the mixed bosonic-fermionic ("supersymmetric") Gaussian integral, which exhibits a surprising self-normalization property. Time permitting, we will mention applications of the Grassmann integral to the representation of self-avoiding walk as a supersymmetric quantum field theory.
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Yariv Mizrahi
Thu 6 Nov 2014, 12:30pm SPECIAL
Room 200 of the Graduate Student Centre
Doctoral Exams
Room 200 of the Graduate Student Centre
Thu 6 Nov 2014, 12:30pm-2:30pm

Details

ABSTRACT We introduce a new class of parallel parameter learning algorithms for Markov random fields (MRFs) with untied parameters, which are efficient for a large class of practical models. The algorithms parallelize naturally over cliques and, for graphs of bounded degree, have complexity that is linear in the number of cliques. We refer to these algorithms with the acronym LAP, which stands for Linear And Parallel. Unlike their competitors, the marginal versions of the proposed algorithms are fully parallel and for log-linear models they are also data efficient, requiring only the local sufficient statistics of the data to estimate parameters. LAP algorithms are ideal for parameter learning in big graphs and big data applications. The correctness of the newly proposed algorithms relies heavily on the existence and uniqueness of the normalized potential representation of an MRF. We capitalize on this theoretical result to develop a new theory of correctness and consistency of LAP estimators corresponding to different local graph neighborhoods. This theory also establishes a general condition on composite likelihood decompositions of MRFs that guarantees the global consistency of distributed estimators, provided the local estimators are consistent. We introduce a conditional variant of LAP that enables us to attack parameter estimation of fully observed models of arbitrary connectivity, including fully connected Boltzmann distributions. We show consistency for this distributed estimator, and relate it to distributed pseudo-likelihood estimators. Finally, for linear and non-linear inverse problems with a sparse forward operator, we present a new algorithm, named iLAP, which decomposes the inverse problem into a set of smaller dimensional inverse problems that can be solved independently.
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Uriya First
UBC
Thu 6 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126
Rational isomorphism of quadratic forms and related objects
room MATH 126
Thu 6 Nov 2014, 3:30pm-4:30pm

Abstract

Let R be a discrete valuation ring with fraction field F. Two algebraic objects (say, quadratic forms) defined over R are said to be rationally isomorphic if they become isomorphic after extending scalars to F. In the case of unimodular quadratic forms, it is a classical result that rational isomorphism is equivalent to isomorphism. This has been recently extended to "almost umimodular" forms by Auel, Parimala and Suresh. I will present further generalizations to related objects: hermitian forms over involutary R-algebras, quadratic spaces equipped with a group action ("G-forms"), and systems of quadratic forms. The results can be regarded as versions of the Grothendieck–Serre conjecture for certain non-reductive groups. (Joint work with Eva Bayer–Fluckiger.)
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Berkeley
Fri 7 Nov 2014, 1:30pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Moduli spaces from microlocal geometry
ESB 4127 (host: UBC)
Fri 7 Nov 2014, 1:30pm-2:30pm

Abstract

 TBA
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UBC
Fri 7 Nov 2014, 3:00pm
Department Colloquium
MATX 1100
A mysterious 3/4 and happy 1/2
MATX 1100
Fri 7 Nov 2014, 3:00pm-4:00pm

Abstract

I will discuss: 1. A new problem concerning monotone subsequences in random data;  2. Several approaches towards its solution;  3. Relations to some old problems from analysis, Ramsey theory and even probability. Based on work with Louigi Adarrio-Berry, Guillaume Chapuy, Luc Devroye, Gabor Lugosi, Neil Olver, Yuval Peres and Richard Balka.

Note for Attendees

Refreshments will be served at 2:45pm in the Math Lounge area, MATH 125 before the colloquium.
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Mathematics, UVIC
Mon 10 Nov 2014, 3:00pm
Institute of Applied Mathematics
LSK 460
Disease dynamics on random contact networks
LSK 460
Mon 10 Nov 2014, 3:00pm-4:00pm

Abstract

Contact networks are graphs modeling population contact patterns. They can represent contact heterogeneity and fixed partners. On random contact networks without clustering (triangles), contact heterogeneity implies that the basic reproduction number (indicating the risk for disease invasion) is determined by the average degree of a node found by following a random edge. that partners are fixed imply that a node cannot reinfect its neighbors before its neighbours recover, and thus two diseases with identical transmissibility and duration of infection have different basic reproduction numbers on the same contact network if one induced lifetime immunity while the other does not. When the average degree of a neighbor becomes large, the two basic reproduction numbers become the same. Another major difference between disease dynamics on networks and in homogeneously mixed populations is that, on networks, the basic reproduction number does not scale linearly with the population size in a growing population, as predicted by classical models. Instead, it may reach maximum when the population is still growing.

Note for Attendees

 tea and cookies available before the talk in the IAM lounge (LSK 306)
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UBC
Mon 10 Nov 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Versal actions with a twist
ESB 4127 (host: UBC)
Mon 10 Nov 2014, 3:00pm-4:00pm

Abstract

The term “versal” is best understood by subtracting “unique” from both sides of the formula

               Universal = unique + versal.

In this talk based on joint work with Alex Duncan, I will discuss competing notions of versality for the action of an algebraic group G on an algebraic variety X and relate these notions to properties (such as existence and density) of rational points on twisted forms of X. I will then present examples, where this relationship can be used to prove that certain group actons are versal or, conversely, that certain varieties have rational points.

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UAlberta
Wed 12 Nov 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
“Quantum is airy, but is Airy quantum?”
ESB 4127 (host: UAlberta)
Wed 12 Nov 2014, 3:00pm-4:00pm

Abstract

According to Merriam-Webster, “airy” means “having a light or careless quality that shows a lack of concern”. That describes pretty accurately quantum physics. But Airy was also a mathematician and physicist that did a lot of things, and somehow got his name attached to a very simple complex curve. It turns out that this so-called Airy curve encapsulates intersection numbers on the moduli space of curves via topological recursion. Moreover, the Airy curve can be quantized; the resulting Schrodinger differential operator recursively constructs intersection numbers through WKB analysis. A natural question then is to ask whether this circle of ideas holds in a much more general setting; given a complex curve that encapsulates some nice enumerative invariants via topological recursion, does there exist a (unique?) quantization of the complex curve that reconstructs the invariants recursively via WKB analysis? This question has closed connections with many fundamental conjectures in enumerative geometry and other areas of mathematics, such as the AJ conjecture in knot theory, and Witten’s conjecture for intersection numbers. In recent work with B. Eynard we construct such a quantization in a number of different settings; in this talk I will focus on the case of the r-Airy curve, which generates intersection numbers on the moduli space of r-spin curves.
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UBC
Wed 12 Nov 2014, 3:10pm
Probability Seminar
ESB 2012
The uniform spanning tree in two dimensions and its scaling limit.
ESB 2012
Wed 12 Nov 2014, 3:10pm-4:10pm

Abstract

 
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UBC
Wed 12 Nov 2014, 3:15pm
Topology and related seminars
ESB 4133
Differentiable Stacks and Foliation Theory, Part I
ESB 4133
Wed 12 Nov 2014, 3:15pm-4:15pm

Abstract

Differentiable stacks are generalizations of smooth manifolds suitable for modelling poor quotients, such as quotients by non-free Lie group actions. In this talk, we will define differentiable stacks and explain how they can also be used to model the leaf space of a foliation. In the following week, we will explain some recent results of ours about a nice subclass of differentiable stacks, called etale differentiable stacks, and explain some applications to foliation theory.
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Kamran Farkhar
UBC
Wed 12 Nov 2014, 3:30pm
Symmetries and Differential Equations Seminar
Math 125
A study of Rotating Fluids through Lie Symmetries
Math 125
Wed 12 Nov 2014, 3:30pm-4:30pm

Abstract

In this talk, we consider the unsteady motion of the conducting fluid in the rotating Cartesian coordinates system. By using Lie symmetries, we successfully reduced the system of partial differential equations to an ordinary differential equation and thereby do the analysis. We firstly, obtained steady state solutions which lead to infinite number of time-dependent solutions via three arbitrary functions of time. Finally, the plots of the solutions along with their physical interpretation are presented to understand the flow behavior.
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Deanna Needell
Claremont Mckenna College
Thu 13 Nov 2014, 12:00pm
Mathematics of Information and Applications Seminar
ESB 4133 (PIMS Lounge)
Stochastic gradient pursuit methods and their ties to random matrix theory
ESB 4133 (PIMS Lounge)
Thu 13 Nov 2014, 12:00pm-1:00pm

Abstract

In this talk we will give a brief overview of stochastic gradient pursuit and the closely related Kaczmarz method for solving linear systems, or more generally convex optimization problems. We will present some new results which tie these methods together and prove the best known convergence rates for these methods under mild Lipschitz conditions. The methods empirically and theoretically rely on probability distributions to dictate the order of sampling in the algorithms. It turns out that the choice of distribution may drastically change the performance of the algorithm, and the theory has only begun to explain this phenomenon. 

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Franz-Viktor Kuhlmann
University of Saskatchewan
Thu 13 Nov 2014, 2:00pm SPECIAL
MATH 102
Algebra Seminar: Extremal fields, tame fields, large fields
MATH 102
Thu 13 Nov 2014, 2:00pm-3:00pm

Details

In the year 2003 I first heard of the notion of extremal valued fields when Yuri Ershov gave a talk at a conference in Teheran. He proved that algebraically complete discretely valued fields are extremal. However, the proof contained a mistake, and it turned out in 2009 through an observation by Sergej Starchenko that Ershov's original definition leads to all extremal fields being algebraically closed. In joint work with Salih Durhan (formerly Azgin) and Florian Pop, we chose a more appropriate definition and then characterized extremal valued fields in several important cases.

We call a valued field (K,v) extremal if for all natural numbers n and all polynomials f in K[X_1,...,X_n], the set {f(a_1,...,a_n) | a_1,...,a_n in the valuation ring} has a maximum (which is allowed to be infinity, which is the case if f has a zero in the valuation ring). This is such a natural property of valued fields that it is in fact surprising that it has apparently not been studied much earlier. It is also an important property because Ershov's original statement is true under the revised definition, which implies that in particular all Laurent series fields over finite fields are extremal. As it is a deep open problem whether these fields have a decidable elementary theory and as we are therefore looking for complete recursive axiomatizations, it is important to know the elementary properties of them well. That these fields are extremal seems to be an important ingredient in the determination of their structure theory, which in turn is an essential tool in the proof of model theoretic properties.

Further, it came to us as a surprise that extremality is closely connected with Pop's notion of "large fields". Also the notion of tame valued fields plays a crucial role in the characterization of extremal fields. A valued field K with algebraic closure K^ac is tame if it is henselian and the ramification field of the extension K^ac|K coincides with the algebraic closure.

In my talk I will introduce the above notions, try to explain their meaning and importance also to the non-expert, and discuss in detail what is known about extremal fields and how the properties of large and of tame fields appear in the proofs of the characterizations we give. Finally, I will present some challenging open problems, the solution of which may have an impact on the above mentioned problem for Laurent series fields over finite fields.
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Morningside Center of Mathematics and Purdue
Thu 13 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126
Introduction to Mochizuki's works on inter-universal Teichmuller theory
room MATH 126
Thu 13 Nov 2014, 3:30pm-4:30pm

Abstract

Inter-universal Teichmuller theory, as developed by Mochizuki in the past decade, is an analogue for number fields of the classical Teichmuller theory, and also of the p-adic Teichmuller theory of Mochizuki. In this theory, the ring structure of a number field is subject to non-ring theoretic deformation. Absolute anabelian geometry, a refinement of anabelian geometry, plays a crucial role in inter-universal Teichmuller theory. In this talk, we will try to give an introduction to these ideas.
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UC Berkeley
Fri 14 Nov 2014, 3:00pm
Department Colloquium
MATX 1100
The fundamental theorem of arithmetic for metric measure spaces
MATX 1100
Fri 14 Nov 2014, 3:00pm-4:00pm

Abstract

A metric measure space (mms) is simply a complete, separable metric space equipped with a probability measure that has full support.  A fundamental insight of Gromov is that the space of such objects is much ``tamer'' than the space of complete, separable metric spaces per se because mms carry within themselves a canonical family of approximations by finite structures: one takes the random mms that arises from picking some number of points independently at random and equipping it with the induced metric and uniform probability measure.  A natural (commutative and associative) binary operation on the space of mms is defined by forming the Cartesian product of the two underlying sets equipped with the sum of the two metrics and the product of the two probability measures.  There is a corresponding notion of a prime  mms and an analogue of the fundamental theorem of arithmetic in the sense that any mms has a factorization into countably many prime mms which is unique up to the order of the factors.  Moreover,  a rich Fourier theory enables one to analyze convolutions of probability measures on the space of mms and obtain counterparts of classical results in the theory of infinitely divisible and stable probability measures on Euclidean spaces due to L\'evy, It\^o, Hin\u{c}in, and LePage.  This is joint work with Ilya Molchanov (Bern).

Note for Attendees

Refreshments will be served at 2:45pm in the Math Lounge area, MATH 125 before the colloquium.
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Jussieu
Mon 17 Nov 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Applications of birational motives
ESB 4127 (host: UBC)
Mon 17 Nov 2014, 3:00pm-4:00pm

Abstract

I will give the definition of birational motives and explain how they can be used in various areas of algebraic geometry: counting rational points over finite fields, defining the "Tate-Shafarevich motive" of an abelian variety over a function field, shedding a new light on Roitman's theorem on torsion 0-cycles.

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Weiwei Ao
UBC
Tue 18 Nov 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
On Non-topological Solutions of the rank 2 Chern-Simons System
ESB 2012
Tue 18 Nov 2014, 3:30pm-4:30pm

Abstract

In this talk, I will talk about the Chern-Simons equation arising from the study of  physics of high critical temperature superconductivity. A long-standing open problem is the existence of non-topological solutions. We proved the existence of non-topological solutions for the rank 2 Chern-Simons system. This is joint work with Professor Changshou Lin and Juncheng Wei
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DePaul University
Tue 18 Nov 2014, 4:00pm
Discrete Math Seminar
ESB 4127
Non-messing-up: a surprising sorting result
ESB 4127
Tue 18 Nov 2014, 4:00pm-5:00pm

Abstract

We will discuss a sorting phenomenon for data in a rectangular array, called the "non-messing-up" property. Consider a collection of distinct numbers arranged in a rectangle. The non-messing-up property says that if you put the numbers of each row into increasing order, and then do the same thing to the (possibly new) numbers of each column, then the (possibly new) numbers in each row will still be in increasing order. In other words, the "in increasing order" feature of the rows doesn't get messed up, even though the values in the rows may change! We will explore what it means to generalize this property, and will look at some of these generalizations in detail.
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UBC
Wed 19 Nov 2014, 3:00pm
Undergraduate Colloquium
MATH 203
Sage: An Open-Source Mathematical Software System
MATH 203
Wed 19 Nov 2014, 3:00pm-4:00pm

Abstract

Algorithms and computer algebra systems play an invaluable role in modern day mathematics in both pure and applied fields. In this talk I will discuss the open source mathematical software system called Sage. Started and led by William Stein currently at the University of Washington and released in 2005, Sage is a free alternative to commercial mathematical computing languages such as Maple and MATLAB. I will demonstrate the functionality of Sage by discussing a select number of problems in number theory such as the prime number theorem, sociable numbers, and counting unique entries in the multiplication table.
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Cornell University
Wed 19 Nov 2014, 3:10pm
Probability Seminar
ESB 2012
Random walks on metric measure spaces
ESB 2012
Wed 19 Nov 2014, 3:10pm-4:10pm

Abstract

A metric space is a length space if the distance between two points equals the infimum of the lengths of curves joining them. For a measured length space, we characterize Gaussian estimates for iterated transition kernel for random walks and parabolic Harnack inequality for solutions of a corresponding discrete time version of heat equation by geometric assumptions (Poincaré inequality and Volume doubling property). Such a characterization is well known in the setting of diffusion over Riemannian manifolds (or more generally local Dirichlet spaces) and random walks over graphs (due to the works of A. Grigor'yan, L. Saloff-Coste, K. T. Sturm, T. Delmotte, E. Fabes & D. Stroock). However this random walk over a continuous space raises new difficulties. I will explain some of these difficulties and how to overcome them. We will discuss some motivating examples and applications.
 
This is joint work with Laurent Saloff-Coste. (in preparation)
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UBC
Wed 19 Nov 2014, 3:15pm
Topology and related seminars
ESB 4133
Differentiable Stacks and Foliation Theory, Part II
ESB 4133
Wed 19 Nov 2014, 3:15pm-4:15pm

Abstract

We will introduce infinity-topoi as generalized topological spaces, and show how using this language unifies the notion of manifold with that of etale differentiable stacks (generalized orbifolds) and their higher-categorical analogues. We will then give a completely categorical description of etale stacks in terms of a representability theorem. This theorem gives a recipe for constructing moduli stacks of geometric structures, and we will explain some examples of how this produces moduli-stacks presented by Lie groupoids that have been well studied in the foliation theory literature. Finally, we will explain how a generalization of Segal's theorem follows which describes the homotopy type of certain classifying spaces, and will explain the connection to the classification of foliations with transverse structures.
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Guillermo Martinez-Dibene
UBC
Thu 20 Nov 2014, 12:30pm
Graduate Student Seminar
Math 225
Weak Convergence in Measure
Math 225
Thu 20 Nov 2014, 12:30pm-2:00pm

Abstract

The purpose of this talk is give some of the ideas behind Prohorov's metric and weak convergence of probability measures. Then, I will briefly discuss the most important basic result in the topic: Prohorov's theorem.

Geometric motivations will be used to explain both the definition and the theorem. Also, we will discuss random measures and the definition of weak convergence in measure (and if time permits, I will talk a bit about what I have been working during my stay at UBC). Finally, the version of the Portmanteau theorem for this context will be stated and I will talk about what was that motivated it.

Note for Attendees

 Sushi will be provided between the two talks.
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Daniel Satanove
UBC
Thu 20 Nov 2014, 12:30pm
Graduate Student Seminar
Math 225
What is...a universal property?
Math 225
Thu 20 Nov 2014, 12:30pm-2:00pm

Abstract

Some times in algebra, we run across mysterious objects defined in terms of so-called "universal properties." What are they even? What do they mean? We explore this problem from the view of category theory, and the way it suggests we should look at objects.

Note for Attendees

 Sushi will be provided between the two talks.
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Asia Matthews
Queen's University
Thu 20 Nov 2014, 12:30pm
Lunch Series on Teaching & Learning
Math 126
Altering advanced mathematics problems to bring about mathematical thinking
Math 126
Thu 20 Nov 2014, 12:30pm-1:00pm

Abstract

Discovery, Structuring, and Justification are three diverse processes of mathematical thinking that might be brought out from subtle alterations in a problem statement.  I will discuss some examples and explain why I think this is a valuable practice in undergraduate education.
 
 
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Université Blaise Pascal/UBC
Thu 20 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126
On the modularity of reducible mod l Galois representations
room MATH 126
Thu 20 Nov 2014, 3:30pm-4:30pm

Abstract

In this talk I will discuss modularity of reducible mod l Galois representations. By analogy with the irreducible case, I will state several questions regarding characterization and optimization of the weights and levels of the various cuspidal forms attached to such representations. Finally I'll give an application of these results to the determination of an explicit lower bound for the highest degree of the coefficient fields of newforms of prime level and trivial Nebentypus. This is a joint work with Ricardo Menares.
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The University of Auckland
Fri 21 Nov 2014, 3:00pm
Department Colloquium
Math Annex 1100
Reducing lectures, making students responsible, and offering semi-authentic mathematical experiences.
Math Annex 1100
Fri 21 Nov 2014, 3:00pm-4:00pm

Abstract

 In the Mathematics Department of The University of Auckland a major research project into undergraduate mathematics learning outcomes has required the development of three innovative ways to deliver undergraduate mathematics. One of these involves reducing lectures to less than one per week, handing responsibility for most of their mathematical learning to students using web or text resources. We then use the staff time saved to provide semi-authentic mathematical experiences in which students work in small groups for up to two hours at a time guided by a lecturer on open-ended mathematical situations. Such sessions require new teaching skills and new learning orientations. There is some evidence that we have made progress on the development of mathematical process skills.
Our research shows that, with our small trial groups, students perform at similar levels on the conventional assessments as do the students in the standard courses.

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UAlberta
Mon 24 Nov 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Modules of differentials for Lie algebras
ESB 4127 (host: UBC)
Mon 24 Nov 2014, 3:00pm-4:00pm

Abstract

In this talk, I will attempt to introduce/discuss modules of differentials for Lie algebras modelled after the corresponding notion for rings. This is relevant to the structure of certain infinite dimensional Lie algebras. This is joint work with Arturo Pianzola.
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Andrew Wathen
Mathematics Department, University of Oxford, UK
Tue 25 Nov 2014, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Preconditioning for models of coupled magma/mantle dynamics
ESB 4133 (PIMS Lounge)
Tue 25 Nov 2014, 12:30pm-1:30pm

Abstract


We will describe some recent work in the numerical simulation of problems of Geodynamics. The relevant partial differential equations share some of the features of the well-known Stokes equations, but there are significant differences. Our work has been to create rapid solvers for the large systems of equations arising from finite element approximation. We will briefly describe the relevant models and our preconditioned Krylov subspace iterative solvers which enable some of the first computations on these models.

This is joint work with Sander Rhebergen, Richard Katz, Garth Wells, John Rudge and Laura Alisic.

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Monica Musso
Pont. Cat. Univ. Chile
Tue 25 Nov 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Nondegeneracy of nonradial nodal solutions to Yamabe problem
ESB 2012
Tue 25 Nov 2014, 3:30pm-4:30pm

Abstract

 We prove the existence of a sequence of nondegenerate, in the sense of Duyckaerts-Kenig-Merle, nodal nonradial solutions to the critical Yamabe problem or stationary energy-critical wave equation.
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Tyler Helmuth
Tue 25 Nov 2014, 4:00pm SPECIAL
Graduate Student Center, Room 203
Doctoral Exam
Graduate Student Center, Room 203
Tue 25 Nov 2014, 4:00pm-6:30pm

Details

Spin systems such as the Ising model are central topics in statistical mechanics and probability theory. In the late 1960s Symanzik made the important discovery that properties of spin systems could be expressed in terms of the behaviour of random walks. This thesis contributes to the understanding of these connections by developing and analyzing random walk representations of graphical models arising in statistical mechanics.
Concretely, the results of this thesis can be divided into two parts. The first part is a lace expansion analysis of a model called loop-weighted walk. Loop-weighted walk is a non-Markovian model of random walks that are discouraged (or encouraged), depending on the value of a parameter, from completing loops. The model arises naturally as a random walk representation of correlations in a statistical mechanics model called the cycle gas. A challenging aspect of this model is that it is not repulsive, meaning the weight of the future of a walk may either increase or decrease if the past is forgotten. Loop-weighted walk is the first finite range walk model with this property to be analyzed with lace expansion techniques.
The second part of this thesis is an essentially elementary derivation of a random walk representation for the partition function of the Ising model on any finite graph. Such representations have a long history for planar graphs. For non-planar graphs the additional ingredient needed is a way to compute the intersection numbers of curves on surfaces. The representations for non-planar graphs lead to random walk representations of spin-spin correlation functions that were previously unknown.
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Kseniya Garaschuk
UBC
Tue 25 Nov 2014, 4:00pm
Discrete Math Seminar
ESB 4127
Some aspects of rational triangle decompositions.
ESB 4127
Tue 25 Nov 2014, 4:00pm-5:00pm

Abstract

Given a simple graph $G$, a triangle decomposition of $G$ is a set of subgraphs isomorphic to $K_3$ whose edges partition the edge set of $G$. Further, a rational triangle decomposition of $G$ is a non-negative rational weighting of the copies of $K_3$ in $G$ such that the total weight on any edge of $G$ equals one. In this thesis, we will explore sufficient conditions for rational triangle decomposability. A famous conjecture in the area due to Nash-Williams states that any sufficiently large graph (satisfying some divisibility conditions) with minimum degree at least $3/4v$ is admits a triangle decomposition; the same conjecture stands for rational triangle decomposability (no divisibility conditions required). By perturbing and restricting the coverage matrix of a complete graph, we show that minimum degree of at least $22/23v$ is sufficient to guarantee that the given graph is rationally triangle decomposable. This density bound is a great improvement over the previously known results and is derived using estimates on the matrix norms and structures originating from association schemes.
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UAlberta
Wed 26 Nov 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
TBA
ESB 4127 (host: UAlberta)
Wed 26 Nov 2014, 3:00pm-4:00pm

Abstract

 TBA
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Stefan Adams
Warwick University
Wed 26 Nov 2014, 3:10pm
Probability Seminar
ESB 2012
Phase Transitions in Continuum Delaunay Potts Models
ESB 2012
Wed 26 Nov 2014, 3:10pm-4:10pm

Abstract

We discuss recent results on phase transitions of  Delaunay Potts models in dimension two where the interaction depends on Delaunay edges respectively Delaunay triangles.

This work is an extension of the Lebowitz & Lieb soft-core continuum Potts model to geometrically dependent interaction systems. The main tool is a FK (Fortuin-Kasteleyn)  random cluster representation adapted to the Delaunay structure and percolation in the FK model.  If time permits we discuss the Voronoi-Ising model where the interaction is function of the length of the common boundary and its connection to variants of the RSW (Russo-Seymour-Welsh) theorem in continuum percolation. 

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MIT
Wed 26 Nov 2014, 3:15pm
Topology and related seminars
ESB 4133
The six operations of Grothendieck in equivariant motivic homotopy theory
ESB 4133
Wed 26 Nov 2014, 3:15pm-4:15pm

Abstract

The formalism of six operations encodes the functorial behavior of (co)homology theories. It was first introduced by Grothendieck for the l-adic cohomology of schemes, and was later developed in a variety of other geometric contexts: D-modules on schemes, spectra parametrized by topological spaces, motivic spectra parametrized by schemes, etc. Equivariant homotopy theory is also best understood as a formalism of six operations for topological stacks. In this talk I will discuss the basics and the significance of this formalism, and I will then describe an extension of motivic homotopy theory to algebraic stacks.
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Abdul Kara
Witwatersrand University
Wed 26 Nov 2014, 3:30pm
Symmetries and Differential Equations Seminar
MATH 125
Symmetry structures of manifolds Part II
MATH 125
Wed 26 Nov 2014, 3:30pm-4:30pm

Abstract


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Oxford University
Thu 27 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126
Auto-correlations of divisor functions in function fields
room MATH 126
Thu 27 Nov 2014, 3:30pm-4:30pm

Abstract

In this seminar I will discuss a function field analogue of a classical problem in analytic number theory, concerning the auto-correlations of divisor functions, in the limit of a large finite field.
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University of Oregon
Fri 28 Nov 2014, 2:00pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
ESB 4133 (PIMS lounge)
Geometric flow on almost Hermitian manifolds towards a symplectic structure
ESB 4133 (PIMS lounge)
Fri 28 Nov 2014, 2:00pm-3:00pm

Abstract

 We propose  geometric flows to study the existence of a symplectic structure on an almost Hermitian manifold. We prove the short-time existence and uniqueness, and show some examples. 

Note for Attendees

 Note unusual day and time.
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UBC
Fri 28 Nov 2014, 3:00pm
Department Colloquium
MATX 1100
Graduate Research Award lecture: Magnetized Target Fusion: Insights from Mathematical Modelling
MATX 1100
Fri 28 Nov 2014, 3:00pm-4:00pm

Abstract

Magnetized target fusion reactors are a modern design to for hydrogen fusion energy on earth. The design entails confining a plasma with a magnetic field and crushing it in an imploding shell of molten metal. Such a design has many unresolved questions in terms of its feasibility as a power source and the most important elements in making it efficient. In this talk, we will look into two of the approaches undertaken to explore these questions. Firstly, through a coordinate transformation and implementing a novel flux-limited, split-step, finite volume scheme for nonlinear coupled hyperbolic partial differential equations, we do a parameter sensitivity analysis for the design performance. Secondly, by a careful series of asymptotic arguments, we establish a leading order asymptotic expression for the plasma compression. This expression is qualitatively consistent with the numerical work, but it also gives new insights into how the device operates. We will conclude with a look into the viability of magnetized target fusion and its future work.

Note for Attendees

Refreshments will be served at 2:45pm in the Math Lounge area, MATH 125 before the colloquium.


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