Dana C. Ernst, Angie Hodge & Andrew Schultz

Thu 1 Oct 2015, 10:30am
Math Education Research Reading

"Enhancing Proof Writing via CrossInstitutional Peer Review”

Thu 1 Oct 2015, 10:30am11:30am
Abstract
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UBC

Fri 2 Oct 2015, 12:00pm
Graduate Student Seminar
Math 103

The continued fraction of Euler's number

Math 103
Fri 2 Oct 2015, 12:00pm1:00pm
Abstract
This will be a short talk on the derivation of the continued fraction of e = 2.718281828...
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UBC Math

Fri 2 Oct 2015, 3:00pm
Department Colloquium
MATX 1100

Bounding hard squares

MATX 1100
Fri 2 Oct 2015, 3:00pm4:00pm
Abstract
Start labelling the vertices of the square grid with 0's and 1's with the condition that any pair of neighbouring vertices cannot both be labelled 1. If one considers the 1's to be the centres of small squares (rotated 45 degrees) then one has a picture of squareparticles that cannot overlap. This problem of
"hardsquares" appears in different areas of mathematics  for example it has appeared separately as a lattice gas in statistical mechanics, as independent sets in combinatorics and as the goldenmean shift in symbolic dynamics.
A core question in this model is to quantify the number of legal configurations  the entropy. In this talk I will discuss the what is known about the entropy and describe our recent work finding rigorous and precise bounds for hardsquares and related problems.
This is work together with Yaoban Chan.
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University of Washington

Mon 5 Oct 2015, 3:00pm
Algebraic Geometry Seminar
MATH 126

Projectivity of the moduli space of stable logvarieties

MATH 126
Mon 5 Oct 2015, 3:00pm4:00pm
Abstract
This is a report on joint work with Zsolt Patakfalvi. We prove a strengthening of Kollár's Ampleness Lemma and use it to prove that any proper coarse moduli space of stable logvarieties of general type is projective. We also confirm the IitakaViehweg conjecture on the subadditivity of logKodaira dimension for fiber spaces whose general fiber is of log general type.
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UBC/PIMS

Mon 5 Oct 2015, 3:00pm
Harmonic Analysis Seminar
Math Annex 1102

Discrete Analogues in Harmonic Analysis: Quadratic Carleson

Math Annex 1102
Mon 5 Oct 2015, 3:00pm4:30pm
Abstract
Since the late eighties, when Bourgain proved his celebrated pointwise ergodic theorems, discrete analogues in harmonic analysis have come into vogue. Indeed, much work has been devoted to studying maximal functions and (maximal truncations of) singular integrals. The Carleson operator  strictly more singular than either above operator  is a natural operator to try adapt to the discrete setting: Eli Stein has been successful in "transferring" the continuous result to the discrete setting. In particular, he has established the L^2(\Z) boundedness of the discrete Carleson operator
\[ \sup_{\lambda}  \sum_{m \neq 0} f(nm) e^{2\pi i \lambda m}/m .\]
The purpose of this talk will be to study a discrete analogue of the quadratically modulated Carleson operator:
\[ \sup_{\lambda}  \sum_{m \neq 0} f(nm) e^{2\pi i \lambda m^2}/m  \]
where \lambda ranges over certain subsets of (0,1].
This will be the first talk of the sequence, and very little background is required  though the argument will eventually combine elements from analytic number theory, probability theory, and harmonic analysis.
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Department of Mathematics, UBC

Tue 6 Oct 2015, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Relative Equilibria with a Dominant Vortex

ESB 4133 (PIMS Lounge)
Tue 6 Oct 2015, 12:30pm1:30pm
Abstract
In fluids, the presence of a dominant vortex has an organizing effect on the surrounding flow. We exploit this effect to simplify the stability problem for relative equilibria of (N+1) interacting point vortices, where N vortices have infinitesimal circulation and one vortex is strong in relation. Within this framework, existence and stability of equilibria reduces to characterizing critical points of a function defined on a circle. In the case that all vortices have circulation of the same sign, this function is potentiallike, with minima corresponding to stable configurations and maxima and saddle points corresponding to unstable solutions. Surprisingly, typical stable configurations exhibit asymmetry.
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University of Aveiro

Tue 6 Oct 2015, 2:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126

An Introduction to Convolutional codes

Math 126
Tue 6 Oct 2015, 2:00pm3:00pm
Abstract
A followup talk on multidimensional convolutional codes will be given on Thursday, October 8.
Coding theory  theory of error correcting codes  is one of the most interesting and applied parts of mathematics.Coding theory methods are often elegant applications of very basic concepts and methods of (abstract) algebra. IIn this talk we shall start by giving a brief general overview of this area before introducing the main topic of the talk, namely, convolutional codes.
These codes are mathematically more involved than the standard block codes as they posses a very rich algebraic structure. In this context the data is considered as a sequence. Even though the data is split into blocks of a fixed rate as in block codes, the relative position of each block in the sequence is taken into account. The blocks are not encoded independently and previous nodes in the sequence have an effect over the next encoded node. Because of this, convolutional codes have memory. From a mathematical point of view they can be seen as F[x]submodules of F[x]^n, where F is a finite field and F[x] is the ring of polynomials over F.
The aim of this talk is to introduce this powerful class of codes, their properties and their use in practice. We shall conclude by presenting some of the most fascinating open problems in the design of convolutional codes.
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UBC

Tue 6 Oct 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

On type II singularity formulation of harmonic map flows

ESB 2012
Tue 6 Oct 2015, 3:30pm4:30pm
Abstract
I will consider the following classical harmonic map flow from a general twodimensional domain D to S^2:
u_t=\Delta u +\nabla u^2 u, u: D \to S^2
We develop a parabolic gluing method to construct finite time blowup solutions of Type II in general domains. We show that type II blowup solutions with blowup rate
(Tt)/\log^2 (Tt)
is stable and generic in arbitrary domains (without any symmetry). I will also discuss the construction of multiple blowups, reverse bubbling, bubbling trees, bubbling at infinity. As a byproduct we can perform new geometric surgeries. (Joint work with Manuel del Pino and Juan Davila.)
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UBC and SFU

Tue 6 Oct 2015, 4:00pm
Discrete Math Seminar
ESB 4127

Bounds for randomized rumour spreading protocols

ESB 4127
Tue 6 Oct 2015, 4:00pm5:00pm
Abstract
Consider a social network modelled as a graph, with people and friendships represented by vertices and edges, respectively. Suppose that a person knows a piece of information, and as time passes, talks to other people and spreads it. How long it takes until everyone knows the rumour? The answer, which we call the "spread time", certainly depends on the graph's structure and how the rumour spreads. In this talk we discuss two well known randomized rumour spreading protocols (known as push&pull protocols) and survey the known results on their spread times on various graphs.
Based on joint work with H. Acan, A. Collevecchio, and N. Wormald.
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University of British Columbia and Pacific institute for the Mathematical Sciences

Wed 7 Oct 2015, 3:00pm
Probability Seminar
ESB 2012

Restrictions of Brownian motion

ESB 2012
Wed 7 Oct 2015, 3:00pm4:00pm
Abstract
It is classical that the zero set and the set of record times of a linear Brownian motion have Hausdorff dimension almost surely. Can we find a larger random subset on which a Brownian motion is monotone? Perhaps surprisingly, the answer is negative. We outline the short proof, which is an application of Kaufman's dimension doubling theorem for planar Brownian motion. This is a joint work with Yuval Peres.
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University of Utah

Wed 7 Oct 2015, 3:15pm
Topology and related seminars
ESB 4133

Subgroups of the automorphism group of a free product

ESB 4133
Wed 7 Oct 2015, 3:15pm4:15pm
Abstract
I will discuss classification results for subgroups of Out(Fn) (analogous to Ivanov's classification of subgroups of mapping class groups of surfaces), and more generally of automorphism groups of free products. In particular, I will present a version of the Tits alternative for the automorphism group of a free product. This is partly joint work with Vincent Guirardel.
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Thu 8 Oct 2015, 10:30am
Math Education Research Reading
Math 126

History of Research in Mathematics Education

Math 126
Thu 8 Oct 2015, 10:30am11:30am
Abstract
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University of Aveiro

Thu 8 Oct 2015, 3:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math Annex 1102

Multidimensional Convolutional Codes

Math Annex 1102
Thu 8 Oct 2015, 3:00pm4:00pm
Abstract
An introductory talk on one dimensional convolutional codes will be given on Tuesday, October 6.
Multidimensional (nD) convolutional codes generalize one dimensional (1D) convolutional codes and correspond to multidimensional systems widely studied in the systems theory literature. These codes have a practical potential in applications as they are very suitable to encode data recorded in n dimensions, e.g., pictures, videos, storage media, wireless applications, etc. However, in comparison to 1D convolutional codes, little is known in the area of nD convolutional codes and much more needs to be done to make it attractive for practical applications. From a mathematical point of view, these codes can be viewed as F[x_1,...,x_n]submodules of F[x_1,...,x_n]^n, where F is a finite field and F[x_1,...,x_n] is the ring of polynomials in several variables over F. In this talk we present a construction of an nD convolutional code based on superregular matrices with excellent errorcorrecting capabilities.
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University of Auckland

Fri 9 Oct 2015, 3:00pm
SPECIAL
Institute of Applied Mathematics
C680 HSBC Hall, Robson Square Campus (downtown)

The dynamics of aircraft as ground vehicles

C680 HSBC Hall, Robson Square Campus (downtown)
Fri 9 Oct 2015, 3:00pm4:00pm
Abstract
Aircraft are designed to fly but also need to operate efficiently and safely as vehicles on the ground. The tricycle configuration of commercial aircraft presents challenges for manoeuvres, such as highspeed turns off a runway. The talk will present results of a collaboration with Airbus into the stability of ground manoeuvres, whose central idea is to employ tools from bifurcation analysis to relevant industryvalidated aircraft models. Compared to standard extensive numerical simulations, this approach has been demonstrated to have potential efficiency benefits during the design stage. In particular, it allows for detailed studies of the nature of instabilities that need to be avoided in practice. As an example, we show that the sudden loss of lateral stability of a midsize passenger aircraft turning on the ground is due to a canard phenomenon that arises due to a nonobvious slowfast splitting.
This is joint work with Etienne Coetzee (Airbus), James Rankin (INRIA France), Mathieu Desroches (INRIA France) and Mark Lowenberg (University of Bristol).
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University of Auckland

Fri 9 Oct 2015, 4:00pm
SPECIAL
Institute of Applied Mathematics
C680 HSBC Hall, Robson Square Campus (downtown)

Shaken but not stirred: using mathematics in earthquakes

C680 HSBC Hall, Robson Square Campus (downtown)
Fri 9 Oct 2015, 4:00pm5:00pm
Abstract
Predicting the behaviour of a structure when subjected to an earthquake is an important problem from Civil Engineering. Here, we consider a planar posttensioned frame, which can be modelled as a twodegreeoffreedom system that is equivalent to the analytical model of a tied rocking block on an elastic foundation. The frame remains structurally sound as long as the tilt angle of the frame does not exceed a certain maximal angle. A standard approach to studying the dynamics would be to run simulations, where it is assumed that the earthquake is a pure sine wave with varying frequency and amplitude. Such a bruteforce approach establishes a region in the frequencyamplitude plane for which the structural stability of the frame eventually fails. We propose a novel approach that calculates the failure region in a much more efficient way by determining the failure boundary directly. Our method is based on continuation of a suitable twopoint boundary value problem. Our computations demonstrate that the failure boundary is only piecewise smooth and the results highlight further interesting details of how the dynamics is organised in the frequencyamplitude plane.
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Davidson College

Tue 13 Oct 2015, 2:00pm
Number Theory Seminar
room IRMACS 10901 (SFU)

Oscillations in sums involving the Liouville function (note different day and time)

room IRMACS 10901 (SFU)
Tue 13 Oct 2015, 2:00pm3:00pm
Abstract
The Liouville function λ(n) is the completely multiplicative arithmetic function defined by λ(p) = –1 for each prime p. Pólya investigated its summatory function L(x) = Σ_{n≤x }λ(n), and showed for instance that the Riemann hypothesis would follow if L(x) never changed sign for large x. While it has been known since the work of Haselgrove in 1958 that L(x) changes sign infinitely often, oscillations in L(x) and related functions remain of interest in analytic number theory. We review some connections between oscillations in this function and its relatives with the Riemann hypothesis and other problems in number theory, and describe some recent work on this topic. In particular, we describe a method involving substantial computation that establishes new bounds on the magnitude of the oscillations of L(x). This is joint work with Tim Trudgian.
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Politechic University of Catalonia

Tue 13 Oct 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

On singular solutions for the fractional Yamabe problem

ESB 2012
Tue 13 Oct 2015, 3:30pm4:30pm
Abstract
Abstract: We construct some ODE solutions for the fractional Yamabe problem in conformal geometry. The fractional curvature, a generalization of the usual scalar curvature, is defined from the conformal fractional Laplacian, which is a nonlocal operator constructed on the conformal infinity of a conformally compact Einstein manifold.
These ODE solutions are a generalization of the usual Delaunay and, in particular, solve the fractional Yamabe problem
$$ (\Delta)^\gamma u= c_{n, {\gamma}}u^{\frac{n+2\gamma}{n2\gamma}}, u>0 \ \mbox{in} \ \r^n \backslash \{0\},$$
with an isolated singularity at the origin.
This is a fractional order ODE for which new tools need to be developed. The key of the proof is the computation of the fractional Laplacian in polar coordinates.
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University of Kentucky

Tue 13 Oct 2015, 4:00pm
Topology and related seminars
ESB 4133

The etalocal motivic sphere

ESB 4133
Tue 13 Oct 2015, 4:00pm5:00pm
Abstract
The Hopf map eta is nilpotent in the stable homotopy groups of spheres. This is not so for the motivic Hopf map, considered as an element of the motivic stable homotopy groups of spheres. This suggests that the etalocal part of motivic stable homotopy theory is an interesting object of study. We will describe this for the base fields C and R.
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Université Paris Diderot

Wed 14 Oct 2015, 3:00pm
Probability Seminar
ESB 2012

Cutoff for nonbacktracking random walks on sparse random graphs

ESB 2012
Wed 14 Oct 2015, 3:00pm4:00pm
Abstract
A finite ergodic Markov chain exhibits cutoff if its distance to stationarity remains close to 1 over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Here we consider nonbacktracking random walks on random graphs with a given degree sequence. Under a general sparsity condition, we establish the cutoff phenomenon, determine its precise window, and prove that the cutoff profile approaches a remarkably simple, universal shape. This is a joint work with Justin Salez (ParisDiderot).
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Thu 15 Oct 2015, 10:30am
Math Education Research Reading
MATH 126

Clickers in the Large Classroom: Current Research and BestPractice Tips

MATH 126
Thu 15 Oct 2015, 10:30am11:30am
Abstract
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SFU

Thu 15 Oct 2015, 12:00pm
Mathematics of Information and Applications Seminar
ESB 4133 (PIMS Lounge)

Compressed sensing with local structure: theory, applications and benefits

ESB 4133 (PIMS Lounge)
Thu 15 Oct 2015, 12:00pm1:00pm
Abstract
Compressed sensing concerns the recovery of signals and images from seemingly incomplete data sets. Introduced nearly a decade ago, it has since become an intensive area of research in applied mathematics, engineering and computer science. However, many practical problems in which compressed sensing is applied, e.g. imaging, are not fully explained by existing theory. In this talk I will present a new framework for compressed sensing that seeks to bridge this gap. This framework is based on replacing some standard principles of compressed sensing with new local notions; specifically, sparsity in levels, local coherence in levels and multilevel random subsampling. I will demonstrate a series of nearoptimal recovery guarantees based on these local concepts that explains the effectiveness of compressed sensing in such applications. Moreover, this framework is not just useful in understanding existing compressed sensing approaches. In the final part of the talk I will demonstrate how leveraging local sparsity through appropriatelydesigned locally incoherent sensing matrices leads to substantially improved compressed sensing techniques in a range of other applications.
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UBC

Fri 16 Oct 2015, 12:00pm
Graduate Student Seminar
Math 103

A large subset of the real numbers avoiding nontrivial solutions to a linear equation

Math 103
Fri 16 Oct 2015, 12:00pm1:00pm
Abstract
In 1998, Tamas Keleti constructed a subset of the reals of Hausdorff dimension 1 that does not contain 4 distinct points x_1, x_2, x_3, x_4 satisfying
x_2  x_1 = x_4  x_3.
I will describe this construction and some further directions that the construction can be taken.
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UBC Mathematics

Fri 16 Oct 2015, 3:00pm
Department Colloquium
MATX 1100

Numerical Computation on Curved Surfaces

MATX 1100
Fri 16 Oct 2015, 3:00pm4:00pm
Abstract
Despite the appearance sometimes given in textbooks, not all differential equations are posed on straight lines and rectangles. This talk will introduce some easytouse techniques for computing numerical solutions to partial differential equations (PDEs) posed on curved surfaces and other general domains.
I will show some applications in thinfilm flows, reactiondiffusion equations, bulksurface coupling, point clouds, and image processing.
The talk will also outline how a close encounter with instability improved our understanding and numerical analysis of these methods.
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University of Fribourg

Mon 19 Oct 2015, 3:00pm
Algebraic Geometry Seminar
MATH 126

Motivic classes of classifying stacks and their invariants

MATH 126
Mon 19 Oct 2015, 3:00pm4:00pm
Abstract
After introducing the class of the classifying stack of a (finite) group, BG, in the Grothendieck ring of algebraic stacks, I will present certain cohomological invariants for a group  the Ekedahl invariants.
I am going to show that the class of BG is trivial if G is a finite subgroup of GL_3(k) or if G is a finite linear (or projective) reflection group. (k is a algebraically closed field of characteristic zero.) I will also show that the Ekedahl invariants of the discrete 5Heisenberg group are trivial.
These results relate naturally to Noether's Problem and to its obstruction, the Bogomolov multiplier.
At the end of the talk, I will link these results to the study of the motivic classes of the quotient varieties V/G by showing that such classes and the classes of BG exhibit the same combinatorial structure. Therefore, despite the title and technical terminology I will aim at making the talk enjoyable also by the combinatorial community.
(Partial joint work with Emanuele Delucchi.)
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UBC/PIMS

Mon 19 Oct 2015, 3:00pm
Harmonic Analysis Seminar
Math Annex, 1102

Discrete Analogues in Harmonic Analysis: Quadratic Carleson, II

Math Annex, 1102
Mon 19 Oct 2015, 3:00pm4:30pm
Abstract
In the first talk in this lecture series, we introduced discrete analogues in harmonic analysis, and discussed Bourgain's celebrated polynomial ergodic theorem. In this second lecture in the series, we will apply Bourgain's approximation arguments in the study of the discrete quadratic Carleson operator,
\[ C_\Lambda f(n) := \sup_{\lambda \in \Lambda}  \sum_{m \neq 0} e(\lambda m^2)/m f(nm)  \]
where $\Lambda \subset [0,1]$ is a set of modulation parameters, and $e(t) := e^{2\pi i t}$.
In particular, we will reduce matters to a multifrequency maximal multiplier theorem, which we will study using three separate techniques:
 Comparison to a multifrequency multifrequency maximal multiplier theorem involving truncations of the Hilbert transform;
 A Fourieranalytic entropy/chaining argument; and
 A TT* argument from the theory of oscillatory integrals.
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University of Toronto

Mon 19 Oct 2015, 4:15pm
Algebraic Geometry Seminar
MATH 126

Theta lifts and currents on Shimura varieties

MATH 126
Mon 19 Oct 2015, 4:15pm5:15pm
Abstract
The Shimura varieties X attached to orthogonal and unitary groups come equipped with a large collection of socalled special cycles. Examples include Heegner divisors on modular curves and HirzebruchZagier cycles on Hilbert modular surfaces. We will review work of Borcherds and Bruinier using regularised theta lifts for the pair (SL_2,O(V)) to construct Green currents for special divisors. Then we will explain how to construct other interesting currents on X using the dual pair (Sp_4,O(V)). We will show that one obtains currents in the image of the regulator map of a certain motivic complex of X. Finally, we will describe how an argument using the SiegelWeil formula allows to relate the values of these currents to the product of a special value of an Lfunction and a period on a certain subgroup of Sp_4.
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PIMS/University de Tours

Wed 21 Oct 2015, 3:00pm
Probability Seminar
ESB 2012

Discrete harmonic functions in the quadrant

ESB 2012
Wed 21 Oct 2015, 3:00pm4:00pm
Abstract
In this talk we shall be interested in discrete harmonic functions in cones (in particular, in the quarter plane). The generating function of these harmonic functions satisfies a functional equation (closed to a wellknown functional equation that appears in the context of enumeration of confined walks in combinatorics). We shall show the link between these harmonic functions and a oneparameter family of conformal mappings. One of the motivations to that study is to condition (in the sense of Doob) random walks never to leave cones.
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Reed College

Wed 21 Oct 2015, 3:15pm
Topology and related seminars
ESB 4133

Tensor triangular geometry of the stable motivic homotopy category

ESB 4133
Wed 21 Oct 2015, 3:15pm4:15pm
Abstract
In Balmer's framework of tensor triangular geometry, the prime thick tensor ideals in a tensor triangulated category C form a space which admits a continuous map to the Zariski spectrum Spec^h(End_u(1)) of homogeneous prime ideals in the graded endomorphism ring of the unit object. (Here the grading is induced by an element u of the Picard group of C.) If C is the stable motivic homotopy category and u is the punctured affine line, then this endomorphism ring is the MilnorWitt Ktheory ring of the base field. I will describe work by my student, Riley Thornton, which completely determines the homogeneous Zariski spectrum of MilnorWitt Ktheory in terms of the orderings on the base field. I will then comment on work in progress which uses the structure of this spectrum to study the thick subcategories of the stable motivic homotopy category.
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Thu 22 Oct 2015, 10:30am
Math Education Research Reading
Math 126

"Beyond Plug and Chug: an Analysis of Calculus I Homework"

Math 126
Thu 22 Oct 2015, 10:30am11:30am
Abstract
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SFU

Thu 22 Oct 2015, 3:30pm
Number Theory Seminar
room MATH 126

An arithmetic graph invariant with applications in quantum field theory

room MATH 126
Thu 22 Oct 2015, 3:30pm4:30pm
Abstract
I will give an overview of things we know about c_{2} invariant of a graph. This is an invariant investigated principally by Brown and Schnetz which comes from counting points on the hypersurface defined by the Kirchhoff polynomial of a graph. This invariant predicts many properties of the Feynman integral of the graph. It connects with deep things like modular forms and motives. Many computations involving it come down to playing around with polynomials defined from the graph and so its also combinatorial. The fun and power of it come from the interplay of all three of these things.
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UBC/PIMS

Mon 26 Oct 2015, 3:00pm
Harmonic Analysis Seminar
Math Annex 1102

Discrete Analogues in Harmonic Analysis: Quadratic Carleson, III

Math Annex 1102
Mon 26 Oct 2015, 3:00pm4:30pm
Abstract
In the second talk in the series on the discrete quadratic Carleson operators,
\[ C_\Lambda f(n) := \sup_{\lambda \in \Lambda}  \sum_{m \neq 0} e^{2\pi i \lambda m^2}/m f(nm), \Lambda \subset [0,1] \]
we reduced matters to a multifrequency maximal multiplier theorem.
In this third talk we will prove that the operator norm of the multifrequency maximal multiplier is slowly growing in the number of distinguished frequencies. We use three separate techniques to do so; the highlight of our approach is a novel entropy argument.
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UBC

Mon 26 Oct 2015, 3:00pm
Algebraic Geometry Seminar
MATH 126

Nonfinitely generated Cox rings

MATH 126
Mon 26 Oct 2015, 3:00pm4:00pm
Abstract
Cox rings of algebraic varieties were defined by Hu and Keel in relation to the minimal model program. The main question in the theory is to determine if the Cox ring of a variety is finitely generated. Such varieties are called Mori Dream Spaces. In this talk I will discuss examples of varieties that are not Mori Dream Spaces. These include toric surfaces blown up at a point and the moduli spaces of rational curves with n points. This is a joint work with Jose Gonzalez.
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Department of Civil Engineering, UBC

Tue 27 Oct 2015, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

An earthquake early warning network for BC  how does it work?

ESB 4133 (PIMS Lounge)
Tue 27 Oct 2015, 12:30pm1:30pm
Abstract
This talks will describe the concept of earthquake early warning and will include a description of the different methods and approaches used to detect earthquake shaking. An overview of the work being done in BC to establish and implement an EEW network for BC will be presented. This includes a description of the hardware and software that has been, and is being, developed. The future directions of the network will be presented and the opportunities for collaboration with various research groups at UBC will be discussed.
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University of Tennessee, Knoxville

Tue 27 Oct 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

Gradient estimates and global existence of smooth solutions to a crossdiffusion system

ESB 2012
Tue 27 Oct 2015, 3:30pm4:30pm
Abstract
We investigate the global time existence of smooth solutions for the ShigesadaKawasakiTeramoto system of crossdiffusion equations of two competing species in population dynamics. If there are selfdiffusion in one species and no crossdiffusion in the other, we show that the system has a unique smooth solution for all time in bounded domains of any dimension. We obtain this result by deriving global W^{1,p}estimates of Calder\'{o}nZygmund type for a class of nonlinear reactiondiffusion equations with selfdiffusion. These estimates are achieved by employing CaffarelliPeral perturbation technique together with a new twoparameter scaling argument.
The talk is based on the joint work with L. Hoang (Texas Tech) and T. Nguyen (U. of Akron).
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UBC and SFU

Tue 27 Oct 2015, 4:00pm
Discrete Math Seminar
ESB 4127

Cops and a Fast Robber on Planar and Random Graphs

ESB 4127
Tue 27 Oct 2015, 4:00pm5:00pm
Abstract
We study a variant of the Cops and Robber game, in which the robber has unbounded speed, i.e., can take any path from her vertex in her turn, but she is not allowed to pass through a vertex occupied by a cop. Let c(G) denote the number of cops needed to capture the robber in a graph G, and let tw(G) denote the treewidth of G. We show that if G is planar then c(G) = Theta(tw(G)), and there is a polynomialtime constantfactor approximation algorithm for computing c(G). We also determine, up to constant factors, the value of c(G) of the random graph G(n,p) for all admissible values of p, and show that when the average degree goes to infinity, c(G) is typically asymptotic to the domination number.
This is joint work with Noga Alon.
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Cornell University

Wed 28 Oct 2015, 3:00pm
Probability Seminar
ESB 2012

Circles in the Sand

ESB 2012
Wed 28 Oct 2015, 3:00pm4:00pm
Abstract
I will describe the role played by an Apollonian circle packing in the scaling limit of the abelian sandpile on the square grid Z^2. The sandpile solves a certain integer optimization problem. Associated to each circle in the packing is a locally optimal solution to that problem. Each locally optimal solution can be described by an infinite periodic pattern of sand, and the patterns associated to any four mutually tangent circles obey an analogue of the Descartes Circle Theorem. Joint work with Wesley Pegden and Charles Smart.
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UBC Math

Wed 28 Oct 2015, 3:15pm
Topology and related seminars
ESB 4133

A simple universal property of Thom ring spectra

ESB 4133
Wed 28 Oct 2015, 3:15pm4:15pm
Abstract
A stable spherical fibration is classified by a map X → BGL₁(S) and Lewis showed that if this map is an infinite loop map or an nfold loop map then the Thom spectrum is an E_∞ or E_nring spectrum, respectively. Ando, Blumberg, Hopkins, Gepner and Rezk introduced a new approach to Thom spectra using the language of ∞categories. Using their approach, we will explain how to apply some simple (∞)category theory to study multiplicative structures on Thom spectra, proving a generalization of Lewis's theorem and moreover characterizing the ring structure by a universal property. As an application I'll discuss a new (slightly simpler) proof of a remarkable theorem of Mahowald's realizing the EilenbergMacLane spectrum HF₂ as a Thom spectrum of a double loop map.
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Thu 29 Oct 2015, 10:30am
Math Education Research Reading
Math126

"Socioeconomic Influence on Mathematical Achievement: What Is Visible and What Is Neglected"

Math126
Thu 29 Oct 2015, 10:30am11:30am
Abstract
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Carleton University

Thu 29 Oct 2015, 3:00pm
Number Theory Seminar
room MATH 126

A method for computing Arthurpackets at Archimedean places

room MATH 126
Thu 29 Oct 2015, 3:00pm4:00pm
Abstract
Let G be a connected reductive algebraic group defined over a number field. The harmonic analysis of the adelic points of G leads to a decomposition of the regular representation into automorphic representations. The irreducible subrepresentations in this decomposition form the socalled discrete spectrum. When G=GL_{n} the discrete spectrum has a nice description. Langlands' principle of functoriality suggests that the discrete spectrum of other groups might be described in terms of the discrete spectrum of GL_{n}. Arthur has recently provided such a description for symplectic and special orthogonal groups in terms of sets of representations called A(rthur)packets. The structure of Apackets is not well understood, and relies in part on their local analogues. We will outline a method for computing Apackets for real groups.
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Emory University

Thu 29 Oct 2015, 4:00pm
Number Theory Seminar
room MATH 126

Reciprocity obstructions to Hasse principle over function fields of padic curves

room MATH 126
Thu 29 Oct 2015, 4:00pm5:00pm
Abstract
A variety X over a number field k is said to satisfy Hasse principle of it has a rational point provided it has a rational point over completions of k at all its places. Manin defined an obstruction in terms of the Brauer group to detect the failure of Hasse principle for varieties over number fields which is referred to as the BrauerManin obstruction. This obstruction is the only obstruction to Hasse principle for torsors under connected linear algebraic groups over k. We shall explain a reciprocity obstruction to Hasse principle for varieties over function fields of padic curves. This obstruction can be used to produce examples of principal homogeneous spaces under tori which fail Hasse principle over function fields of padic curves.
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UBC

Fri 30 Oct 2015, 12:00pm
Graduate Student Seminar
Math 103

Spheres of spheres over spheres: An analysis of the group structure of the nsphere, S^n and the Hopf fibration.

Math 103
Fri 30 Oct 2015, 12:00pm1:00pm
Abstract
Do you like spheres? If not, you are wrong, and probably won't like this talk. To the remaining reasonable people out there hold on to your socks. It is an elementary fact that the 0sphere S^0=\{\pm 1\} is the group \mathbb{Z}_2 and the circle S^1 is also the group e^{i\theta}. Is that just by chance, can all groups be given a group structure? If not what makes the ones that can so special? We will analyse which spheres have this property (turns out only 3.5ish do) and how to find the group structure when they do.
The question now becomes, what can we say about the spheres that can't be groups? Can we exploit the symmetries of S^n and the sphere groups above to salvage some geometric structure? To answer these questions we will begin by give a very elementary introduction to fibre bundles (emphasis on the ``very''), and discuss how we can think of higher order spheres as a bunch of copies (ie. fibres) of sphere groups by constructing the Hopf fibration. Time permitting, we will give an application of this abstract jargon to help visualize the spin \frac{1}{2}system in quantum mechanics and introduce the bloch sphere.
This is meant to be very elementary, if you understood the first paragraph, you will understand this talk. The goal will be to focus on intuition and avoid technical details like the plague.
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Emory University

Fri 30 Oct 2015, 3:00pm
Department Colloquium
ESB 2012

PIMS/UBC Distinguished Colloquium: Localglobal principles for quadratic forms

ESB 2012
Fri 30 Oct 2015, 3:00pm4:00pm
Abstract
The classical theorem of HasseMinkowski asserts that a quadratic form over a number field represents zero nontrivially provided it represents zero nontrivially over its completions at all its places. We discuss analogous local global principles over function fields of padic curves. Such localglobal principles in the general setting for homogeneous spaces have implications to the understanding of the arithmetic of these fields.
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Note for Attendees
Pizza and pop will be provided.